Related papers: Subexponential growth of early Christianity
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…
The probability of the survival of the population of individuals of both sexes of given mature age, procreation rate and structure stability has been searched in the numerical experiment. The populations with long period of reproduction and…
We propose an extremely simple mathematical model that is shown to be able to account for more than 99 per cent of all the variation in economic and demographic macrodynamics of the world for almost two millennia of its history. This…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
This paper proposes a non-phenomenological model of population growth that is based on the interactions between the individuals that compose the system. It is assumed that the individuals interact cooperatively and competitively. As a…
The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic…
A phenomenological model with an extreme accuracy is proposed for the cosmic time variation of the primordial fundamental constants (e, h, G and c) and the leptonic masses. The model is purely exploratory in that at the very early times the…
We analyze the growth rates of atmospheric carbon dioxide and human population, by comparing the relative merits of two benchmark models, the exponential law and the finite-time-singular (FTS) power law. The later results from positive…
In this paper we study the very early phases of the evolution of our Galaxy by means of a chemical evolution model which reproduces most of the observational constraints in the solar vicinity and in the disk. We have restricted our analysis…
Various approaches to model the progression of a dynasty in terms of power are discussed. The efficiency-discounted exponential growth (EDEG) approach is presented, and the effects of changing decay type and growth rate are demonstrated.…
In this working paper, I developed a suite of macroeconomic models that shed light on the intricate relationship between economic development, health, and fertility. These innovative models conceptualize health as an intermediate good,…
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…
(abridged) When preplanetary bodies reach proportions of ~1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the…
Recent analysis of early COVID-19 data from China showed that the number of confirmed cases followed a subexponential power-law increase, with a growth exponent of around 2.2 [B.\,F.~Maier, D.~Brockmann, {\it Science} {\bf 368}, 742…
Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized uniform…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
We introduce a new method of proving upper estimates of growth of finitely generated groups and constructing groups of intermediate growth using graphs of their actions. These estimates are of the form $\exp(n^\alpha)$ for some $\alpha<1$,…
We study a mathematical model of cell populations dynamics proposed by M. Rotenberg and investigated by M. Boulanouar. Here, a cell is characterized by her maturity and speed of maturation. The growth of cell populations is described by a…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…
Using current empirical data from 10,000 BCE to 2023 CE, we re-examine a hyperbolic pattern of human population growth, which was identified by von Foerster et al. in 1960 with a predicted singularity in 2026. We find that human population…