More From Solomon I. Khmelnik

Fluid Flow in Tube with Obstacle: the New Calculation Method and the MATLAB-program. By Solomon I. Khmelnik
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In [1] the variational principle of the extremum for a viscous incompressible and compressible fluid is proposed, from which it follows that the Navier-Stokes equations are the conditions for the... More > unique extremum of a certain functional. A method is also proposed for the search for this extremum, which is simultaneously a method for solving these equations. Here we based on this method describe the program for calculating the Fluid Flow in Tube with Obstacle - calculating the velocity and pressure of the liquid at all points of the tube.< Less
Navier-Stokes equations. On the existence and the search method for global solutions. By Solomon I. Khmelnik
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In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Naviet-Stokes equations represent the... More > extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum. We formulate the conditions of reaching this extremum, which are at the same time necessary and sufficient conditions of this functional global extremum existence.< Less
Уравнения Навье-Стокса. Существование и метод поиска глобального решения. By Solomon I. Khmelnik
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Формулируется и доказывается... More > вариационный принцип экстремума для вязкой несжимаемой и сжимаемой жидкости, из которого следует, что уравнения Навье-Стокса являются условиями экстремума некоторого функционала. Описывается метод поиска решения этих уравнений, который состоит в движении по градиенту к экстремуму этого функционала. Формулируются условия достижения этого экстремума, которые являются одновременно необходимыми и достаточными условиями существования глобального экстремума этого функционала.< Less
Inconsistency Solution of Maxwell's Equations By Solomon I. Khmelnik
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A new solution of Maxwell equations for a vacuum, for wire with constant and alternating current, for the capacitor, for the sphere, etc. is presented. First it must be noted that the proof of the... More > solution's uniqueness is based on the Law of energy conservation which is not observed (for instantaneous values) in the known solution. The solution offered: • Complies with the energy conservation law in each moment of time, i.e. sets constant density of electromagnetic energy flux; • Reveals phase shifting between electrical and magnetic intensities; • Explains existence of energy flux along the wire that is equal to the power consumed. A detailed proof is given for interested readers. Experimental proofs of the theory are considered. Explanation is proposed for the experiments, which have not yet been explained. The work offers some technical applications of the solution obtained.< Less