Physical Mathematics

In theory of relativity, Finsler geometry is a without motion there is no position, in universe. In this paper, we study the motion of photon and massless particles for Schwarzschild metric in Finsler space time in the case of Kropina-Finsler space with constant flag curvature. Then, we analyzed qualitatively of potential energy of particles at various distances near Schwarzschild black hole and the results are compared with in the Riemannain geometry in particular Lorenz case. Also, described the scattering of particles near Schwarzschild black hole in Finsler space time by finding capture cross section of absorption by the black hole.

This work is due for the solution of the big problem which is the solution of the Schrödinger equation to have a new model or system that can have other consequences on the whole matter which leads to a resolution of all the quantum problems to link to physics, which makes theories in quantum physics easier to answer on major and complex questions. The solution of the Schrödinger equation is based on the connection between quantum mechanics and relativity. It is a drift of this connection so we have this system is completely solved and gives a great interpretation of all the particles and waves and all macroscopic or microscopic systems e.g. galaxies; the planets; the moons etc. for example, particles, waves, electrons, protons, etc. will be noted.

This study investigates the Soret effects on Natural convection flow of Nano fluids over an infinite vertical plate, in the presence of thermal radiation and applied magnetic field. The fluid is assumed to be electrically conducting water based Cu-nanofluid. The Tiwari and Das model is used to model the Nano fluid, whereas Rosseland approximation is used for thermal radiation effect. Solutions for time dependent velocity, temperature and concentration equations are obtained using Laplace transform technique. The physical quantities of engineering interest such as skin friction and Sherwood number are also computed. The obtained analytical solutions satisfy all imposed initial and boundary conditions. The effect of various parameters controlling the physical situation is discussed with the aid of line graphs. During the course of computation, excellent result was found from various physical parameters embedded in the problem.

The Hartmann layers of conducting fluid between parallel plates under the influence of the transvers magnetic field are considered. The standard boundary conditions with zero velocities on the plates are used. The perturbations are used to obtain the exact solution for the given system. It is shown explicitly that no instability near the stationary solution can be found by perturbations in 2-dim cases. In 3-dim case the instability arises just when quaternionic perturbations applied. We use analytical solutions to obtain explicit results and wave perturbations for considered system. Our results are agreed with experimental facts which was solved by other authors and confirms the wellknown fact that traversal magnetic field overcomes the instability. Similarly we obtained the exact solution by using new quaternionic method and this way of nonlinear system consideration can deliver a variety of possibilities for finding new solutions.