November 25th, 2021

лошадь, диаграмма, Фейнман

Многократное рассеяние света ансамблем наночастиц

Multiple scattering of light in nanoparticle assemblies: user guide for the TERMS program:
Dmitri Schebarchov, Atefeh Fazel-Najafabadi, Eric C. Le Ru, Baptiste Auguié
We introduce TERMS, an open-source Fortran program to simulate near-field and far-field optical properties of clusters of particles. The program solves rigorously the Maxwell equations via the superposition T-matrix method, where incident and scattered fields are decomposed into series of vector spherical waves.
TERMS implements several algorithms to solve the coupled system of multiple scattering equations that describes the electromagnetic interaction between neighbouring scatterers. From this formal solution, the program can compute a number of physically-relevant optical properties, such as far-field cross-sections for extinction, absorption, scattering and their corresponding circular dichroism, as well as local field intensities and degree of optical chirality. By describing the incident and scattered fields in a basis of spherical waves the T-matrix framework lends itself to analytical formulas for orientation-averaged quantities, corresponding to systems of particles in random orientation; TERMS offers such computations for both far-field and near-field quantities of interest. This user guide introduces the program, summarises the relevant theory, and is supplemented by a comprehensive suite of stand-alone examples in the website accompanying the code.
Comments: 42 pages
лошадь, диаграмма, Фейнман

Численный поиск решений уравнения Ван-дер-Поля с произвольной точностью

Аппроксимация Паде и всякое такое, 42 страницы.

Computing the solutions of the van der Pol equation to arbitrary precision
Paolo Amore
We describe an extension of the Taylor method for the numerical solution of ODEs that uses Padé approximants to obtain extremely precise numerical results. The accuracy of the results is essentially limited only by the computer time and memory, provided that one works in arbitrary precision. In this method the stepsize is adjusted to achieve the desired accuracy (variable stepsize), while the order of the Taylor expansion can be either fixed or changed at each iteration (variable order).
As an application, we have calculated the periodic solutions (limit cycle) of the van der Pol equation with an unprecedented accuracy for a large set of couplings (well beyond the values currently found in the literature) and we have used these numerical results to validate the asymptotic behavior of the period, of the amplitude and of the Lyapunov exponent reported in the literature. We have also used the numerical results to infer the formulas for the asymptotic behavior of the fast component of the period and of the maximum velocity, which have never been calculated before.
Comments: 42 pages; 12 figures; 17 tables