Phase Transitions

History shows that up to 1870’s, the thermodynamic cycles, particularly Carnot’s cycle, were the most important heuristic instruments as much to formulate the general laws of physics as well to deduce the experimental laws. From this moment on, this instrument falls into disuse with surprising rapidity. At the end of this decade emerges a new thermodynamic formulation, proposed by Gibbs, the thermodynamics of the potentials. This sudden transition from thermodynamic of cycles to potentials was triggered by the difficult to approach the emergence of the phase transition phenomena with the diagrammatic method. The main objective of the article is, then, to analyze the consequences of the substitution, by Gibbs, of the diagrammatic by the geometric method, particularly, its heuristic potential related to the proposal of the formulation of the thermodynamic of potentials.

The formation of solid solutions of the type [Ba(HOC2H4OH)4][Ti1−x Gex (OC2H4O)3] as Ba(Ti1−x /Gex )O3 precursors and the phase evolution during thermal decomposition of [Ba(HOC2H4OH)4][Ti0.9Ge0.1(OC2H4O)3] (1) are described herein. The 1,2-ethanediolato complex 1 decomposes above 589 °C to a mixture of BaTiO3 and BaGeO3. A heating rate controlled calcination procedure, up to 730 °C, leads to a nm-sized Ba(Ti0.9/Ge0.1)O3 powder (1a) with a specific surface area of S = 16.9 m2/g, whereas a constant heating rate calcination at 1,000 °C for 2 h yields a powder (1b) of S = 3.0 m2/g. The shrinkage and sintering behaviour of the resulting Ba(Ti0.9/Ge0.1)O3 powder compacts in comparison with nm-sized BaTiO3 powder compacts (2a) has been investigated. A two-step sintering procedure of nm-sized Ba(Ti0.9/Ge0.1)O3 compacts (1a) leads, below 900 °C, to ceramic bodies with a relative density of ≥90%. Furthermore, the cubic ⇆ tetragonal phase transition temperature has been detected by dilatometry, and the temperature dependence of the dielectric constant (relative permittivity) has also been measured.

Electronic structure and refractive indices of SbSI crystal in paraelectric and ferroelectric phases were investigated by full-potential linearized augmented plane wave method with density functional theory. The temperature dependence of refractive indices along a-, b-, and c -axes and birefringence Δn = nc  − na as a function of photon energy were calculated near the phase transitions. The theoretical results were compared with experimental measurements of birefringence. Comparison between calculated increment of the birefringence δ(Δn 0 = nc  − na ) and experimental spontaneous polarization indicates the existence of the second-order phase transition at Tc 2 ≈ 240 K and confirms its relation to the P s.

The goal of this work is to compile the basic components for the construction of an electromagnetic field theory of consciousness that meets the standards of a fundamental theory. An essential cornerstone of the conceptual framework is the vacuum state of quantum electrodynamics which, contrary to the classical notion of the vacuum, can be viewed as a vibrant ocean of energy, termed zero-point field (ZPF). Being the fundamental substrate mediating the electromagnetic force, the ubiquitous ZPF constitutes the ultimate bedrock of all electromagnetic phenomena. In particular, resonant interaction with the ZPF is critical for understanding rapidly forming, long-range coherent activity patterns that are characteristic of brain dynamics. Assuming that the entire phenomenal color palette is rooted in the vibrational spectrum of the ZPF and that each normal mode of the ZPF is associated with an elementary shade of consciousness, it stands to reason that conscious states are caused by the coupling of the brain to a particular set of normal modes selectively filtered from the full frequency spectrum of the ZPF. From this perspective, the brain is postulated to function as a resonant oscillator that couples to a specific range of ZPF modes, using these modes as a keyboard for the composition of an enormous variety of phenomenal states. Theoretical considerations suggest that the brain-ZPF interface is controlled by altering the concentrations of neurotransmitters, placing the detailed study of the neurotransmitter-ZPF interaction at the center of future research activities.

