Solution of multidimensional system with XY differentiation of probability density equations for identification of silver nanoparticles on fibers

• Published in: IOP conference series. Materials Science and Engineering 2020-08, Vol.905 (1), p.12014
• Main Authors: Emelyanov, V M, Dobrovolskaya, T A, Emelyanov, V V
• Format: Article
• Language: English
• Subjects: accuracy of nanoparticle identification; Density; Differential equations; Fibers; Mathematical analysis; Nanoparticles; Polarization; polyester fiber; Polyesters; probability of intersection of distribution ellipses; Raman spectra; recognition accuracy; Silver; silver nanoparticles; system of multidimensional equations
• ISSN: 1757-8981; 1757-899X
• DOI: 10.1088/1757-899X/905/1/012014

The article presents the results of compiling and solving a system of multidimensional differential correlation equations of probability densities for identifying colloidal silver nanoparticles on polyester fibers with multidimensional correlation components of Raman polarization spectra. A method is proposed for increasing the accuracy and speed of identification of silver nanoparticles on polyester fibers, taking into account the longitudinal and transverse polarization of laser radiation over the entire range of the Raman spectrum with the analysis of two peaks sequentially and in order at the same time along the X-side and along the Y-side of the fibers. To implement the method, a program was developed in the Mathcad software. When solving the system using the nonlinear quadratic and differential equations with respect to XY, the probability density equations of distribution ellipses obtained very high accuracy p0 and p1 up to 10−16.