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We present EvoEMD, a framework to calculate the evolution of cosmic relics in a Universe with an early matter-dominated (EMD) era. There are mainly two aspects to consider in this regard. First, an EMD era changes the Hubble expansion rate…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
We investigate the orbit-crossing time (T_c) of protoplanet systems both with and without a gas-disk background. The protoplanets are initially with equal masses and separation (EMS systems) scaled by their mutual Hill's radii. In a…
In this paper, we study an integro-differential equation which describes the evolutionary dynamics of a population structured by a phenotypic trait. This population undergoes asexual reproduction, competition, selection, and mutation. We…
We begin with the premise that the law of entropy could prove to be fundamental for the evolution of intelligent life and the advent of technological civilization. Building on recent theoretical results, we combine a modern approach to…
The current picture of terrestrial planet formation relies heavily on our understanding of the dynamical evolution of planetesimals -- asteroid-like bodies thought to be planetary building blocks. In this study we investigate the growth of…
Polarization has been detected at early times for all types of supernova, indicating that such systems result from or quickly develop some form of asymmetry. In addition, the detection of strong line polarization in supernovae is suggestive…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
Motivated by certain problems of statistical physics we consider a stationary stochastic process in which deterministic evolution is interrupted at random times by upward jumps of a fixed size. If the evolution consists of linear decay, the…
An evolving Riemannian manifold $(M,g_t)_{t\in I}$ consists of a smooth $d$-dimensional manifold $M$, equipped with a geometric flow $g_t$ of complete Riemannian metrics, parametrized by $I=(-\infty,T)$. Given an additional $C^{1,1}$ family…
By analogue of [1,2] we define a cubic stochastic process and study evolution (dynamics) of a system $E$ which contains at least three elements.
The spatial logistic model is a system of point entities (particles) in $\mathbb{R}^d$ which reproduce themselves at distant points (dispersal) and die, also due to competition. The states of such systems are probability measures on the…
In [44], we qualitatively studied some classical results implied by the specification property for dynamical systems with non-uniform specification. In this paper, we perform quantitative studies on how properties of topological theory and…
Cyanobacterial blooms (CBs) pose significant global challenges due to their harmful toxins and socio-economic impacts, with nutrient availability playing a key role in their growth, as described by ecological stoichiometry (ES). However,…
We consider a particle moving in continuous time as a Markov jump process; its discrete chain is given by an ordinary random walk on ${\mathbb Z}^d$ , and its jump rate at $({\mathbf x},t)$ is given by a fixed function $\varphi$ of the…
Why can the world resist the law of entropy increase and produce self-organizing structure? Does the entropy of an isolated system always only increase and never decrease? Can be thermodymamic degradation and self-organizing evolution…
What is habitability? Can we quantify it? What do we mean under the term habitable or potentially habitable planet? With estimates of the number of planets in our Galaxy alone running into billions, possibly a number greater than the number…
After it was proposed that life on Earth might descend from seeding by an earlier civilization, some authors noted that this alternative offers a testable aspect: the seeds could be supplied with a signature that might be found in extant…
Since Newton, all classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. The boundary conditions creating the phase space of all possible values of the variables are…
A class of evolution quasistatic systems which leads, after a suitable time discretization, to recursive nonlinear programs, is considered and optimal control or identification problems governed by such systems are investigated. The…