In this article, we study parameter-dependent systems of reaction-diffusion equations on the sphere, which are equivariant under the group SO(3) of all rigid rotations on a sphere. Two main types of spatial-temporal patterns that can appear in such systems are rotating waves (equilibrium in a co-rotating frame) and modulated rotating waves (periodic solution in a corotating frame). The transiti...

We present first results of the non-linear evolution of rotating relativistic stars obtained with an axisymmetric relativistic hydrodynamics code in a fixed spacetime. As initial data we use stationary axisymmetric and perturbed configurations. We find that, in order to prevent (numerical) angular momentum loss at the surface layers of the star a high-resolution grid (or a numerical scheme that...

New optical methods now allow experimentalists to track the trajectories of Lagrangian tracer particles in fluid flows at high Reynolds numbers. Independently, quaternions are used in the aerospace and computer graphics industries to track the paths of objects undergoing three-axis rotations. It is shown here that quaternions are a natural way of selecting an appropriate ortho-normal quaternion...

in this paper, a new method for determining position and orientation of a coordinate system using its image is presented. this coordinate system is a three dimensional non-orthogonal system in respect to the two dimensional and orthogonal camera coordinate system.  in real world, it’s exactly easy to select three directions on an object so that they don’t be orthogonal and on a plane. the image...

We have studied the wave properties of the cold and isothermal plasma in the vicinity of the Schwarzschild black hole event horizon. The Fourier analyzed perturbed 3+1 GRMHD equations are taken on the basis of which the complex dispersion relations are obtained for non-rotating, rotating non-magnetized and rotating magnetized backgrounds. The propagation and attenuation vectors along with the r...

In this paper a Hamiltonian analogue of the well-known meandering transition from rotating waves to modulated rotating and modulated travelling waves in systems with the Euclidean symmetry of the plane is presented. In non-Hamiltonian systems, for example in spiral wave dynamics, this transition is a Hopf bifurcation in a corotating frame, as external parameters are varied, and modulated travel...

We study spin and charge currents pumped by precessing magnetization of a single ferromagnetic layer within F I N or F I F F-ferromagnet; I-insulator; N-normal metal multilayers of nanoscale thickness attached to two normal-metal electrodes with no applied bias voltage between them. Both simple one-dimensional model, consisting of a single precessing spin and a potential barrier as the “sample,...

‎for a finite group $g$ let $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$‎. ‎the aim of this paper is to classify all the non-nilpotent groups with $nu(g)=3$‎.

Neurophysiological studies focus on memory retrieval as a reproduction of what was experienced and have established that neural discharge is replayed to express memory. However, cognitive psychology has established that recollection is not a verbatim replay of stored information. Recollection is constructive, the product of memory retrieval cues, the information stored in memory, and the subjec...