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We introduce fourth fundamental form $IV,$ and $i$-th curvature formulas of hypersurfaces in the four dimensional Euclidean geometry ${\mathbb{E}}^{4}$. Defining fourth fundamental form and $i$-th curvatures for hypersurfaces, we calculate…
These notes fill in results about oriented percolation that are required for the paper [3] ("Forward clusters for degenerate random environments"). Since these are essentially modifications of results found in other sources (but adapted to…
Mechanical models for tumor growth have been used extensively in recent years for the analysis of medical observations and for the prediction of cancer evolution based on imaging analysis. This work deals with the numerical approximation of…
Growing anthropogenic pressures have increased the need for robust predictive models. Meeting this demand requires approaches that can handle bigger data to yield forecasts that capture the variability and underlying uncertainty of…
We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield…
Time evolution of a "little bang" created in heavy ion collisions can be divided into two phases, the pre-equilibrium and hydrodynamic. At what moment the evolution becomes hydrodynamic and is there any universality in the hydrodynamic…
I review the basic ``gravitational instability'' model for the growth of structure in the expanding Universe. This model requires the existence of small initial irregularities in the density of a largely uniform universe. These grow through…
We provide a review on semi-empirical models of galaxy formation and evolution. We present a brief census of the three main modeling approaches to galaxy evolution, namely hydrodynamical simulations, semi-analytic models, and semi-empirical…
Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…
We introduce the special issue on the Statistical Mechanics of Climate published on the Journal of Statistical Physics by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great…
Numerical methods play an ever more important role in astrophysics. This is especially true in theoretical works, but of course, even in purely observational projects, data analysis without massive use of computational methods has become…
Planets are expected to conclude their growth through a series of giant impacts: energetic, global events that significantly alter planetary composition and evolution. Computer models and theory have elucidated the diverse outcomes of giant…
The work provides possible mechanisms of physics of thunderstorm clouds. We tried to consider the problems of the hail clouds in a completely different view. The article is based on the latest scientific achievement of modern theoretical…
Aims: Revisit and improvement of the main results obtained in the study of the tidal evolution of several massive CoRoT planets and brown dwarfs and of the rotation of their host stars. Methods: Simulations of the past and future evolution…
In order to improve the frequency dispersion effects of irrotational shallow water models in coastal oceanography, several full dispersion versions of classical models were formally derived in the literature. The idea, coming from G.…
The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is…
One possible method for the year-ahead prediction of hurricane numbers would be to make a year-ahead prediction of sea surface temperature (SST), and then to apply relationships that link SST to hurricane numbers. As a first step towards…
In this review I give a summary of the state-of-the-art for what concerns the chemo-dynamical numerical modelling of galaxies in general and of dwarf galaxies in particular. In particular, I focus my attention on (i) initial conditions;…
Emergence is a phenomenon taken for granted in science but also still not well understood. We have developed a model of artificial genetic evolution intended to allow for emergence on genetic, population and social levels. We present the…
The climate change dispute is about changes over time of environmental characteristics (such as rainfall). Some people say that a possible change is not so much in the mean but rather in the extreme phenomena (that is, the average rainfall…