Properties of the Geometric Phase in Electromechanical Oscillations of Carbon-Nanotube-Based Nanowire Resonators

The geometric phase is an extra phase evolution in the wave function of vibrations that is potentially applicable in a broad range of science and technology. The characteristics of the geometric phase in the squeezed state for a carbon-nanotube-based nanowire resonator have been investigated by means of the invariant operator method. The introduction of a linear invariant operator, which is useful for treating a complicated time-dependent Hamiltonian system, enabled us to derive the analytical formula of the geometric phase. By making use of this, we have analyzed the time behavior of the geometric phase based on relevant illustrations. The influence of squeezing parameters on the evolution of the geometric phase has been investigated. The geometric phase, in large, oscillates, and the envelope of such oscillation increases over time. The rate of the increase of the geometric phase is large when the parameters, such as the classical amplitude of the oscillation, the damping factor, and the amplitude of the driving force, are large. We have confirmed a very sharp increase of the geometric phase over time in the case that the angular frequency of the system reaches near the resonance angular frequency. Our development regarding the characteristics of the geometric phase is crucial for understanding the topological features in nanowire oscillations.

Crossover Designs in Nutrition and Dietetics Research

This article is the 12th installment in a statistical series exploring the importance of research design, epidemiologic methods, and statistical analysis as applied to nutrition and dietetics research. The purpose of this series is to assist registered dietitian nutritionists in interpreting nutrition research and aid nutrition researchers in applying scientific principles to produce high-quality nutrition research. This article focuses on the use of crossover designs in nutrition and dietetics research. The purpose is to distinguish the crossover design from the randomized clinical trial, define important terms, illustrate a 2×2 crossover design, discuss potential confounding variables in the crossover design, describe the analysis and interpretation of crossover data, present sample size considerations, provide examples of the use of the crossover design in nutrition and dietetics, and discuss additional considerations when the independent variable has more than two levels.