Work

Bernstein Polynomials: A Bridge Between the Weierstrass Theorem and a Landau Temperature Fluctuation Problem

Year: 2025

Type: article

Abstract: We address a Landau temperature fluctuation problem by applying Bernstein polynomials and the Weierstrass approximation theorem.We consider the problem detailed in [X.Wang and Q.H. Liu, Temperature fluctuations for a finite system of classical spin-1/2 particles, Annals of Physics 322 (2007), 2168-2178] in which temperature fluctuations diverge as the temperature of a particle system tends to 0. An application of Bernstein polynomials allows us to solve this issue by proving that the m'th moment of the configurational temperature of a finite particle system tends to the temperature of the surroundings, implying the fluctuations in the temperature must tend to 0.

Source: SIAM Undergraduate Research Online

DOI: 10.1137/25s172954x

Author: Aiden Rohrbach

Institution: University of Rochester

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: From Quantum Many-body Dynamics to Fluid Equations and Back