First-principles derivation of density functional formalism for quenched-annealed systems

We derive from first principles (without resorting to the replica trick) a density functional theory for fluids in quenched disordered matrices (QA-DFT). We show that the disorder-averaged free energy of the fluid is a functional of the average density profile of the fluid as well as the pair correlation of the fluid and matrix particles. For practical reasons it is preferable to use another functional: the disorder-averaged free energy plus the fluid-matrix interaction energy, which, for fixed fluid-matrix interaction potential, is a functional only of the average density profile of the fluid. When the matrix is created as a quenched configuration of another fluid, the functional can be regarded as depending on the density profile of the matrix fluid as well. In this situation, the replica-Ornstein-Zernike equations which do not contain the blocking parts of the correlations can be obtained as functional identities in this formalism, provided the second derivative of this functional is interpreted as the connected part of the direct correlation function. The blocking correlations are totally absent from QA-DFT, but nevertheless the thermodynamics can be entirely obtained from the functional. We apply the formalism to obtain the exact functional for an ideal fluid in an arbitrary matrix, and discuss possible approximations for non-ideal fluids.Comment: 19 pages, uses RevTeX

The Shared Reward Dilemma

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically, for a group of players that collect payoffs by playing a pairwise Prisoner's Dilemma game with their partners, we consider an external entity that distributes a fixed reward equally among all cooperators. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared a vast variety of scenarios arises, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the $n$-player game as well as of its evolutionary dynamics.Comment: Major rewriting, new appendix, new figure

A density functional theory for general hard-core lattice gases

We put forward a general procedure to obtain an approximate free energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.Comment: 4 pages, 1 eps figure, uses RevTeX

Fundamental-measure density functional for the fluid of aligned hard hexagons: New insights in fundamental measure theory

In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for a new, admittedly academic, model, but to investigate the structure of fundamental measure theory. A model of aligned hard hexagons has similarities with the hard disk model. Both share "lost cases", i.e. admit configurations of three particles in which there is pairwise overlap but not triple overlap. These configurations are known to be problematic for fundamental measure functionals, which are not able to capture their contribution correctly. This failure lies in the inability of these functionals to yield a correct low density limit of the third order direct correlation function. Here we derive the functional by projecting aligned hard cubes on the plane x+y+z=0. The correct dimensional crossover behavior of these functionals permits us to follow this strategy. The functional of aligned hard cubes, however, does not have lost cases, so neither had the resulting functional for aligned hard hexagons. The latter exhibits, in fact, a peculiar structure as compared to the one for hard disks. It depends on a uniparametric family of weighted densities through a new term not appearing in the functional for hard disks. Apart from studying the freezing of this system, we discuss the implications of the functional structure for new developments of fundamental measure theory.Comment: 10 pages, 9 figures, uses RevTeX

Reaching the millennium development goal for child mortality : improving equity and efficiency in Ecuador's health budget

health care; infant mortality; health policy;

Rewarding cooperation in social dilemmas

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared we can cast a vast variety of scenarios, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the nplayer game as well as of the evolutionary dynamics. Beyond, we extend our analysis to a general class of public good games where competition among individuals with the same strategy exists.

What do emulsification failure and Bose-Einstein condensation have in common?

Ideal bosons and classical ring polymers formed via self-assembly, are known to have the same partition function, and so analogous phase transitions. In ring polymers, the analogue of Bose-Einstein condensation occurs when a ring polymer of macroscopic size appears. We show that a transition of the same general form occurs within a whole class of systems with self-assembly, and illustrate it with the emulsification failure of a microemulsion phase of water, oil and surfactant. As with Bose-Einstein condensation, the transition occurs even in the absence of interactions.Comment: 7 pages, 1 figure, typeset with EUROTeX, uses epsfi

Catastrophic regime shifts in model ecological communities are true phase transitions

Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in external conditions. Usual models introduce nonlinearities in the macroscopic dynamics of the ecosystem that lead to different stable attractors among which the shift takes place. Here we propose an alternative explanation of catastrophic regime shifts based on a recent model that pictures ecological communities as systems in continuous fluctuation, according to certain transition probabilities, between different micro-states in the phase space of viable communities. We introduce a spontaneous extinction rate that accounts for gradual changes in external conditions, and upon variations on this control parameter the system undergoes a regime shift with similar features to those previously reported. Under our microscopic viewpoint we recover the main results obtained in previous theoretical and empirical work (anomalous variance, hysteresis cycles, trophic cascades). The model predicts a gradual loss of species in trophic levels from bottom to top near the transition. But more importantly, the spectral analysis of the transition probability matrix allows us to rigorously establish that we are observing the fingerprints, in a finite size system, of a true phase transition driven by background extinctions.Comment: 19 pages, 11 figures, revised versio

A white dwarf-neutron star relativistic binary model for soft gamma-ray repeaters

A scenario for SGRs is introduced in which gravitational radiation reaction effects drive the dynamics of an ultrashort orbital period X-ray binary embracing a high-mass donor white dwarf (WD) to a rapidly rotating low magnetised massive neutron star (NS) surrounded by a thick, dense and massive accretion torus. Driven by GR reaction, sparsely, the binary separation reduces, the WD overflows its Roche lobe and the mass transfer drives unstable the accretion disk around the NS. As the binary circular orbital period is a multiple integer number ($m$) of the period of the WD fundamental mode (Pons et al. 2002), the WD is since long pulsating at its fundamental mode; and most of its harmonics, due to the tidal interaction with its NS orbital companion. Hence, when the powerful irradiation glows onto the WD; from the fireball ejected as part of the disk matter slumps onto the NS, it is partially absorbed. This huge energy excites other WD radial ($p$-mode) pulsations (Podsiadlowski 1991,1995). After each mass-transfer episode the binary separation (and orbital period) is augmented significantly (Deloye & Bildsten 2003; Al\'ecyan & Morsink 2004) due to the binary's angular momentum redistribution. Thus a new adiabatic inspiral phase driven by GR reaction starts which brings the binary close again, and the process repeats. This model allows to explain most of SGRs observational features: their recurrent activity, energetics of giant superoutbursts and quiescent stages, and particularly the intriguing subpulses discovered by BeppoSAX (Feroci et al. 1999), which are suggested here to be {\it overtones} of the WD radial fundamental mode (see the accompanying paper: Mosquera Cuesta 2004b).Comment: This paper was submitted as a "Letter to the Editor" of MNRAS in July 17/2004. Since that time no answer or referee report was provided to the Author [MNRAS publication policy limits reviewal process no longer than one month (+/- half more) for the reviewal of this kind of submission). I hope this contribution is not receiving a similar "peer-reviewing" as given to the A. Dar and A. De Rujula's "Cannonball model for gamma-ray bursts", or to the R.K. Williams' "Penrose process for energy extraction from rotating black holes". The author welcomes criticisms and suggestions on this pape

Properties improvement of poly(o-methoxyaniline) based supercapacitors : experimental and theoretical behaviour study of self-doping effect

The support of this research by FAPESP (2011/10897-2, 2013/07296-2), CsF-PVE (99999.007708/2015-07), CAPES and CNPq is gratefully acknowledged. We also thank the University of Aberdeen for providing computational time on MaxwellPeer reviewedPostprin