Related papers: On the Classification Scheme for Phenomenological …
When a system is brought to a metastable state, nuclei of the equilibrium phase form and grow. This is the well-known nucleation and growth of first-order phase transitions. Near a critical point of a continuous phase transition, critical…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
A tendency in biological theorizing is to formulate principles above or equal to Evolution by Variation and Selection of Darwin and Wallace. In this letter I analyze one such recent proposal which did so for the developmental ascendency. I…
Although big bang cosmology effectively models even the most puzzling observational data, it offers no insight into why the cosmological expansion should occur at all. In this paper it is suggested that a finite Universe poses particular…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
We establish a partial regularity result for solutions of parabolic systems with general $\varphi$-growth, where $\varphi$ is an Orlicz function. In this setting we can develop a unified approach that is independent of the degeneracy of…
Historical economic growth in countries of the former USSR is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used, but not analysed, during the formulation of this theory. Unified Growth Theory does…
A growth equation with a generalized conservation law characterized by an integral kernel is introduced. The equation contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and Molecular-Beam Epitaxy growth equations as special cases and allows…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
One of the fundamental postulates of the Unified Growth Theory is the claimed existence of three distinctly different regimes of economic growth governed by three distinctly different mechanisms of growth. However, Galor also proposed that…
We analyze the growth statistics of Swedish trade unions and find a universal functional form for the probability distribution of growth rates of union size, and a power law dependence of the standard deviation of this distribution on the…
We consider a nonlocal functional equation that is a generalization of the mathematical model used in behavioral sciences. The equation is built upon an operator that introduces a convex combination and a nonlinear mixing of the function…
Population dynamics models play an important role in a number of fields, such as actuarial science, demography, and ecology, as they help explain past fluctuations and predict future population. The accuracy of these models is often…
These lecture notes discuss several related features of the exactly solvable two-dimensional corner growth model with exponentially distributed weights. A key property of this model is the availability of a fairly explicit stationary…
We extend the results of B. Bollobas, O. Riordan, J. Spencer, G. Tusnady, and Mori. We consider a model of random tree growth, where at each time unit a new node is added and attached to an already existing node chosen at random. The…
Bacterial growth models are commonly used for the prediction of microbial safety and the shelf life of perishable foods. Growth is affected by several environmental factors such as temperature, acidity level and salt concentration. In this…
A possible solution to the dark energy problem is that Einstein's theory of general relativity is modified. A suite of models have been proposed that, in general, are unable to predict the correct amount of large scale structure in the…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…
Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her…