Search results for "matrix method"

2019

Abstract The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalised to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be o…

Spectral properties of a variable period Bragg grating including a segment isolated of external deformations

2017

In this work the behavior of a Bragg grating of variable period (usually called a linearly chirped fiber Bragg grating — CFBG) is analyzed when a small portion of it is fixed so that its properties remain unchanged, while the rest of the grating is affected by a longitudinal deformation. The system was simulated using the Transfer Matrix Method to obtain its behavior under different levels of deformation and it was observed the appearance of negative peaks in the spectral response (transmission peaks). The analysis allowed characterizing the system with different sizes of the fixed portion (defects) (0.5 to 6 mm), for a grating with 10 cm long and 3 nm spectral width.