arXiv subjects
Publications and source records attributed to Pablo Fernández.
We report on some statistical regularity properties of greatest common divisors: for large random samples of integers, the number of coprime pairs and the average of the gcd's of those pairs are approximately normal, while the maximum of those gcd's (appropriately normalized) follows approximately a Fréchet distribution approximately. We also consider $r$-tuples instead of pairs, and moments other than the average.
This paper is devoted to the study of statistical properties of the greatest common divisor and the least common multiple of random samples of positive integers.
Cell mechanical properties are fundamental to the organism but remain poorly understood. We report a comprehensive phenomenological framework for the nonlinear rheology of single fibroblast cells: a superposition of elastic stiffening and viscoplastic kinematic hardening. Our results show, that in spite of cell complexity its mechanical properties can be cast into simple, well-defined rules, which provide mechanical cell strength and robustness via control of crosslink slippage.
We report a cylindrical-peristaltic shape transformation in axons exposed to a controlled osmotic perturbation. The peristaltic shape relaxes and the axon recovers its original geometry within minutes. We show that the shape instability depends critically on swelling rate and that volume and membrane area regulation are responsible for the shape relaxation. We propose that volume regulation occurs via leakage of ions driven by elastic pressure, and analyse the peristaltic shape dynamics taking into account the internal structure of the axon. The results obtained provide a framework for understanding peristaltic shape dynamics in nerve fibers occurring in vivo.
We present a first-principles calculation of the electronic properties of crystalline silicon and gallium arsenide in a uniform electric field. Polarized Wannier-like functions which are confined in a finite region are obtained by minimizing a total-energy functional which depends explicitly on the macroscopic polarization of the solid. The polarization charge density and the electronic dielectric constant are computed via finite differences. The results coincide with those of the linear response approach in the limit of vanishing electric field and infinite localization region.
We present a self-consistent, real-space calculation of the Wannier functions of Si and GaAs within density functional theory. We minimize the total energy functional with respect to orbitals which behave as Wannier functions under crystal translations and, at the minimum, are orthogonal. The Wannier functions are used to calculate the total energy, lattice constant, bulk modulus, and the frequency of the zone-center TO phonon of the two semiconductors with the accuracy required nowadays in ab-initio calculations. Furthermore, the centers of the Wannier functions are used to compute the macroscopic polarization of Si and GaAs in zero electric field. The effective charges of GaAs, obtained by finite differentiation of the polarization, agree with the results of linear response theory.