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Method Of Characteristics For Solving The Problem Of Gas Outflow From An Elementary Sec-Tion Of A Gas Pipeline, Madaminjon K. Mahkamov, S.S. Akhmadjonov, I.K. Khujaev
Method Of Characteristics For Solving The Problem Of Gas Outflow From An Elementary Sec-Tion Of A Gas Pipeline, Madaminjon K. Mahkamov, S.S. Akhmadjonov, I.K. Khujaev
Scientific Bulletin. Physical and Mathematical Research
Numerous problems based on equations of hyperbolic type are solved by the method of characteristics when boundary conditions of the first, second and third kinds are set on the boundary. These include, in particular, the problems of pipeline transportation of various media. The quasi-one-dimensional equations of conservation of mass and momentum are linearized and separate equations are drawn up for a specific indicator (flow rate, gas pressure) of the process. This approach is associated with the tradition of forming boundary conditions and solving problems only with respect to a specific indicator, in particu-lar, with respect to pressure, velocity, and flow …
A New Approach To The Potential Energy Of Solids, Radhika Chauhan, Sanjeev K. Verma, Anushri Gupta, Anita Kumari, B. D. Indu
A New Approach To The Potential Energy Of Solids, Radhika Chauhan, Sanjeev K. Verma, Anushri Gupta, Anita Kumari, B. D. Indu
Karbala International Journal of Modern Science
A general theory is developed to investigate the expression for potential energy without using (i) empirical results and (ii) process of parameterizing. The simple approach of thermodynamics is adopted to obtain the expressions for the interaction energy of solids in terms of interatomic separation and crystal volume. The new findings have been applied to obtain the expressions for bulk modulus and pressure. The variation of the potential energy function, which provides a means to understand the stability of a crystal has been found in excellent agreements to the earlier results. The use of obtained harmonic and anharmonic force constants may …