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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…
We do several simple calculations and measurements in an effort to gain understanding of global warming and the carbon cycle. Some conclusions are interesting: (i) There has been global warming since the end of the "little ice age" around…
Analysis of the urban population fraction data for sixteen populous countries over the last fifty years reveals a universal increase in urbanization, exhibiting four qualitatively distinct temporal patterns: (i) continuously accelerating…
The state of earth's climate is constrained by well-known physical principles such as energy balance and the conservation of energy. Increased greenhouse gas concentrations affect the atmospheric optical depth, and physical consistency…
The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate…
We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equations with constraints and homogenization, we obtain results…
In physics, I noticed subjects not explained by formulas were often not studied, like how uncontrolled growth systems changed form. Weather, businesses, societies, environments, communities, cultures, groups, relationships, lives, and…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
Many species see their range shifted poleward in response to global warming and need to keep pace in order to survive. To understand the effect of climate change on species ranges and its consequences on population dynamics, we consider a…
Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
A model is proposed to explain the observed correlation between monthly fluctuations in atmospheric CO2 concentrations and temperatures. The model relies on the oceans being in a temperature-dependent equilibrium with the atmosphere. When…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the…
The last few million years on planet Earth have witnessed two remarkable phases of hominid development, starting with a phase of biological evolution characterised by rather rapid increase of the size of the brain. This has been followed by…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
One of the strongest arguments against the cosmological constant as an explanation of the current epoch of accelerated cosmic expansion is the existence of an earlier, dynamical acceleration, i.e. inflation. We examine the likelihood that…
Despite well-meaning scenarios that propose global CO2 emissions will decline presented in every IPCC report since 1988, the trend of global CO2 increase continues without significant change. Even if any individual nation manages to flatten…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
Real GDP growth rate in developed countries is found to be a sum of two terms. The first term is the reciprocal value of the duration of the period of mean income growth with work experience, Tcr. The current value of Tcr in the USA is 40…