Related papers: A generalized $q$ growth model based on nonadditiv…
In `entropic cosmology', instead of a cosmological constant $\Lambda$, an extra driving term is added to the Friedmann equation and the acceleration equation, taking into account the entropy and the temperature on the horizon of the…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way.…
We present significantly advanced studies of the previously introduced physical growth mechanism and unite it with biochemical growth factors. Obtained results allowed formulating the general growth law which governs growth and evolutional…
We present a simple, unified approach to determining the growth law for the characteristic length scale, $L(t)$, in the phase ordering kinetics of a system quenched from a disordered phase to within an ordered phase. This approach, based on…
It was recently published by M. Nauenberg [1] a quite long list of objections about the physical validity for thermal statistics of the theory sometimes referred to in the literature as {\it nonextensive statistical mechanics}. This…
The thermodynamics and covariant kinetic theory have been elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis'…
We consider generalizations of the Kardar--Parisi--Zhang equation that accomodate spatial anisotropies and the coupled evolution of several fields, and focus on their symmetries and non-perturbative properties. In particular, we derive…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
The shape of large on-lattice Eden clusters grown from a single seed is ruled by the underlying lattice anisotropy. This is reflected on the linear growth with time of the interface width ($w\sim t$), in contrast with the KPZ universality…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
We review models of compositional growth, which were introduced to explain the growth statistics of various quantities ranging from firm sizes to GDP. In these models, entities are decomposed into units that grow independently. Thus, the…
We briefly review a perspective along which the Boltzmann-Gibbs statistical mechanics, the strongly chaotic dynamical systems, and the Schroedinger, Klein-Gordon and Dirac partial differential equations are seen as linear physics, and are…
We study asymptotic behavior of sub-solutions to non-uniformly elliptic equations with nonstandard growth. In particular, Harnack type inequalities are proved. Our approach gives new results for the cases with (p,q) nonlinearity and…
Recently, in [P. Jizba and J. Korbel, Physica A 444, 2016, 808-827], four generalized Shannon-Khinchin [GSK] axioms have been proposed and a generalized entropy which uniquely satisfies the GSK axioms has been derived. In this comment, we…
The bouncing evolution of an universe in Loop Quantum Cosmolgy can be described very well by a set of effective equations, involving a function $sin \; x$. Recently, we have generalised these effective equations to $(d + 1)$ dimensions and…
A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond.…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural)…
Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential…