In the field of holomorphic dynamics in one complex variable, hedgehog is the local invariant set arising about a Cremer point and endowed with a very complicate shape as well as relating to very weak numerical conditions. We give a solution to the open problem of its digital visualization, featuring either a time saving approach and a far-reaching insight.

The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and an arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a scaling analysis of the corresponding spatially homogeneous system is performed. This approach points to the relevance of the nonlinear Boltzmann equation f...

An open problem in numerical analysis is to explain why molecular dynamics works. The difficulty is that numerical trajectories are only accurate for very short times, whereas the simulations are performed over long time intervals. It is believed that statistical information from these simulations is accurate, but no one has offered a rigourous proof of this. In order to give mathematicians a c...

In this study, we focus on the stability analysis of equilibrium points of population dynamics with delay when the Allee effect occurs at low population density is considered. Mainly, mathematical results and numerical simulations illustrate the stabilizing effect of the Allee effects on population dynamics with delay.

Andrea Baronchelli Dipartimento di Fisica, Università “La Sapienza” and SMC-INFM, P.le A. Moro 2, 00185 ROMA, (Italy) Abstract The models of statistical physics used to study collective phenomena in some interdisciplinary contexts, such as social dynamics and opinion spreading, do not consider the effects of the memory on individual decision processes. On the contrary, in the Naming Game, a rec...

The suitability of principal component analysis (PCA) to yield slow collective coordinates for use within a dimension reduced description of conformational motions in proteins is evaluated. Two proteins are considered, T4 lysozyme and crambin. We present a quantitative evaluation of the convergence of conformational coordinates obtained with principal component analysis. Detailed analyses of (>...

To study the possibility of a fluid-fluid phase transition, we analyze a three-dimensional soft-core isotropic potential for a one-component system. We utilize two independent numerical approaches, (i) integral equation in the hypernetted-chain approximation and (ii) molecular dynamics simulations, and find for both approaches a fluid-fluid phase transition as well as the conventional gas-liqui...

We study the rate of activated motion over multiple barriers, in particular the correlated double jump of an adatom diffusing on a missing-row reconstructed platinum (110) surface. We develop a transition path theory, showing that the activation energy is given by the minimum-energy trajectory which succeeds in the double jump. We explicitly calculate this trajectory within an effective-medium ...

the phytoplankton structure and dynamics were analysed in relation to abiotic variables inpaso de las piedras reservoir, argentina. phytoplankton driving forces were explored using a functionalapproach. a total of 15 functional groups were identified among which d, p, h1, f, j and c were the mostimportant. a canonical variate analysis indicated that the categorization of the species in function...