title: ÐÐ¾Ð»Ð¸Ð½Ð¾Ð¼Ð¸Ð°Ð»ÑÐ½Ð°Ñ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸Ñ ÐºÐ¾Ð»ÐµÐ±Ð°ÑÐµÐ»ÑÐ½ÑÑ ÑÐ²Ð¾Ð¹ÑÑÐ² Ð½ÐµÑÐ¿Ð¾ÑÑÐ´Ð¾ÑÐµÐ½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼ ÑÐ°Ð·Ð½Ð¾Ð¹ ÑÐ°Ð·Ð¼ÐµÑÐ½Ð¾ÑÑÐ¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Polynomial approximation of vibrational properties of disordered systems of different dimensionality
Creators: name: Ð Ð°Ð¹ÐºÐ¾Ð², ÐÐ³Ð¾ÑÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: ÐÐ¾Ð»Ð½Ñ
ÐÐ¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸Ñ
Ð°Ð¼Ð¾ÑÑÐ½ÑÐ¹ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»
ÐºÐ¾Ð»ÐµÐ±Ð°ÑÐµÐ»ÑÐ½ÑÐµ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð°
Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÑÑÑÐºÑÑÑÐ½ÑÐ¹ ÑÐ°ÐºÑÐ¾Ñ
Ð¿Ð¾Ð»Ð¸Ð½Ð¾Ð¼Ñ Ð¯ÐºÐ¾Ð±Ð¸
Ð½ÐµÐ¾ÑÑÐ¸ÑÐ°ÑÐµÐ»ÑÐ½ÑÐµ ÑÐ´ÑÐ°
Ð¼ÐµÑÐ¾Ð´ Ð¿Ð¾Ð»Ð¸Ð½Ð¾Ð¼Ð¸Ð°Ð»ÑÐ½ÑÑ ÑÐ´ÐµÑ
amorphous materials
vibrational properties
dynamical structure factor
Jacobi polynomials
nonnegative kernels
kernel polynomial method

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description: The given work is devoted to the development and application of a numerical method for approximating vibrational properties with the use of Jacobi polynomials. In the course of this work, a generalization of the kernel polynomial method was developed that uses the family of Jacobi polynomials, which allows obtaining approximations with arbitrary power-law behavior near the edges of the interval. An optimal kernel was obtained that ensures the non-negativity of the approximation, which is a necessary condition for many applications. The developed method makes it possible to approximate such important vibrational characteristics as the density of states and the dynamic structure factor. A model of wave attenuation in disordered systems of different dimensionality was constructed, and the method was used for its numerical analysis, the results of which showed good agreement with the predicted attenuation rates. The density of states of amorphous silicon was also calculated, demonstrating the presence of a boson peak, and the attenuation of flexural modes in amorphous graphene was studied, showing a dependence on the fourth power of the wave vector. The developed method has wide applicability for the numerical study of the properties of amorphous vibrational systems.