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The Gross–Pitaevskii equation (GPE, named after Eugene P. Gross [1] and Lev Petrovich Pitaevskii [2]) describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and the pseudopotential interaction model. A Bose–Einstein condensate (BEC) is a gas of bosons that are in the same quantum state, and ...
A double pendulum consists of two pendulums attached end to end.. In physics and mathematics, in the area of dynamical systems, a double pendulum also known as a chaotic pendulum is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. [1]
In many practical partial differential equations, one has a term that involves derivatives (such as a kinetic energy contribution), and a multiplication with a function (for example, a potential). In the spectral method, the solution ψ {\displaystyle \psi } is expanded in a suitable set of basis functions, for example plane waves,
The assumption m ≥ n in the algorithm statement is necessary, as otherwise the matrix is not invertible and the normal equations cannot be solved (at least uniquely).. The Gauss–Newton algorithm can be derived by linearly approximating the vector of functions r i.
Specific potential energy. In classical mechanics and gravitational physics, massic gravitational potential energy (MGPE) is a fundamental concept that relates to the gravitational potential a body possesses due to its position in a gravitational field relative to a reference point. This energy is associated with the gravitational force acting ...
The following tables provide a comparison of computer algebra systems (CAS). [1] [2] [3] A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language.
Catastrophic cancellation. In numerical analysis, catastrophic cancellation[1][2] is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one long and the other long, and they are measured with a ruler that is ...
Spyder is an open-source cross-platform integrated development environment (IDE) for scientific programming in the Python language. Spyder integrates with a number of prominent packages in the scientific Python stack, including NumPy, SciPy, Matplotlib, pandas, IPython, SymPy and Cython, as well as other open-source software. [4][5] It is ...