in this paper a mathematical simulation of a simplified internal combustion engine is presented. to contribute engine kinematics and its geometry, simple relations are derived for constrained motions. the equation of motion for the piston forms a singular boundary value problem. the uniqueness of the solution was studied in the banach space. for solving governing equations an iterative numerica...

Self-similar shock solutions in spherically symmetric polytropic gas flows are constructed and analyzed in contexts of proto-star formation processes. Among other possible solutions, we model a similarity shock across the sonic critical curve with an inner free-fall core collapse and a simultaneous outer expansion of the extended envelope; the separation or stagnation surface between these two ...

It is shown that expansion waves for the compressible Navier-Stokes equations are nonlinearly stable. The expansion waves are constructed for the compressible Euler equations based on the inviscid Burgers equation. Our result shows that Navier-Stokes equations and Euler equations are timeasymptotically equivalent on the level of expansion waves. The result is proved using the energy method, mak...

In this paper a mathematical simulation of a simplified internal combustion engine is presented. To contribute engine kinematics and its geometry, simple relations are derived for constrained motions. The equation of motion for the piston forms a singular boundary value problem. The uniqueness of the solution was studied in the Banach space. For solving governing equations an iterative numerica...

In this paper, a generic self-similar flux rope model is proposed to probe the internal state of CMEs in order to understand the thermodynamic process and expansion of CMEs in interplanetary space. Using this model, three physical parameters and their variations with heliocentric distance can be inferred based on coronagraph observations of CMEs’ propagation and expansion. One is the polytropic...

Analysis of compression mechanisms requires a prediction of the pressure during the compression and expansion processes. A common model is the polytropic process, PV = constant. This paper presents a method for determining the best polytropic exponent to use and suggests values for some common refrigerants used in the air conditioning and refrigeration industry. INTRODUCTION When a gas undergoe...

We explore large-scale hydrodynamics of H II regions for various self-similar shock flows of a polytropic gas cloud under self-gravity and with quasi-spherical symmetry. We formulate cloud dynamics by invoking specific entropy conservation along streamlines and obtain global self-similar “champagne flows” for a conventional polytropic gas with shocks as a subclass. Molecular cloud cores are ion...

The dynamic stability of the spherical gravitational evolution (collapse or expansion) for a homogeneous polytropic gas with any exponent γ, is studied using the lagrangian formalism. We obtain the analytical expression for density perturbations at the first order. In the case γ = 4/3, the Jeans’ criterion is easily generalized to a self-similar expanding background. The collapsing case is foun...

We consider the Riemann problem for relativistic flows of polytropic fluids and find relations for the flow characteristics. Evolution of physical quantities takes especially simple form for the case of cold magnetized plasmas. We find exact explicit analytical solutions for one-dimensional expansion of magnetized plasma into vacuum, valid for arbitrary magnetization. We also consider expansion...