On the Adjudication of Conflicting Claims: An Experimental Study

This paper reports an experimental study on three well known solutions for claims problems, that is, the constrained equal-awards, the proportional, and the constrained equal-losses rules. To do this, we first let subjects play three games designed such that the unique equilibrium allocation coincides with the recommendation of one of these three rules. Moreover, we also let subjects play an additional game, that has the property that all (and only) strategy profiles in which players coordinate on the same rule constitute a strict Nash equilibrium. While in the first three games subjects? play easily converges to the unique equilibrium rule, in the last game the proportional rule overwhelmingly prevails as a coordination device. We also administered a questionnaire to a different group of students, asking them to act as an impartial arbitrator to solve (among others) the same claims situations played in the lab. Also in this case, the proportional solution was selected by the vast majority of respondentsExperimental Economics, Claims problems, Proportional rule

Rare-gas solids under pressure: A path-integral Monte Carlo simulation

Rare-gas solids (Ne, Ar, Kr, and Xe) under hydrostatic pressure up to 30 kbar have been studied by path-integral Monte Carlo simulations in the isothermal-isobaric ensemble. Results of these simulations have been compared with available experimental data and with those obtained from a quasiharmonic approximation (QHA). This comparison allows us to quantify the overall anharmonicity of the lattice vibrations and its influence on several structural and thermodynamic properties of rare-gas solids. The vibrational energy increases with pressure, but this increase is slower than that of the elastic energy, which dominates at high pressures. In the PIMC simulations, the vibrational kinetic energy is found to be larger than the corresponding potential energy, and the relative difference between both energies decreases as the applied pressure is raised. The accuracy of the QHA increases for rising pressure.Comment: 9 pages, 6 figure

Molar volume of solid isotopic helium mixtures

Solid isotopic helium mixtures have been studied by path-integral Monte Carlo simulations in the isothermal-isobaric ensemble. This method allowed us to study the molar volume as a function of temperature, pressure, and isotopic composition. At 25 K and 0.2 GPa, the relative difference between molar volumes of isotopically-pure crystals of 3He and 4He is found to be about 3%. This difference decreases under pressure, and for 12 GPa it is smaller than 1%. For isotopically-mixed crystals, a linear relation between lattice parameters and concentrations of helium isotopes is found, in agreement with Vegard's law. The virtual crystal approximation, valid for isotopic mixtures of heavier atoms, does not give reliable results for solid solutions of helium isotopes.Comment: 7 pages, 5 figure

The phase diagram of ice: a quasi-harmonic study based on a flexible water model

The phase diagram of ice is studied by a quasi-harmonic approximation. The free energy of all experimentally known ice phases has been calculated with the flexible q-TIP4P/F model of water. The only exception is the high pressure ice X, in which the presence of symmetric O-H-O bonds prevents its modeling with this empirical interatomic potential. The simplicity of our approach allows us to study ice phases at state points of the T-P plane that have been omitted in previous simulations using free energy methods based on thermodynamic integration. The effect in the phase diagram of averaging the proton disorder that appears in several ice phases has been studied. It is found particularly relevant for ice III, at least for cell sizes typically used in phase coexistence simulations. New insight into the capability of the employed water model to describe the coexistence of ice phases is presented. We find that the H-ordered ices IX and XIV, as well as the H-disordered ice XII, are particularly stable for this water model. This fact disagrees with experimental data. The unexpected large stability of ice IX is a property related to the TIP4P-character of the water model. Only after omission of these three stable ice phases, the calculated phase diagram becomes in reasonable qualitative agreement to the experimental one in the T-P region corresponding to ice Ih, II, III, V, and VI. The calculation of the phase diagram in the quantum and classical limits shows that the most important quantum effect is the stabilization of ice II due to its lower zero-point energy when compared to that one of ices Ih, III, and V.Comment: 13 pages, 8 figures, 5 table

Kinetic-growth self-avoiding walks on small-world networks

Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value . For random networks, this mean attrition length scales as a power of the network size, and diverges in the thermodynamic limit (large system size N). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, grows with system size as N^{1/2}, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)^{-4}. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.Comment: 10 pages, 7 figure

Solid helium at high pressure: A path-integral Monte Carlo simulation

Solid helium (3He and 4He) in the hcp and fcc phases has been studied by path-integral Monte Carlo. Simulations were carried out in the isothermal-isobaric (NPT) ensemble at pressures up to 52 GPa. This allows one to study the temperature and pressure dependences of isotopic effects on the crystal volume and vibrational energy in a wide parameter range. The obtained equation of state at room temperature agrees with available experimental data. The kinetic energy, E_k, of solid helium is found to be larger than the vibrational potential energy, E_p. The ratio E_k/E_p amounts to about 1.4 at low pressures, and decreases as the applied pressure is raised, converging to 1, as in a harmonic solid. Results of these simulations have been compared with those yielded by previous path integral simulations in the NVT ensemble. The validity range of earlier approximations is discussed.Comment: 7 pages, 5 figure