Using the Gibbs Function as a Measure of Human Brain Development Trends from Fetal Stage to Advanced Age

We propose to use a Gibbs free energy function as a measure of the human brain development. We adopt this approach to the development of the human brain over the human lifespan: from a prenatal stage to advanced age. We used proteomic expression data with the Gibbs free energy to quantify human brain’s protein–protein interaction networks. The data, obtained from BioGRID, comprised tissue samples from the 16 main brain areas, at different ages, of 57 post-mortem human brains. We found a consistent functional dependence of the Gibbs free energies on age for most of the areas and both sexes. A significant upward trend in the Gibbs function was found during the fetal stages, which is followed by a sharp drop at birth with a subsequent period of relative stability and a final upward trend toward advanced age. We interpret these data in terms of structure formation followed by its stabilization and eventual deterioration. Furthermore, gender data analysis has uncovered the existence of functional differences, showing male Gibbs function values lower than female at prenatal and neonatal ages, which become higher at ages 8 to 40 and finally converging at late adulthood with the corresponding female Gibbs functions.

Transformed values of Gibbs functions for some molecules, ions and radicals involved in biochemical reactions.

The transformed values of the Gibbs function for a number of radicals are calculated: H, OH, ,SH, NH2, CH3, etc. These data can be used in consideration of the thermodynamics of biochemical reactions involving free radicals.

Virtual Work & d’Alembert’s Principle

This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, applied force and constraint force. Holonomic constraints and non-holonomic constraint equations are then investigated. The corresponding principles of Gauss (Gauss’s least constraint) and Jourdain are also documented and compared to d’Alembert’s approach before being generalised into the Mangeron–Deleanu principle. Kane’s equations are derived from Jourdain’s principle. The chapter closes with a detailed covering of the Gibbs–Appell equations as the most general equations in classical mechanics. Their reduction to Hamilton’s principle is examined and they are used to derive the Euler equations for rigid bodies. The chapter also discusses Hertz’s least curvature, the Gibbs function and Euler equations.

A Finite Element Implementation of a Fully Coupled Mechanical–Chemical Theory

A finite element implementation with UEL user-defined element (UEL) subroutines in ABAQUS for fully coupled mechanical–chemical processes, which accounts for deformation, mass diffusion, and chemical reactions based on irreversible thermodynamics, is presented. The finite element formulations are deduced from the Gibbs function variational principle. To demonstrate the robustness of the numerical implementation, one- and two-dimensional numerical simulations with different boundary conditions are conducted. The results present the validity and capability of the UEL subroutines and the coupled theory, and show the interaction among deformation, mass diffusion and chemical reaction. This work provides a valuable tool to the researchers for the study of coupled problems.

Flexoelectric Effect on Vibration of Piezoelectric Microbeams Based on a Modified Couple Stress Theory

A novel electric Gibbs function was proposed for the piezoelectric microbeams (PMBs) by employing a modified couple stress theory. Based on the new Gibbs function and the Euler-Bernoulli beam theory, the governing equations which incorporate the effects of couple stress, flexoelectricity, and piezoelectricity were derived for the mechanics of PMBs. The analysis of the effective bending rigidity shows the effects of size and flexoelectricity can greaten the stiffness of PMBs so that the natural frequency increases significantly compared with the Euler-Bernoulli beam, and then the mechanical and electrical properties of PMBs are enhanced compared to the classical beam. This study can guide the design of microscale piezoelectric/flexoelectric structures which may find potential applications in the microelectromechanical systems (MEMS).