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  2. Polytropic process - Wikipedia

    en.wikipedia.org/wiki/Polytropic_process

    A polytropic process is a thermodynamic process that obeys the relation: = where p is the pressure , V is volume , n is the polytropic index , and C is a constant. The polytropic process equation describes expansion and compression processes which include heat transfer.

  3. Polytrope - Wikipedia

    en.wikipedia.org/wiki/Polytrope

    Neutron stars are well modeled by polytropes with index between n = 0.5 and n = 1. A polytrope with index n = 1.5 is a good model for fully convective star cores [5] [6] (like those of red giants), brown dwarfs, giant gaseous planets (like Jupiter). With this index, the polytropic exponent is 5/3, which is the heat capacity ratio (γ) for ...

  4. Lane–Emden equation - Wikipedia

    en.wikipedia.org/wiki/Lane–Emden_equation

    The particular choice of a polytropic gas as given above makes the mathematical statement of the problem particularly succinct and leads to the Lane–Emden equation. The equation is a useful approximation for self-gravitating spheres of plasma such as stars, but typically it is a rather limiting assumption.

  5. Heat capacity ratio - Wikipedia

    en.wikipedia.org/wiki/Heat_capacity_ratio

    Therefore, the heat capacity ratio in this example is 1.4. Another way of understanding the difference between C P and C V is that C P applies if work is done to the system, which causes a change in volume (such as by moving a piston so as to compress the contents of a cylinder), or if work is done by the system, which changes its temperature ...

  6. Lyapunov exponent - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_exponent

    To introduce Lyapunov exponent consider a fundamental matrix () (e.g., for linearization along a stationary solution in a continuous system), the fundamental matrix is ⁡ (() |) consisting of the linearly-independent solutions of the first-order approximation of the system.

  7. Matrix exponential - Wikipedia

    en.wikipedia.org/wiki/Matrix_exponential

    It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n × n real or complex matrix. The exponential of X, denoted by e X or exp(X), is the n × n matrix given by the power series = =!

  8. Discharge coefficient - Wikipedia

    en.wikipedia.org/wiki/Discharge_coefficient

    In a nozzle or other constriction, the discharge coefficient (also known as coefficient of discharge or efflux coefficient) is the ratio of the actual discharge to the ideal discharge, [1] i.e., the ratio of the mass flow rate at the discharge end of the nozzle to that of an ideal nozzle which expands an identical working fluid from the same initial conditions to the same exit pressures.

  9. Critical exponent - Wikipedia

    en.wikipedia.org/wiki/Critical_exponent

    The critical exponents can be derived from the specific free energy f(J,T) as a function of the source and temperature. The correlation length can be derived from the functional F[J;T]. In many cases, the critical exponents defined in the ordered and disordered phases are identical.