Les interactions entre molécules des diverses phases impliquées dans les phénomènes de mouillage engendrent des interactions entre interfaces, qui influencent de façon profonde l'existence et la nature des transitions de mouillage. Cet ouvrage contribue à la compréhension de ce lien complexe entre interactions et transitions de mouillage, à partir de l'étude expérimentale du mouillage des alcanes sur l'eau et de considérations théoriques.
La thèse dont est issu cet ouvrage a été récompensée par le prix Ilya Prigogine 2001 de la meilleure thèse en thermodynamique.
Les toutes premières pages de l'ouvrage sont téléchargeables ici.

We clarify several subtle points in the CPN-1 model in 2 + 1 dimensions. It is shown that as a consequence of local gauge invariance the nA particles, belonging to fundamental representation of SU(N) do not appear in the spectrum (in any number of dimensions) regardless of the nature of the interaction between them. In 2 + 1 dimensions we analyse the phase structure of the theory from the point of view of realization of the relevant symmetries: SU(N)/ZN ⊗ UΦ(1) ⊗ UE(1). The symmetries UΦ(1) and UE(1) are gauge invariant analogs of the magnetic flux and electric charge symmetries in scalar QED. The charge of UE(1) is not related to the global part of the local U(1) transformations (which counts the difference between the number of n and the number of n∗ excitations). At the phase transition point the flavour SU(N) ZN is broken down to U(N−1) while the mode of implementation of the UΦ(1) is changed from Kosterlitz-Thouless to Wigner-Weyl. We provide a gauge invariant order parameter for the flavour symmetry breaking and identify the massless “photon” with the Kosterlitz-Thouless zero mode of UΦ(1).

We study self-organization of collective motion as a thermodynamic phenomenon in the context of the first law of thermodynamics. It is expected that the coherent ordered motion typically self-organises in the presence of changes in the (generalized) internal energy and of (generalized) work done on, or extracted from, the system. We aim to explicitly quantify changes in these two quantities in a system of simulated self-propelled particles and contrast them with changes in the system's configuration entropy. In doing so, we adapt a thermodynamic formulation of the curvatures of the internal energy and the work, with respect to two parameters that control the particles' alignment. This allows us to systematically investigate the behavior of the system by varying the two control parameters to drive the system across a kinetic phase transition. Our results identify critical regimes and show that during the phase transition, where the configuration entropy of the system decreases, the rates of change of the work and of the internal energy also decrease, while their curvatures diverge. Importantly, the reduction of entropy achieved through expenditure of work is shown to peak at criticality. We relate this both to a thermodynamic efficiency and the significance of the increased order with respect to a computational path. Additionally, this study provides an information-geometric interpretation of the curvature of the internal energy as the difference between two curvatures: the curvature of the free entropy, captured by the Fisher information, and the curvature of the configuration entropy.

"Patterns in War Dynamics. WARning 2020". In this study, complexity and network science are applied to the dynamics and development of the (International) System. This study shows that the System periodically becomes critical and produces "systemic wars". The typical dynamics that are revealed in this study are a consequence of laws of physics that apply also to the System. Systemic wars are instrumental in rebalancing the System, and in periodically producing "upgraded" international orders that allow for further growth and development. The patterns that can be observed in the war dynamics of the System, make it possible to predict these dynamics and the System's direction of development.
Data-analysis shows that the System will again become critical around 2020 (+/- two years).
This study shows that intensifying war dynamics pose an existential threat to human kind: Systemic wars will cause increasing damage and suffering and will put our climate system at (additional) risk: Fundamental change is a prerequisite for our survival.
This study was initially published in 2016. The publication "On the Thermodynamics of War and Social Evolution" (2019) provides a scientific explanation for the war dynamics that can be observed.

William Shakespeare has developed the plot of his play Macbeth through the effective use of transitions<br> to the major characters. Among them, the character that is most prone to regular transitions in life is the<br> central character of Macbeth. This research paper explores the trajectory of transitions through which<br> Shakespeare develops the plot of his play through the character of Macbeth concerning his changing<br> situations and positions. While analysing the play with the help of Schlossberg's Transition theory,<br> specifically through the concept of 4S's, the perspicacity of Macbeth's trajectory of different transitions in<br> the pattern of one after the other is visible throughout the play. With the help of textual and<br> interpretative analysis of the play, the situation, psychological aspects, support and strategies to cope<br> with the transition in Macbeth are explored in the research. Through the pers...

This is an extension of the project I did where I computationally realised a 3D cubic lattice based on Ising model. In this project the focus is not just looking at the structure of various properties of the lattice at and around its critical temperature, but actually determining the critical temperature itself.

The study On the Thermodynamics of War and Social Evolution, shows that patterns can be identified in the war dynamics of the System, and that a relationship exists between these war dynamics and social evolution. The research suggests that Prigogine’s idea about non-equilibrium systems being able to attain highly ordered states in response to an increase of energy flux, can also be successfully applied to the social sciences. These new insights could have profound implications for our understanding of war (dynamics), and for our ability to better control and prevent war, in the future.I argue that the System can be considered a non-equilibrium system, and that the (relationship between) war dynamics - and the patterns they produce - and social evolution, can be explained from a (non-equilibrium) thermodynamic perspective: Interactions between components of the System (individual humans, communities, societies, states, etc.) are irreversible, and result in the production of entropy - tensions - in the System.
These tensions (entropy) serve as a source of order and are regulated by means of a dissipative structure that also puts kinetic activity (war) to use, to ensure the most efficient path to thermodynamic equilibrium of the System.

Conformal field theories arise near a phase transition when there are no scale involved. One usually talks about thermal phase transitions but a lot of the recent interest in condensed matter physics has been around quantum phase transitions which are phase transitions that happen as the coupling parameter is varied. In this case it turns out that the phase transition as well as the new phase arising from it, the quantum critical phase can be described in terms of the modifications of a conformal field theory.

We study a model of cell segregation in a population composed of two cell types. Starting from a model initially proposed in [3], we aim to understand the impact of a cell division process on the system’s segregation abilities. The original model describes a population of spherical cells interacting with their close neighbors by means of a repulsion potential and which centers are subject to Brownian motion. Here, we add a stochastic birth-death process in the agent-based model, that approaches a logistic growth term in the continuum limit. We address the linear stability of the spatially homogeneous steady states of the macroscopic model and obtain a precise criterion for the phase transition, which links the system segregation ability to the model parameters. By comparing the criterion with the one obtained without logistic growth, we show that the system’s segregation ability is the result of a complex interplay between logistic growth, diffusion and mechanical repulsive interacti...

This are some notes on Statistical mechanics.
The topics are
-Recap of thermodynamics                                                     
-Thermodynamic of phase transitions                                                   
-recap of theory of ensamble                                                                               
-Statistical mechanics and phase transition                                                             
-Models (Ising in particular)                                                                                         
-Role of symmetry (symmetry breaking), dimension and range of interaction 
-Mean field theory (and Vann der Walls)                                                                   
-Landau Theory                     
-Ginzburg criterium
-Scaling theory (Windom)
-Renormalization group
-Symmetry breaking in other parts of physics (particles physics)

Introduction of interlath reverted austenite is an effective method to design ductile lath martensitic steels. The challenge in this concept is that all reverted austenite films have similar mechanical stability, hence, they all undergo transformation-induced plasticity (TRIP) at the same strain level. Here we propose a new thermo-mechanical treatment route to activate the TRIP effect over a broad strain regime and refer to it as 'spectral TRIP effect'. It aims at spreading the micro-mechanical stability of reverted austenite grains by widening the austenite nucleation barrier in martensite. To validate the proposed thermo-mechanical treatment route, an as-quenched medium-Mn martensitic steel was cold rolled prior to the reversion treatment at 600 C. Microstructure characterization was carried out by electron backscatter diffraction (EBSD) and electron channeling contrast imaging (ECCI). Mechanical tests show that the approach is effective. The spectral TRIP effect improves both, the strength and the ductility due to the well dispersed size distribution and the associated size-dependent deformation and phase transformation behavior of the reverted austenite grains, extending TRIP-related work hardening over a broad strain range.

During the last two decades our scientic group has developed new nonlinear methods of analysis applied to various physical systems. In this review study we present our scientic contribution to nonlinear science, including also some novel concepts as for the constructive role of complexity in modern physical theory. The experimental verification of chaos existence in physical systems remains one of the
most significant problems of non linear science and complexity. The extended chaotic algorithm presented in the following as well as the results concerning its application at different experimental time series reveal the universal character of the complexity theory for the far from equilibrium dynamics of spatially extended physical systems. The
developed methodology that was used compromises different types of computational tools as well as theoretical concepts for the physical interpretation of the experimental information. As we present here the strong dispute and criticism of chaos hypothesis in physical systems during the last two decades was fruitful and challenged us to develop a novel composition of experimental and theoretical knowledge of universal character for the far from equilibrium dynamics. The solar and magnetospheric dynamics included in space plasma processes, the environmental and seismic dynamics, the human brain or the on{chip workload are distinct systems which were studied by our group revealing common chaotic characteristics and chaotic phase transition
processes. Moreover, the intellectual struggle for the comprehension of the theoretical presuppositions of the experimentally observed universal chaotic character of spatially distributed systems lead us to the fundamentals of complexity theory as manifested at the macroscopic and microscopic level of physical reality. From this point of view, some common characteristics of macroscopic and microscopic complexity included in the scientific knowledge of the recent two or three decades can be used as a road for the physical theory unification. That is complexity, scaling, chaos, quanticity and
fractality could be supported as different manifestations of a unified physical law from the microscopic to the macroscopic and cosmological level. As we can argue, determinism and probabilism can also be unied through chaoticity. Moreover, the rising of new physical knowledge reveals that under the macroscopic or the microscopic
physical phenomena there exist a fundamental and multilevel acting unit physical process that produces physical reality rather than a fundamental essence or simple substance from which cosmos can be build.

Summary:
This chapter presents a descriptive and illustrative account of phase behavior in the seven naturally occurring petroleum fluids and ties all the known eleven phase-transition concepts in a unified narrative. The figures and tables contained in this report are designed so that they could effectively support the discussion about molecular make-up of petroleum fluids, P- and T-effects on phase behavior and phase transition points.
      Seven naturally occurring hydrocarbon fluids are known as petroleum fluids. They include, in the order of their fluidity, natural gas, gas condensate (or NGL), light crude, intermediate crude, heavy oil, tar sand and oil shale.  In this report we present a generalized description of the various phase transitions, which may occur in petroleum fluids with emphasis on heavy organics deposition. 
      At first the nature of every petroleum fluid is presented.  Their constituents including their so-called impurities are identified and categorized. Heavy fractions in petroleum fluids are discussed and their main families of constituents are presented including petroleum wax, diamondoids, asphaltenes and petroleum resins.  Then the generalized petroleum fluids phase behavior is discussed in light of the known theory of phase transitions. The effects of variations of composition, temperature and pressure on the phase behavior of petroleum fluids are introduced.  Finally eleven distinct phase-transition points of petroleum fluids are presented and their relation with state variables and constituents of petroleum fluids are identified.  This report is to generalize and relate phase behaviors of all the seven naturally occurring petroleum fluids into a unified perspective.  This work is the basis to develop a comprehensive computational model for phase behavior prediction of all the petroleum fluids, which is of major interest in the petroleum industry