Some exact analytical formulas are presented for the generalized Roche model of rotating star. The gravitational field of the central core is described by the model of two equal-mass point centers placed symmetrically at rotation axis with the pure imaginary z coordinates. The all basic parameters of the critical figure of the rotating massless envelope are presented in analytical form. The exi...

A simplified model of the spatially dependent deposition profile in chemical vapor deposition reactors with planetary wafer rotation is developed. The model focuses on reactors operated in “depletion” mode, a situation where the precursor species have undergone a sequence of gas-phase decomposition reactions leaving only the deposition species to diffuse to and react on the substrate surface, g...

Rotating squares appeared to be distorted into pincushions with concave sides. These illusory shape changes were caused by a perceived compression along the curved path of motion.

We study the rotating wave patterns in an excitable medium in a disk. This wave pattern is rotating along the given disk boundary with a constant angular speed. To study this pattern we use the wave front interaction model proposed by Zykov in 2007. This model is derived from the FitzHugh-Nagumo equation and it can be described by two systems of ordinary differential equations for wave front an...

In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0, 1]. These solutions are introduced by a suitable limiting process of Bäcklund transformations applied to seed solutions of the Weyl class. It turns out that this class of solutions contains the general relativistic gravitational field of an arbitrary differentia...

In this paper energy method is used to calculate rotor response with loose rotating disk on it. System equation of motion is obtained based on energy method and Lagrange equation. Mathematical modeling of loose disk in a rotor bearing system has resulted in terms similar to unbalance and gyroscopic effect in the system equation of motion. The effect of loose disk axial position and orthotropic ...

We discuss the solution of accretion disk when the black hole is chosen to be rotating. We study, how the fluid properties get affected for different rotation parameters of the black hole. We know that no cosmic object is static in Universe. Here the effect of the rotation of the black hole to the space-time is considered following an earlier work of the author, where the pseudo-Newtonian poten...

An experimental study of heat transfer into a thin liquid film on a rotating heated disk is described. Deionized water was introduced at the center of a heated, horizontal disk with a constant film thickness and uniform radial velocity. Radial distribution of the disk surface temperatures was measured using a thermocouple/slip ring arrangement. Experiments were performed for a range of liquid f...

The interstellar gas flow in the inner disk of M31 is modelled using a new, two dimensional, grid based, hydrodynamics code. The potential of the stellar bulge is derived from its surface brightness profile. The bulge is assumed to be triaxial and rotating in the same plane as the disk in order to explain the twisted nature of M31’s central isophotes and the non circular gas velocities in the i...

If a Kerr black hole is connected to a disk rotating around it by a magnetic field, the rotational energy of the Kerr black hole provides an energy source for the radiation of the disk in addition to disk accretion. The black hole exerts a torque on the disk, which transfers energy and angular momentum between the black hole and the disk. If the black hole rotates faster than the disk, energy a...