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The non-linear σ-model was introduced by Gell-Mann & Lévy (1960, §6), who named it after a field corresponding to a spinless meson called σ in their model. [1] This article deals primarily with the quantization of the non-linear sigma model; please refer to the base article on the sigma model for general definitions and classical (non ...
SNOPT, for Sparse Nonlinear OPTimizer, is a software package for solving large-scale nonlinear optimization problems written by Philip Gill, Walter Murray and Michael Saunders. SNOPT is mainly written in Fortran , but interfaces to C , C++ , Python and MATLAB are available.
Unfortunately, the "sigma meson" is not described by the sigma-model, but only a component of it. [1] The sigma model was introduced by Gell-Mann & Lévy (1960, section 5); the name σ-model comes from a field in their model corresponding to a spinless meson called σ, a scalar meson introduced earlier by Julian Schwinger. [2]
acados - Open-source framework for (nonlinear) model predictive control providing fast and embedded solvers for nonlinear optimization. (C, MATLAB and Python interface available) μAO-MPC - Open Source Software package that generates tailored code for model predictive controllers on embedded systems in highly portable C code.
The Volterra series is a model for non-linear behavior similar to the Taylor series.It differs from the Taylor series in its ability to capture "memory" effects. The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of the system depends strictly on the input at that particular time.
SciPy (de facto standard for scientific Python) has scipy.optimize solver, which includes several nonlinear programming algorithms (zero-order, first order and second order ones). IPOPT (C++ implementation, with numerous interfaces including C, Fortran, Java, AMPL, R, Python, etc.) is an interior point method solver (zero-order, and optionally ...
Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. [1] Given a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting regression (such as LASSO and spare Bayesian inference [2]) on a library of nonlinear candidate functions of the snapshots against the ...
In field theory, skyrmions are homotopically non-trivial classical solutions of a nonlinear sigma model [17] with a non-trivial target manifold topology – hence, they are topological solitons. An example occurs in chiral models [ 18 ] of mesons , where the target manifold is a homogeneous space of the structure group