Approximate perfect fluid solutions with quadrupole moment

We investigate the interior Einstein’s equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational fields. Assuming that the deviation from spherically symmetry is small, we linearize the corresponding line element and field equations and find several classes of vacuum and perfect fluid solutions. We find some particular approximate solutions by imposing appropriate matching conditions.

The entropy evolution of a Schwarzschild–(Anti) de Sitter black hole

Based on the definition of the interior volume of spherically symmetry black holes, the interior volume of Schwarzschild–(Anti) de Sitter black holes is calculated. It is shown that with the cosmological constant ([Formula: see text]) increasing, the changing behaviors of both the position of the largest hypersurface and the interior volume for the Schwarzschild–Anti de Sitter black hole are the same as the Schwarzschild–de Sitter black hole. Considering a scalar field in the interior volume and Hawking radiation with only energy, the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy is constructed. The results show that the scalar field entropy is approximately proportional to Bekenstein–Hawking entropy during Hawking radiation. Meanwhile, the proportionality coefficient is also regarded as a constant approximately with the increasing [Formula: see text]. Furthermore, considering [Formula: see text] as a dynamical variable, the modified Stefan–Boltzmann law is proposed which can be used to describe the variation of both the mass and [Formula: see text] under Hawking radiation. Using this modified law, the evolution relation between the two types of entropy is also constructed. The results show that the coefficient for Schwarzschild–de Sitter black holes is closer to a constant than the one for Schwarzschild–Anti de Sitter black holes during the evaporation process. Moreover, we find that for Hawking radiation carrying only energy, the evolution relation is a special case compared with the situation that the mass and [Formula: see text] are both considered as dynamical variables.

Si Nanopowder Based Anode Material for the Lithium Ion Battery Cell

We consider a silicon nanopowder based anode for a lithium ion battery cell. We present the design of the battery cell ready for in situ Raman and X-ray experiments and a technical procedure for the cell manufacturing. From the continuum mechanics point of view, this type of anode can be represented by a spherical nanoparticle surrounded by viscoelastic matrix. During the charging process this nanoparticle undergoes a chemical reaction. Based on the chemical affinity concept we describe how the mechanical properties of the matrix material influence the kinetics of the charging process. We study spherically symmetry problems numerically for different sets of matrix material parameters and show their influence on the reaction front kinetics.

A theoretical study on the elastic deformation of cellular phase and creation of necrosis due to the convection reaction process inside a spherical tumor

Several biological processes, such as convective nutrient transport and convective drug delivery in biological tissues involves the transvascular and interstitial movement of biofluids. This work addresses transvascular and interstitial transport of nutrient inside a spherical tumor. Most of the biological tissues behave like deformable porous material and show mechanical behavior towards the fluid motion, due to the fact, that the forces like the drag, which is associated with fluid flow may compress the tissue material. On the macroscopic level, transport of solutes like nutrients, drug molecules, etc. within the tumor interstitial space is modeled. The hydrodynamic problem is treated with biphasic mixture theory under steady state and spherically symmetry situation. The transvascular transport of nutrient is modeled with the modified Sterling’s equation. The present model describes the overall nutrient distribution and predicts various criteria for the necrosis formation inside the tumor. Present study justifies that the parameters, which controls the nutrient supply to the tumor interstitial space through the blood vessel network inside the tumor, competes with reversible nutrient consumption kinetics of the tumor cells. This study also finds the role of some of those parameters on the deformation of cellular phase of the tumor as a consequence of interstitial fluid flow.

NON-EXISTENCE OF NEW QUANTUM ERGOSPHERE EFFECT OF A VAIDYA-TYPE BLACK HOLE

Hawking evaporation of Dirac particles and scalar fields in a Vaidya-type black hole is investigated by the method of generalized tortoise coordinate transformation. It is shown that Hawking radiation of Dirac particles does not exist for P1, Q2 components but for P2, Q1 components in any Vaidya-type black holes. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein–Gordon particles. We demonstrate that there is no new quantum ergosphere effect in the thermal radiation of Dirac particles in any spherically symmetry black holes.

Stellar Wind Equations in a New Steady State

A set of equations of stellar wind in a new steady state in spherically symmetry is presented. This equations are available also for the deep interior of stars, whereas the usual equations can be applied only to the surface region. The new equations have a variable mass flux which becomes zero at the inner boundary of the mass flow. The velocity also reduces zerj), whereas it diverges at r=0 in the usual continuity equation 4∏r2ρ v=constant. In the surface region, the present equations approach the usual equations.