It seems surprising that the emissivity properties of the accretion disk (\textit{\`{a} la} Page and Thorne) surrounding the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black holes of heterotic string theory have not yet been studied. To fill this gap in the literature, we study the emissivity properties of the thin accretion disks around these black holes both in the Einstein and in the string frame using the Page-Thorne model. For illustration, we choose as a toy model a stellar-sized spherically symmetric black hole and find that, while the emissivity properties do not significantly differ from those of Reissner-Nordstr\"{o}m and Schwarzschild black holes, they remarkably differ at GMGHS extreme limits corresponding to naked singularity and wormhole at higher frequencies. These differences provide a novel way to speculatively conclude about different types of objects from the observational point of view.

Being motivated by the delivery of drugs and vaccines through subcutaneous (SC) injection in human bodies, a theoretical investigation is performed using a two-dimensional mathematical model in the cartesian coordinate. In general, a large variety of biological tissues behave as deformable porous material with anisotropic hydraulic conductivity. Consequently, one can adopt the field equations of mixture theory to describe the behavior of the interstitial fluid and adipose cell present in the subcutaneous layer of skin. During the procedure, a medical person takes a big pinch of the skin of the injection application area between the thumb and index finger and holds. This process pulls the fatty tissue away from the muscle and makes the injection process easier. In this situation, the small aspect ratio (denoted as $\delta$) of the subcutaneous layer (SCL) i.e., $\delta^2\sim0.01$ would simplify the governing equation for tissue dynamics as it becomes a perturbation parameter. This study highlights the issue of the mechanical response of the adipose tissue in terms of the anisotropic hydraulic conductivity variation, the viscosity of the injected drug, the mean depth of subcutaneous tissue, etc. In particular, the computed stress fields can measure the intensity of pain to be experienced by a patient after this procedure. Also, this study discusses the biomechanical impact of the creation of one or more eddy structures (s) near the area of applying injection, which is due to high pressure developed there, increased tissue anisotropy, fluid viscosity, etc.

In the literature, there is no consensus on the origin of the relativistic Sagnac effect, particularly from the standpoint of the rotating observer. The experiments of Wang et al. \cite{wang2003modified,wang2004generalized} has, however, questioned the pivotal role of rotation of the platform in Sagnac effect. Recently, the relative motion between the reflectors which force light to propagate along a closed path and the observer has been ascribed as the cause of the Sagnac effect. Here, we propose a thought experiment on linear Sagnac effect and explore another one proposed earlier to demonstrate that the origin of the Sagnac effect is neither the rotation of frame affecting clock synchronization nor the relative motion between the source and the observer; Sagnac effect originates purely due to asymmetric position of the observer with respect to the light paths. Such a conclusion is validated by analysis of a gedanken Sagnac kind experiment involving rotation.

We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko \textit{et al.} (2014). It turnsout that stability depends more strongly on the dark matter central density $$ than on other parameters of the solution. This property then yields an upper limit on $\rho _{0}$ for each individual galaxy, which we call here $\rho _{0}^{\text{upper}}$, such that stable circular orbits are possible \textit{only} when the constraint $\rho _{0}\leq \rho _{0}^{\text{upper}}$ is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius $R_{\text{DM}}\sim 180$ kpc and find that $\rho _{0}^{\text{upper}}\sim 2.37\times 10^{11}$$M_{\odot }$kpc$^{-3}$. This limit turns out to be about four orders of magnitude larger than the latest data on central density $\rho _{0}$ arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Such consistency indicates that the EiBI solution could qualify as yet another viable alternative model for dark matter.

Recently, Harko et al. (2014) derived an approximate metric of the galactic halo in the Eddington inspired Born-Infeld (EiBI) gravity. In this metric, we show that there is an upper limit $\rho _{0}^{\text{upper}}$ on the central density $\rho _{0}$ of dark matter such that stable circular orbits are possible only when the constraint $\rho _{0}\leq \rho_{0}^{\text{upper}}$ is satisfied in each galactic sample. To quantify different $\rho _{0}^{\text{upper}}$ for different samples, we follow the novel approach of Edery & Paranjape (1998), where we use as input the geometric halo radius $R_{\text{WR}}$ from Weyl gravity and equate it with the dark matter radius $R_{\text{DM}}$ from EiBI gravity for the same halo boundary. This input then shows that the known fitted values of $\rho _{0}$ obey the constraint $\rho_{0}\leq\rho_{0}^{\text{upper}}\propto$ ($R_{\text{WR}}$)$^{-2}$. Using the mass-to-light ratios giving $\alpha$, we shall also evaluate $\rho _{0}^{\text{lower}}$$\propto $$(\alpha -1)M_{\text{lum}}R_{\text{WR}}^{-3}$ and the average dark matter density $\left\langle \rho\right\rangle ^{\text{lower}}$. Quantitatively, it turns out that the interval$\rho _{0}^{\text{lower}}$$\leq \rho _{0}\leq $$\rho _{0}^{\text{upper}}$ verifies reasonably well against many dark matter dominated low surface brightness (LSB) galaxies for which values of $\rho _{0}$ are independently known. The interval holds also in the case of Milky Way galaxy. Qualitatively, the existence of a stability induced upper limit $\rho _{0}^{\text{upper}}$ is a remarkable prediction of the EiBI theory.

An interacting Holographic dark energy (HDE) with different infra-red (IR) cutoffs (Hubble horizon and future event horizon) is investigated in the background dynamics of flat Friedmann Lemaitre Robertson Walker (FLRW) universe where gravitational particle creation effects via different form of particle creation rates (1) $\Gamma=3\beta H$ and (2) $\Gamma=3\alpha H_{0}+3\beta H$ are considered. The created particles are considered to be pressureless Dark Matter (DM) which interacts with the HDE through a phenomenological choice of interaction term $Q=3\gamma H \rho_{m}$. We obtain an analytic solution of the cosmological dynamics with Hubble horizon as IR cutoff when the creation rate is taken as $\Gamma=3 \beta H$. We find that the interacting HDE from the Hubble horizon as the IR cutoff can give the late-time acceleration and non-interacting cannot give. On the other hand, employing the Hubble horizon and the future event as IR cutoffs for the model of HDE does not provide the analytic solution when the creation rate is taken as $\Gamma=3\alpha H_{0}+3\beta H$. We then analyze the model separately using the dynamical systems theory. From the analysis, the model (with Hubble horizon as IR cutoff) provides two sets of critical points. One can give a late-time accelerated universe evolving in quintessence, the cosmological constant, or the phantom era. But, it does not show any matter-dominated era. On the other hand, by applying the future event as an IR cutoff, the model provides the complete evolution of the universe. It also exhibits the late-time scaling attractor gives the possible solution of the coincidence problem. Global dynamics of the model are investigated by defining the appropriate Lyapunov function. Finally, the adiabatic sound speeds of all the models have been calculated and plotted numerically to find the stability of the models.

In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as dark energy and pressureless dust as dark matter are the main matter content of the universe. We perform dynamical system analysis to characterize the cosmological evolution of the model with and without interaction in the dark sector separately. First, we convert the evolution equation into an autonomous system of ordinary differential equations by using a suitable choice of dimensionless variables, which are normalized over the Hubble scale. We choose scalar field coupling and potential in such a way that the autonomous system converted to a 2D system. Linear stability theory is employed to the extracted critical points to find the nature. From the analysis, we find some interesting cosmological scenarios, such as late-time scalar-field dominated solutions, which evolve in the quintessence era, cannot solve the coincidence problem. Accelerated scaling attractors are also obtained that correspond to the late phase evolution in agreement with present observational data, and these solutions also provide possible mechanisms to alleviate the coincidence problem. A complete cosmic evolution is obtained from early inflation to a late-time dark energy-dominated phase, connecting through a matter-dominated transient phase of the universe. Furthermore, we find that for different values of the interaction parameter $\alpha$, the evolutionary trajectories of the Hubble parameter, and the distance modulus forecasted by the model are in quite well agreement with observational datasets.

