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t. e. In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure.
Solving an equation f(x) = g(x) is the same as finding the roots of the function h(x) = f(x) – g(x). Thus root-finding algorithms allow solving any equation defined by continuous functions. However, most root-finding algorithms do not guarantee that they will find all the roots; in particular, if such an algorithm does not find any root, that ...
The free energy is the portion of any first-law energy that is available to perform thermodynamic work at constant temperature, i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. [1] Since first-law energy is always conserved, it is evident that free energy is an expendable, second-law ...
Froude number. In continuum mechanics, the Froude number ( Fr, after William Froude, / ˈfruːd / [1]) is a dimensionless number defined as the ratio of the flow inertia to the external force field (the latter in many applications simply due to gravity ). The Froude number is based on the speed–length ratio which he defined as: [2] [3] where ...
In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method. However, the secant method predates Newton's method by over 3000 years.
A free particle with mass in non-relativistic quantum mechanics is described by the free Schrödinger equation: (,) = (,) where ψ is the wavefunction of the particle at position r and time t . The solution for a particle with momentum p or wave vector k , at angular frequency ω or energy E , is given by a complex plane wave :
Equation-free modeling is a method for multiscale computation and computer-aided analysis.It is designed for a class of complicated systems in which one observes evolution at a macroscopic, coarse scale of interest, while accurate models are only given at a finely detailed, microscopic, level of description.
The bigger red dot is the root of the function. In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function ...