A mechanism for pair formation in strongly correlated systems

We start from a Hamiltonian describing non-interacting fermions and add bosons to the model, with a Jaynes-Cummings-like interaction between the bosons and fermions. Because of the specific form of the interaction the model can be solved exactly. In the ground state, part of the electrons form bound pairs with opposite momentum and spin. The model also shows a gap in the kinetic energy of the fermions, but not in the spectrum of the full Hamiltonian. This gap is not of a mean-field nature, but is due to the Pauli exclusion principle.Comment: 13 pages, corrected some notations and made some clarification

The perfect mixing paradox and the logistic equation: Verhulst vs. Lotka

A theoretical analysis of density-dependent population dynamics in two patches sheds novel light on our understanding of basic ecological parameters. Firstly, as already highlighted in the literature, the use of the traditional r-K parameterization for the logistic equation (due to Lotka and Gause) can lead to paradoxical situations. We show that these problems do not exist with Verhulst's original formulation, which includes a quadratic “friction” term representing intraspecific competition (parameter α) instead of the so-called carrying capacity K. Secondly, we show that the parameter α depends on the number of patches, or more generally on area. This is also the case of all parameters that quantify the interaction strengths between individuals, either of the same species or of different species. The consequence is that estimates of interaction strength will vary when population size is measured in absolute terms. In order to obtain scale-invariant parameter estimates, it is essential to express population abundances as densities. Also, the interaction parameters must be reported with all explicit units, such as (m2·individual−1·d−1), which is rarely the case

Evolutionary game theory in growing populations

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperationComment: 4 pages, 2 figures and 2 pages supplementary informatio

The moisture effect on 223Ra and 224Ra measurements using Mn-cartridges

Important processes in the ocean can be evaluated with radioactive nuclides, including radium isotopes. An approach for quantifying radium isotopes in seawater with in-situ pumps has been developed in advance of the GEOTRACES program [1]. Precise measurements of 223Ra and 224Ra by means of the delayed coincidence counting system (RaDeCC) [2] are dependent on the moisture content of the medium [3]. In order to verify the optimum moisture content for this new approach, a set of measurements of the Mn-cartridge standards under different moisture conditions was conducted, as this was done previously for acrylic fiber. At a time, an amount of water equivalent to 5% of the cartridges weight was added, and the activities were determined. The variation of 224Ra activity occurs mainly between 0 to 15% of humidity. Under moisture conditions higher than 15%, the emanation efficiency reaches an optimum plateau until 100% of moisture. This result differs slightly from those found for 224Ra measurements using the acrylic fiber (plateau from 30 to 100 %) [3]. The 223Ra Mn-cartridge standard reaches the plateau under 5% of humidity, and above 50% moisture the activity seems to decrease. Considering the counting error (7%), it is hard to state that the effect of the moisture is critical. However, this decrease can be related to the shorter half-life of the 219Rn compared to the time needed to its diffusion through the water film, which could be a reason for the frequently observed lower efficiency of the 223Ra channel of the RaDeCC system [4]. [1] Henderson et al. (2013) J. Radioanal. Nucl. Chem. 296, 357–362. [2] Moore and Arnold (1996) J. Geophys. Res. 101, 321–1329. [3] Sun and Torgersen (1998) Mar. Chem. 61, 163–171. [4] Charette et al. (2012) Limnol. Oceanogr. 10, 451–463

Gender gaps in urban mobility

Abstract Mobile phone data have been extensively used to study urban mobility. However, studies based on gender-disaggregated large-scale data are still lacking, limiting our understanding of gendered aspects of urban mobility and our ability to design policies for gender equality. Here we study urban mobility from a gendered perspective, combining commercial and open datasets for the city of Santiago, Chile. We analyze call detail records for a large cohort of anonymized mobile phone users and reveal a gender gap in mobility: women visit fewer unique locations than men, and distribute their time less equally among such locations. Mapping this mobility gap over administrative divisions, we observe that a wider gap is associated with lower income and lack of public and private transportation options. Our results uncover a complex interplay between gendered mobility patterns, socio-economic factors and urban affordances, calling for further research and providing insights for policymakers and urban planners

Fluctuations and correlations in an individual-based model of biological coevolution

We extend our study of a simple model of biological coevolution to its statistical properties. Staring with a complete description in terms of a master equation, we provide its relation to the deterministic evolution equations used in previous investigations. The stationary states of the mutationless model are generally well approximated by Gaussian distributions, so that the fluctuations and correlations of the populations can be computed analytically. Several specific cases are studied by Monte Carlo simulations, and there is excellent agreement between the data and the theoretical predictions.Comment: 25 pages, 2 figure

Spherical gravitational collapse in N-dimensions

We investigate here spherically symmetric gravitational collapse in a spacetime with an arbitrary number of dimensions and with a general {\it type I} matter field, which is a broad class that includes most of the physically reasonable matter forms. We show that given the initial data for matter in terms of the initial density and pressure profiles at an initial surface $t=t_i$ from which the collapse evolves, there exist rest of the initial data functions and classes of solutions of Einstein equations which we construct here, such that the spacetime evolution goes to a final state which is either a black hole or a naked singularity, depending on the nature of initial data and evolutions chosen, and subject to validity of the weak energy condition. The results are discussed and analyzed in the light of the cosmic censorship hypothesis in black hole physics. The formalism here combines the earlier results on gravitational collapse in four dimensions in a unified treatment. Also the earlier work is generalized to higher dimensional spacetimes to allow a study of the effect of number of dimensions on the possible final outcome of the collapse in terms of either a black hole or naked singularity. No restriction is adopted on the number of dimensions, and other limiting assumptions such as self-similarity of spacetime are avoided, in order to keep the treatment general. Our methodology allows to consider to an extent the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.Comment: Revtex4, The replaced version matches the published on

Signal to noise ratio in parametrically-driven oscillators

Here we report a theoretical model based on Green's functions and averaging techniques that gives ana- lytical estimates to the signal to noise ratio (SNR) near the first parametric instability zone in parametrically- driven oscillators in the presence of added ac drive and added thermal noise. The signal term is given by the response of the parametrically-driven oscillator to the added ac drive, while the noise term has two dif- ferent measures: one is dc and the other is ac. The dc measure of noise is given by a time-average of the statistically-averaged fluctuations of the position of the parametric oscillator due to thermal noise. The ac measure of noise is given by the amplitude of the statistically-averaged fluctuations at the frequency of the parametric pump. We observe a strong dependence of the SNR on the phase between the external drive and the parametric pump, for some range of the phase there is a high SNR, while for other values of phase the SNR remains flat or decreases with increasing pump amplitude. Very good agreement between analytical estimates and numerical results is achieved.Comment: Submitted to Phys. Rev.

Основні етапи та особливості правового регулювання фінансування будівництва залізниць на території України в другій половині ХІХ – на початку ХХ ст.

Досліджуються питання розвитку та вдосконалення залізничного транспорту України, який постає у державі як одна з ланок поліпшення соціально-економічного життя суспільства. Розкриваються проблеми нормативно-правового регулювання виникнення залізничного транспорту в Україні.Рассматриваются вопросы развития и усовершенствования железнодорожного транспорта Украины, который является для государства звеном улучшения социально-экономической жизни общества. Раскрываются проблемы нормативно-правового регулирования возникновения железнодорожного транспорта в Украине.The guestions of development and improvement of the Ukrainian railvay transport which is consideret to be as one of the directions of making better social-economic life of society are investigated. The problems of normative\loyal regulating of the appearing of railwaj transport in Ukraine (the second half of the nineteenth century)