A comparative study of the Homotopy Analysis method and an improved Renormalization Group method is presented in the context of the Rayleigh and the Van der Pol equations. Efficient approximate formulae as functions of the nonlinearity parameter $\varepsilon$ for the amplitudes $a(\varepsilon)$ of the limit cycles for both these oscillators are derived. The improvement in the Renormalization group analysis is achieved by invoking the idea of nonlinear time that should have significance in a nonlinear system. Good approximate plots of limit cycles of the concerned oscillators are also presented within this framework.

We have discussed here a higher dimensional cosmological model and explained the recent acceleration with a Chaplygin type of gas. Dimensional reduction of extra space is possible in this case. Our solutions are general in nature because all the well known results of 4D Chaplygin driven cosmology are recovered when $d = 0$. We have drawn the best fit graph using the data obtained by the differential age method (CC) and it is seen that the graph favours only one extra dimension. That means the Chaplygin gas is apparently dominated by a 5D world. Relevant to point out that the final equation in this case are highly nonlinear in nature. Naturally it is not possible to obtain explicit solution of the 4D scale factor with time. To circumvent this difficulty, we consider a first order approximation of the key equation which has made it possible to get time explicit solution of 4D scale factor in exact form as well as the expression of extra dimensions. It may be pointed out that for large four dimensional scale factor this solution mimics $\Lambda$CDM model. An analysis of flip time is also studied both analytically and graphically in some detail. It clearly shows that early \emph{flip} occurs for higher dimensions. It is also seen that the rate of dimensional reduction is faster for higher dimensions. So we may conclude that the effect of compactification of extra dimension helps the acceleration.

We investigate uniform rate inflationary universe in the framework of Loop quantum cosmology. The potential for uniform rate inflation in a loop quantized FRW spacetime turns out to be a polymerized version of the corresponding potential in general relativity, which mimics the potentials for a polymerized scalar field and that for hybrid natural inflation (HNI). The potential leads to a cyclic universe with identical epochs separated by quantum bounces which replace the classical singularity. The energy density and Hubble rate are bounded. The predictions for cosmological perturbations depend on the value of the field at the end of inflation. The parameter space is explored to compare the results for spectral index and tensor-to-scalar ratio with observational constraints.

In this paper, we wish to investigate certain observable effects in the recently obtained wormhole solution of the EiBI theory, which generalizes the zero mass Ellis-Bronnikov wormhole of general relativity. The solutions of EiBI theory contain an extra parameter $\kappa$ having the inverse dimension of the cosmological constant $\Lambda$, and is expected to modify various general relativistic observables such as the masses of wormhole mouths, tidal forces and light deflection. A remarkable result is that a non-zero $\kappa$ could prevent the tidal forces in the geodesic orthonormal frame from becoming arbitrarily large near a small throat radius $(r_0 \sim {0})$ contrary to what happens near a small Schwarzschild horizon radius $(M \sim 0)$. The role of $\kappa$ in the flare-out and energy conditions is also analysed, which reveals that the energy conditions are violated. We show that the exotic matter in the EiBI wormhole cannot be interpreted as phantom ({\omega}=(p_{r}/ \rho)<-1) or ghost field ${\phi}$ of general relativity due to the fact that both $\rho$ and $p_{r}$ are negative for all $\kappa$.

In 2011, the theory of $\mathcal I^K$-convergence gets birth as an extension of the concept of $\mathcal{I}^*$-convergence of sequences of real numbers. $\mathcal I^K$-limit points and $\mathcal I^K$-cluster points of functions are introduced and studied to some extent, where $\mathcal{I}$ and $\mathcal{K}$ are ideals on a non-empty set $S$. In a first countable space set of $\mathcal I^K$-cluster points is coincide with the closure of all sets in the filter base $\mathcal{B}_f(\mathcal{I^K})$ for some function $f : S\to X$. Frechet compactness is studied in light of ideals $\mathcal{I}$ and $\mathcal{K}$ of subsets of $S$ and showed that in $\mathcal{I}$-sequential $T_2$ space Frechet compactness and $\mathcal{I}$-Frechet compactness are equivalent. A class of ideals have been identified for which $\mathcal I^K$-Frechet compactness coincides with $\mathcal{I}$-Frechet compactness in first countable spaces.

