Physical Mathematics

In this paper, using the theory of the so-called fractional calculus we show that it is possible to easily obtain the solutions for the confluent hypergeometric equation. Our approach is to be compared with the standard one (Frobenius) which is based on the ordinary calculus of integer order.

The relaxation functions introduced empirically by Debye, Cole-Cole, Cole-Davidson and Havriliak-Negami are, each of them, solutions to their respective kinetic equations. In this work, we propose a generalization of such equations by introducing a fractional differential operator written in terms of the Riemann-Liouville fractional derivative of order γ, 0<γ≤1. In order to solve the generalized equations, the Laplace transform methodology is introduced and the corresponding solutions are then presented, in terms of Mittag-Leffler functions. In the case in which the derivative’s order is γ = 1, the traditional relaxation functions are recovered. Finally, we presented some 2D graphs of these function.

We study the interaction of two charged solid particles in a viscous fluid. It is assumed that the particles move either side-by-side or one after another along the same vertical line under the influence of the buoyancy/gravity force, Coulomb electrostatic force or its modification, and viscous drag force. The drag force consists of two components: the quasi-stationary Stokes drag force and Boussinesq–Basset drag force resulting from the unsteady motion. Solutions of the governing equations are analysed analytically and numerically for the cases of perfect fluid and viscous fluid; the comparison of these two cases is presented.

This is a review paper on isolated, distorted and time-dependent null horizons by providing up-date information on their role in black hole physics. Geometry of totally umbilical null hyper surfaces has been used to establish an interrelation between these three types of horizons in a unified manner. Distorted horizons describe the near isolated black holes which are dis- torted by the presence of faraway matter. On the other hand, time-dependent null horizons are modeled by a family of totally umbilical null hyper surfaces. A sketch of the proofs of the most important results is presented together with sufficient related references.

Online class as an emerging mode of education delivery has brought forth new opportunities and challenges on the face of traditional sit-in class. The opportunities are more obvious than the challenges. Compared to our old school format, the lack of a real human being standing in front of the class is the real game changer. The work reported in this article examines these issues.

In the present study, a laminar flow in a planar 2D right angled T-channel in the presence of a rotating heated cylindrical obstacle placed in the junction area is numerically studied to control the heat transfer and fluid flow. The effect of Reynolds number (20 ≤ Re ≤ 300) and cylinder rotation angle (-5 ≤ É· ≤ 5) on the fluid flow and heat transfer characteristics are studied numerically. It is observed that the flow field and heat transfer rate are influenced by the variation of these parameters.

In this work, we are interested on the numerical and experimental investigations of a NACA2415 airfoil wind turbine placed in an open wind tunnel. The study of the meshing effect on the numerical results was developed using a commercial CFD code based on the resolution of the Navier-Stokes equations in conjunction with the standard k-ε turbulence model. These equations were solved by a finite volume discretization method. The developed numerical results are compared with experimental results to choose the adequate meshing.

The paper represents the results of the study of the four-dimensional Euclidean space with real time (E-space), where 0 ≤ ||VE|| ≤ ∞, in sub-hadronic physics. This closed space has a metric that distinguished from the Minkowski space and the results obtained in the model are different from physical law in the Minkowski space. As it follows from the model of Lagrangian Mechanics, quarks in the central-symmetric attractive potential, kinetic energy of quark diminishes while the speed grows as the quarks exchange their energy-mass with gluons possessing a zero rest mass, so that to ensure the permanent proton mass. This dependence describes the dynamical relation of constituent and current quarks masses. In the quantified motion model it has been stated, that the oscillations of the particles are cyclic, including alternating localization and translation phases, the action per cycle for a free particle equals h . The calculation of charge distribution density in proton, carried out on the basis of this model, conforms to the results of the experimental research. All relations between physical values in the E-space, mapped in the Minkowski space, correspond to the principles of SR and are Lorentz-covariant and the infinite velocity is equal to the velocity of light in the Minkowski space. These models have a transparent physical sense.

In this paper we consider Impulsive stochastic neutral functional differential equations with multiple delays. By using Schaefer’s fixed point theorem, we prove the existence of solutions for stochastic differential equations with impulses

In this note, we extend and improve the corresponding result of Takahashi. Explanation of DeMarr’s theorem is
further generalized for some semi groups of non-expansive self- maps on K by the following considerations which are explained in the paper. The application of Zorn’s lemma and its application are explained. An application of Zorn’s lemma shows that there exists a minimal non-empty compact convex and S-invariant subset.

The connection between the concept of a ‘Lagrangian manifold’ and Liouville’s theorem in classical mechanics and the concept of a global information field in quantum physics is discussed.

In this paper, the meshless method is employed for the numerical solution of the one-dimensional (1D)
convection-diffusion equation based on radical basis functions (RBFs). Coupled with the time discretization and the collocation method, the proposed method is a truly meshless method which requires neither domain nor boundary discretization. The algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme