Ranking structures and Rank-Rank Correlations of Countries. The FIFA and UEFA cases

Ranking of agents competing with each other in complex systems may lead to paradoxes according to the pre-chosen different measures. A discussion is presented on such rank-rank, similar or not, correlations based on the case of European countries ranked by UEFA and FIFA from different soccer competitions. The first question to be answered is whether an empirical and simple law is obtained for such (self-) organizations of complex sociological systems with such different measuring schemes. It is found that the power law form is not the best description contrary to many modern expectations. The stretched exponential is much more adequate. Moreover, it is found that the measuring rules lead to some inner structures, in both cases.Comment: 23 pages, 8 figures, 24 references, 3 tables; to be published in Int. J. Mod. Phys.

A Novel Model of Protein Crystal Growth: Kinetic Limits, Length Scales and the Role of the Double Layer

A kinetic model has been designed that tries to capture some most important physico-chemical properties of crystallization from water-based electrolyte. The crystal growing process is thought to proceed in a conserved system, in which the charged-mass conservation law is obeyed. Although the model phenomenon under study proceeds in a mass-convection regime, it is readily interface-controlled. The interfacial control is identified with the role played by the double-layer, presumably of the Stern type, surrounding the object under growth. The product of supersaturation and individual biomolecule velocity in the double-layer appears to be both the controlling kinetic factor and the asymptotic (kinetic) limit being achieved by the process, i.e. the crystal growth rate approaches the value of the mentioned product. The first successful test of the model was carried out on data representing the lyzosyme crystal growth

A Novel Model of Protein Crystal Growth: Kinetic Limits, Length Scales and the Role of the Double Layer

A kinetic model has been designed that tries to capture some most important physico-chemical properties of crystallization from water-based electrolyte. The crystal growing process is thought to proceed in a conserved system, in which the charged-mass conservation law is obeyed. Although the model phenomenon under study proceeds in a mass-convection regime, it is readily interface-controlled. The interfacial control is identified with the role played by the double-layer, presumably of the Stern type, surrounding the object under growth. The product of supersaturation and individual biomolecule velocity in the double-layer appears to be both the controlling kinetic factor and the asymptotic (kinetic) limit being achieved by the process, i.e. the crystal growth rate approaches the value of the mentioned product. The first successful test of the model was carried out on data representing the lyzosyme crystal growth

Statistical theory of normal grain growth revisited

In this paper, we discuss three physically relevant problems concerning the normal grain growth process.These are: Infinite vs finite size of the system under study (a step towards more realistic modeling); conditions of fine-grained structure formation, with possible applications to thin films and biomembranes, and interesting relations to superplasticity of materials; approach to log-normality, an ubiquitous natural phenomenon, frequently reported in literature. It turns out that all three important points mentioned are possible to be included in a Mulheran-Harding type behavior of evolving grains-containing systems that we have studied previously

Kinetics of temperature or pressure field induced phase transformation in lipid bilayers

A description of kinetics of the temperature or pressure field induced phase transformations in model biomembranes is proposed. It is based on the Avrami-Kolmogorov model combined with concept of chemical reaction fractal-like kinetics. As a result, a non-Debyean (stretched exponential and power-law) relaxation of the phase transformation process is obtained. Possible applications to experimental cases like thermotropic phase transformations in lipids (e.g. dipalmitoyphosphatidylcholine - DPPC) and/or hydration of dioleylphosphatidylethanolamine (DOPE) bilayers caused by pressure are discussed

Kinetics of microdomain formation in two dimensional assemblies

A novel phenomenological approach to the microdomain structure formation or phase transformation in two-dimensional cooperative systems is proposed. The theory offered states that a new structure consists of pieces of islands, microdomains, germs, etc. and deals with modeling of the pattern formation process with increase of area of a new structure or phase. The kinetics of the process is studied. Probabilistic characteristics are obtained and first three moments of the process are analyzed

Kinetics of three-dimensional normal grain growth

Kinetics of three-dimensional normal grain growth and related processes (e.g., soap froth evolutions) described by the Mulheran–Harding model is studied. The model is represented by a diffusion equation with the grain–size–dependent diffusion coefficient. The equation is solved for an arbitrary initial distribution of grain sizes. It is proved that asymptotic kinetics do not depend on the initial state

Evolution of a grain system : from early to late stages

An analytical approach to the d-dimensional grain growth, which is a kind of the heterogeneous nucleation-and-growth phase transformation, is offered. The system is assumed to be driven by capillary forces. Another important operative assumption is that the system evolves under preservation of its hypervolume, which results in considering the process as a random walk in the space of grain sizes. A role of the initial condition imposed on the system behaviour, and how does the system behave upon a prescribed initial state, have been examined. A general conclusion appears, which states that this prescription does not affect the asymptotic system behavior, but may be of importance when inspecting the early-time domain more carefully, cf. the Weibull-type initial distribution. This study is addressed to some analogous theoretical descriptions concerning polycrystals as well as bubbles-containing systems. Some comparison to another modelling, in which a crucial role of local material gradients (fluxes) was emphasized, has been attache