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We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
This review introduces physical processes in protoplanetary disks relevant to accretion and the initial stages of planet formation. After a brief overview of the observational context, I introduce the elementary theory of disk structure and…
We investigate pattern transformations of periodic hydrogel systems that are triggered by swelling-induced structural instabilities. The types of microstructures considered in the present work include single-phase and two-phase voided…
The evolution of the atomic structures of the combinatorial library of Sm-substituted thin film BiFeO3 along the phase transition boundary from the ferroelectric rhombohedral phase to the non-ferroelectric orthorhombic phase is explored…
Chiral crystals, like chiral molecules, cannot be superimposed onto their mirror images -- a fundamental property that has been linked to interesting physical behavior and exploited in functional devices. Among the simplest inorganic…
With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star-planet interactions and how such systems evolve. We address this question by studying systems…
Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering…
Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the…
We have generalized our ``unified'' model of evolutionary ecology by taking into account the possible movements of the organisms from one ``patch'' to another within the same eco-system. We model the spatial extension of the eco-system…
Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might…
We propose an algorithm for evolving spiral curves on a planar domain by normal velocities depending on the so-called crystalline curvatures. The algorithm uses a minimizing movement approach and relies on a special level set method for…
Aims. There are a growing number of giant planets discovered moving around one stellar component of a binary star, most of which have very diverse eccentricity. These discoveries raise the question of their formation and long-term evolution…
The discrete Gaussian model for the surface of a crystal deposited on a disordered substrate is studied by Monte Carlo simulations. A continuous transition is found from a phase with a thermally-induced roughness to a glassy one in which…
There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…
We use a mixed-spin model, with aperiodic ferromagnetic exchange interactions and crystalline fields, to investigate the effects of deterministic geometric fluctuations on first-order transitions and tricritical phenomena. The interactions…
The investigation of collective behaviour in dense assemblies of self-propelled active particles has been motivated by a wide range of biological phenomena. Of particular interest are dynamical transitions of cellular and sub-cellular…
The grain boundary-mediated mechanisms that control plastic deformation of nanocrystalline metals should cause evolution of the grain boundary network, since they directly alter misorientation relationships between crystals. Unfortunately,…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
For two decades now, the importance of microstructure in the mechanical behaviour of a large collection of grains has been a topic of intense research. Many approaches have been developed to study the microstructure in granular materials,…
We study the formation of the protoplanetary disk by the collapse of a primordial molecular cloud, and how its evolution leads to the selection of specific types of planets. We use a hydrodynamical code that accounts for the dynamics,…