Atherosclerosis is a chronic inflammatory cardiovascular disease in which fatty plaque is built inside an artery wall. Early atherosclerotic plaque development is typically characterized by inflammatory tissues primarily consisting of foam cells and macrophages. We present a biphasic model that explores early plaque growth to emphasize the role of cytokines (particularly, Monocyte Chemoattractant Protein-1) and oxidized low-density lipoprotein (oxLDL) in monocyte recruitment and foam cell production, respectively. The plaque boundary is assumed to move at the same speed as the inflammatory tissues close to the periphery. This study discusses the oxLDL cholesterols recruitment inside intima and their internalization by the inflammatory cells. Excessive intracellular cholesterol accumulation becomes toxic to macrophage foam cells, leading to cell death beyond a threshold. Our findings reveal that initially, the plaque evolves rapidly, and the growth rate eventually reduces because of the cholesterol-induced toxicity. The present study manifests that higher oxLDL cholesterol flux reduces plaque growth rate, while elevated cytokines flux promotes the corresponding plaque growth behaviour. Between oxLDL cholesterol and intracellular cholesterol, the second one is much more effective towards the growth of inflammatory tissue. The cholesterol-based toxicity-induced cell death parameters are crucial in flattening the plaque growth profile. A detailed analysis of the model presented in this article provides critical insights into the various biochemical and cellular mechanisms behind early plaque development.

Very recently, HAWC observatory discovered the high-energy gamma ray emission from the solar disk during the quiescent stage of the Sun, extending the Fermi-LAT detection of intense, hard emission between 0.1 - 200 GeV to TeV energies. The flux of these observed gamma-rays is significantly higher than that theoretically expected from hadronic interactions of galactic cosmic rays with the solar atmosphere. More importantly, spectral slope of Fermi and HAWC observed gamma ray energy spectra differ significantly from that of galactic cosmic rays casting doubt on the prevailing galactic cosmic ray ancestry model of solar disk gamma rays. In this work, we argue that the quiet Sun can accelerate cosmic rays to TeV energies with an appropriate flux level in the solar chromosphere, as the solar chromosphere in its quiet state probably possesses the required characteristics to accelerate cosmic rays to TeV energies. Consequently, the mystery of the origin of observed gamma rays from the solar disk can be resolved consistently through the hadronic interaction of these cosmic rays with solar matter above the photosphere in a quiet state. The upcoming IceCube-Gen2 detector should be able to validate the proposed model in future through observation of TeV muon neutrino flux from the solar disk. The proposed idea should have major implications on the origin of galactic cosmic rays.

We consider a spatially flat FLRW universe. We assume that it is filled with dark energy in the form of logotropic dark fluid coupled with dark matter in the form of a perfect fluid having a barotropic equation of state. We employ dynamical system tools to obtain a complete qualitative idea of the evolution of such a universe. It is interesting to note that we ought to consider an approximation for the pressure of the logotropic dark fluid in the form of an infinite series so as to be able to construct the autonomous system required for a dynamical system study. This series form provides us with a power law in the rest-mass energy density of the logotropic dark fluid. We compute the critical points of the autonomous system and analyze these critical points by applying linear stability theory. Our analysis reveal a scenario of late-time accelerated universe dominated by the logotropic fluid which behaves as cosmological constant, preceded by an intermediate phase of the Universe dominated by logotropic fluid which behaves as dark matter in the form of perfect fluid. Moreover, it also crosses the phantom divide line.

It is well known that, in contrast to general relativity, there are two conformally related frames, the Jordan frame and the Einstein frame, in which the Brans-Dicke theory, a prototype of generic scalar-tensor theory, can be formulated. There is a long standing debate on the physical equivalence of the formulations in these two different frames. It is shown here that gravitational deflection of light to second order accuracy may observationally distinguish the two versions of the Brans-Dicke theory.

In the background dynamics of a spatially flat FLRW model of the universe, we investigate an interacting dark energy model in the context of Lyra's geometry. Pressure-less dust is considered as dark matter, mass of which varies with time via scalar field in the sense that decaying of dark matter particles reproduces the scalar field. Here, quintessence scalar field is adopted as dark energy candidate which evolves in exponential potential. Mass of the dark matter particles is also considered to be evolved in exponential function of the scalar field. Cosmological evolution equations are studied in the framework of dynamical systems analysis. Dimension-less variables are chosen properly so that the cosmological evolution equations are converted into an autonomous system of ordinary differential equations. Linear stability is performed to find the nature of critical points by perturbing the system around the critical points in the phase space. Classical stability is also executed by finding out the speed of sound. Dynamical systems explore several viable results which are physically interested in some parameter regions. Late-time scalar field dominated attractors are found by critical points, corresponding to the accelerating universe. Scalar field-displacement vector field scaling solutions are realized that represent late time decelerated universe. Dark energy -dark matter scaling solutions are also exhibited by critical points which correspond to accelerated attractors possessing similar order of energy densities of dark energy and dark matter, that provides the possible solutions of coincidence problem.

Atherosclerosis, a chronic inflammatory cardiovascular disease, leads to arterial constriction caused by the accumulation of lipids, cholesterol, and various substances within artery walls. Such plaque can rupture, resulting in a blood clot that obstructs major arteries and may initiate myocardial infarction, ischemic stroke, etc. Atherosclerotic plaque formation begins with the accumulation of foam cells and macrophages within the intima layer of the arterial wall. At the latter stage, the smooth muscle cells migrated from deeper artery wall layers, contributing to the fibrous cap formation and plaque stabilizing. A developed plaque gradually enters the lumen and narrows down the lumen to impede blood flow. We introduce a two-phase and macroscopic model to investigate the progression of plaque growth in its advanced stage and analyze the minimum gap (Lumen Clearance) within an atherosclerotic artery so that blood cells can pass through. Cardiac troponin, a high specificity and sensitivity biomarker, facilitates early detection of elevated myocardial infarction, Ischemic stroke, etc. risks. This study aims to establish a relationship between the troponin concentration in atherosclerotic arteries and their internal clearance, which could significantly improve our understanding of disease progression. Our observations show that the plaque undergoes rapid evolution in its initial stages, gradually slowing down over time to reach a steady state. At the same time, the lumen clearance exhibits an opposite behavior, decreasing slowly over time. Our study finds a positive correlation between plaque depth and troponin concentration in the blood and a negative relationship between troponin concentrations and lumen clearance in atherosclerotic arteries.

The paper describes lateral density distributions of electrons and muons of cosmic ray extensive air showers (EAS) in the energy regime of the KASCADE experiment. Potential EAS observables are extracted while some suitable lateral distribution functions are introduced to describe these lateral density distributions of simulated/observed cosmic ray showers. Mass-sensitivity of these parameters are demonstrated particularly for the KASCADE electron and muon distributions data. Our studies indicate that the KASCADE data favours an idea of gradual change of cosmic ray mass composition from lighter concentration to heavier concentration in terms of these parameters.

This paper presents an investigation of cosmological dynamics of tachyon fluid coupled to varyingmass dark matter particles in the background of spatially flat FLRW universe. The mechanism of varying mass particles scenario assumes the mass of the dark matter depends on time t through the scalar field ${\phi}$ in the sense that the decaying of dark matter reproduces the scalar field. First, we analyze the model from dynamical systems perspective by converting the cosmological evolution equations into an autonomous system of ordinary differential equations with a suitable transformation of variables. We choose the mass of dark matter as exponential function of scalar field and the exponential potential of the tachyon field is undertaken in such a way that the autonomous system is reduced in three dimensional form. The critical points obtained from the system are non-hyperbolic in nature. The center manifold theory is employed to discuss the nature of the critical points. Numerical investigation also carried out for some critical points. From this analysis, we obtain dust dominated decelerated transient phase of the universe followed by dark energy dominated scaling attractor alleviating the coincidence problem. Next, we perform the statefinder diagnostic approach to compare our model to ${\Lambda}$CDM and finally we study the evolution of the Hubble parameter and the distance modulus and compare this with observational data.