Generalized Gibbs Phase Rule and Multicriticality Applied to Magnetic Systems

A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume–Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.

The Effect of Governmental Health Measures on Public Behaviour During the COVID-19 Pandemic Outbreak

Background: The COVID-19 pandemic resulted in radical changes in many aspects of life. To deal with this, each country has implemented continuous health measures from the beginning of the outbreak. Discovering how governmental actions impacted public behaviour during the outbreak stage is the purpose of this study. Methods: This study uses a hybrid large-scale data visualisation method to analyse public behaviour (epidemic concerns, self-protection, and mobility trends), using the data provided by multiple authorities. Meanwhile, a content analysis method is used to qualitatively code the health measures of three countries with severe early epidemic outbreaks from different continents, namely China, Italy, and the United States. Eight dimensions are coded to rate the mobility restrictions implemented in the above countries. Results: (1) Governmental measures did not immediately persuade the public to change their behaviours during the COVID-19 epidemic. Instead, the public behaviour proceeded in a three-phase rule, which is typically witnessed in an epidemic outbreak, namely the wait-and-see phase, the surge phase and the slow-release phase. (2) The strictness of the mobility restrictions of the three countries can be ranked as follows: Hubei Province in China (with an average score of 8.5 out of 10), Lombardy in Italy (7.125), and New York State in the United States (5.375). Strict mobility restrictions are more likely to cause a surge of population outflow from the epidemic area in the short term, whereas the effect of mobility restrictions is positively related to the stringency of policies in the long term. Conclusion: The public showed generally lawful behaviour during regional epidemic outbreaks and blockades. Meanwhile public behaviour was deeply affected by the actions of local governments, rather than the global pandemic situation. The contextual differences between the various countries are important factors that influence the effects of the different governments’ health measures.

When is a material stable?

This chapter is an introduction to classical thermodynamics that does not assume any knowledge of the subject. The significance of thermodynamic equilibrium in materials is discussed keeping in mind that it is rarely achieved in practice. The concepts of thermodynamic systems, components, work, energy, phase, absolute temperature, heat, potential energy, internal energy, state variables, intensive and extensive variables are introduced and defined. The first and second laws of thermodynamics are introduced. The concept of entropy is discussed in terms of irreversibility, the direction of time and microstates of the system. Configurational entropy is illustrated with the example of a binary alloy. The Helmholtz and Gibbs free energies are introduced and their physical significance is discussed in terms of the conditions for a material to be in equilibrium with its environment. This leads to a discussion of chemical potentials, the Gibbs-Duhem relation for each phase present and the phase rule.

Phase diagrams

Temperature-composition phase diagrams are introduced as maps of the regions of stability of binary systems at constant pressure, usually atmospheric pressure at sea level. Their construction is based on minimisation of the Gibbs free energy as a function of composition at a given temperature. The simple case of miscibility in the solid and liquid states over the full range of composition is discussed first. Eutectic and peritectic phase diagrams result from limited miscibility in the solid state. Intermediate phases, or ordered alloys, usually occur in narrow ranges of composition in phase diagrams, and this is also explained in terms of free energy composition curves. Each phase diagram is shown to obey the phase rule discussed in the previous chapter.

Phase separation in fluids with many interacting components

Fluids in natural systems, like the cytoplasm of a cell, often contain thousands of molecular species that are organized into multiple coexisting phases that enable diverse and specific functions. How interactions between numerous molecular species encode for various emergent phases is not well understood. Here we leverage approaches from random matrix theory and statistical physics to describe the emergent phase behavior of fluid mixtures with many species whose interactions are drawn randomly from an underlying distribution. Through numerical simulation and stability analyses, we show that these mixtures exhibit staged phase separation kinetics and are characterized by multiple coexisting phases at equilibrium with distinct compositions. Random-matrix theory predicts the number of existing phases at equilibrium, validated by simulations with diverse component numbers and interaction parameters. Surprisingly, this model predicts an upper bound on the number of phases, derived from dynamical considerations, that is much lower than the limit from the Gibbs phase rule, which is obtained from equilibrium thermodynamic constraints. Using a biophysically motivated model of pairwise interactions between components, we design ensembles that encode either linear or non-monotonic scaling relationships between number of components and co-existing phases, which we validate through simulation and theory. Finally, inspired by parallels in biological systems, we show that including non-equilibrium turnover of components through chemical reactions can tunably modulate the number of co-existing phases at steady-state without changing overall fluid composition. Together, our study provides a model framework that describes the emergent dynamical and steady-state phase behavior of liquid-like mixtures with many interacting constituents.

Preparation of a solid product with high water content and water retention properties

This work presents the development of a solid product with a high water content (99.08%) and water retention properties. Water was chosen as a potential carrier of a volatile active substance and water retaining properties of material were studied at a temperatures and relative air humidity values with the support of the theory of drying. The study first confirmed the role of Gibbs’ phase rule in the research of solid-gas phase equilibrium, and second presented drying kinetics developed from Fick’s second law and expressed with the first term of the Fourier equation. Solutions of equations for phase equilibrium and mass transfer enabled the calculation of Luikov’s parameters, which are important for equilibrium relations and for the diffusivity of water in a solid for mass transfer prediction. The obtained thermodynamic and kinetic parameters enabled product characterisation that may be important for the prediction of retention times.