Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization

In this paper we investigate quasi equilibrium problems in a real Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered.

Repeated Sequential Prisoner's Dilemma: The Stackleberg Variant

We study the Stackleberg variant of the repeated Sequential Prisoner's Dilemma (SPD). The game goes in two stages, and the two players, the leader and the follower, are asymmetric in both stages. In the first stage of the game, the leader chooses a strategy (for the repeated SPD of the second stage), which is immediately known to the follower. In the second stage, they play repeated SPD: In each round the follower moves after observing the leader's action. Assuming complete rationality, we find some extraordinary properties of this model. (i) The (subgame perfect) equilibrium payoff profile is unique, which lies on the corner of the region predicted by classical folk theorems: It is best for the leader and at the same time worst for the follower, (ii) the leader has simple optimal strategies that are one-step memory and stationary. These features are in great contrast with classical results, where either uniqueness cannot be guaranteed and equilibrium strategies are often quite complicated, or bounded rationality is required. Although full cooperation, i.e., the outcome is always (cooperate, cooperate), is not attainable in our model, at least a half of the optimal social welfare can be guaranteed. We also do a non-equilibrium analysis which makes the usual equilibrium analysis more convincing.

A Pseudobubblepoint Model and Its Simulation for Foamy Oil in Porous Media

Summary This is the second paper of a series in which we study heavy oil in porous media. The first paper dealt with an experimental study (Wang et al. 2008), whereas a mathematical and simulation study is presented here. The research program stems from the need to predict the field performance of a class of heavy-foamy-oil reservoirs. These reservoirs show a better-than-expected primary performance: lower production gas/oil ratios (GORs), higher-than-expected production rates, and higher oil recovery. A mechanism used to account for the observed performance is that the liberated solution gas is entrained in the oil when the reservoir pressure falls below the thermodynamic equilibrium bubblepoint pressure. The presence of entrained gas increases the effective compressibility of the oil phase and prevents gas from becoming a free phase. Hence, the foamy oil behaves as if it had a pseudobubblepoint pressure below the usual equilibrium bubblepoint pressure. This paper describes a pseudobubblepoint model and a methodology that can be used to compute foamy-oil fluid properties from conventional laboratory pressure/volume/temperature (PVT) data. The techniques developed are then used to study foamy oil in the Orinoco belt, Venezuela. The present mathematical model is validated by comparing numerical and experimental results.

The non-equilibrium region of grid-generated decaying turbulence

The previously reported non-equilibrium dissipation law is investigated in turbulent flows generated by various regular and fractal square grids. The flows are documented in terms of various turbulent profiles which reveal their differences. In spite of significant inhomogeneity and anisotropy differences, the new non-equilibrium dissipation law is observed in all of these flows. Various transverse and longitudinal integral scales are measured and used to define the dissipation coefficient $C_{\varepsilon }$. It is found that the new non-equilibrium dissipation law is not an artefact of a particular choice of the integral scale and that the usual equilibrium dissipation law can actually coexist with the non-equilibrium law in different regions of the same flow.

DYNAMICAL DETAILED BALANCE AND LOCAL KMS CONDITION FOR NON-EQUILIBRIUM STATES

The principle of detailed balance is at the basis of equilibrium physics and is equivalent to the Kubo–Martin–Schwinger (KMS) condition (under quite general assumptions). In the present paper we prove that a large class of non-equilibrium quantum systems satisfies a dynamical generalization of the detailed balance condition (dynamical detailed balance) expressing the fact that all the micro-currents, associated to the Bohr frequencies are constant. The usual (equilibrium) detailed balance condition is characterized by the property that this constant is identically zero. From this we deduce a simple and experimentally measurable relation expressing the microcurrent associated to a transition between two levels ∊m→∊n as a linear combination of the occupation probabilities of the two levels, with coefficients given by the generalized susceptivities (transport coefficients). We then give a second characterization of the dynamical detailed balance condition using a master equation rather than the microcurrents. Finally we show that these two conditions are equivalent to a "local" generalization of the usual KMS condition. Summing up: rather than postulating some ansatz on the basis of phenomenological models or of numerical simulations, we deduce, directly in the quantum domain and from fundamental principles, some natural and simple non equilibrium generalizations of the three main characterizations of equilibrium states. Then we prove that these three, apparently very far, conditions are equivalent. These facts support our convinction that these three equivalent conditions capture a universal aspect of non equilibrium phenomena.

Evidence for Selection at thefusedLocus ofDrosophila virilis

The genomic DNA sequence of a 2.4-kb region of the X-linked developmental gene fused was determined in 15 Drosophila virilis strains. One common replacement polymorphism is observed, where a negatively charged aspartic amino acid is replaced by the noncharged amino acid alanine. This replacement variant is located within the serine/threonine kinase domain of the fused gene and is present in ~50% of the sequences in our sample. Significant linkage disequilibrium is detected around this replacement site, although the fused gene is located in a region of the D. virilis X chromosome that seems to experience normal levels of recombination. In a 600-bp region around the replacement site, all eight alanine sequences are identical; of the six aspartic acid sequences, three are also identical. The occurrence of little or no variation within the aspartic acid and alanine haplotypes, coupled with the presence of several differences between them, is very unlikely under the usual equilibrium neutral model. Our results suggest that the fused alanine haplotypes have recently increased in frequency in the D. virilis population.

Evidence for positive selection in the superoxide dismutase (Sod) region of Drosophila melanogaster.

DNA sequence variation in a 1410-bp region including the Cu,Zn Sod locus was examined in 41 homozygous lines of Drosophila melanogaster. Fourteen lines were from Barcelona, Spain, 25 were from California populations and the other two were from laboratory stocks. Two common electromorphs, SODS and SODF, are segregating in the populations. Our sample of 41 lines included 19 SodS and 22 SodF alleles (henceforward referred to as Slow and Fast alleles). All 19 Slow alleles were identical in sequence. Of the 22 Fast alleles sequenced, nine were identical in sequence and are referred to as the Fast A haplotypes. The Slow allele sequence differed from the Fast A haplotype at a single nucleotide site, the site that accounts for the amino acid difference between SODS and SODF. There were nine other haplotypes among the remaining 13 Fast alleles sequenced. The overall level of nucleotide diversity (pi) in this sample is not greatly different than that found at other loci in D. melanogaster. It is concluded that the Slow/Fast polymorphism is a recently arisen polymorphism, not an old balanced polymorphism. The large group of nearly identical haplotypes suggests that a recent mutation, at the Sod locus or tightly linked to it, has increased rapidly in frequency to around 50%, both in California and Spain. The application of a new statistical test demonstrates that the occurrence of such large numbers of haplotypes with so little variation among them is very unlikely under the usual equilibrium neutral model. We suggest that the high frequency of some haplotypes is due to natural selection at the Sod locus or at a tightly linked locus.

The Importance of Radiative Transfer in Stellar Pulsation Models

With the advent of new astrophysical opacities it seems appropriate to discuss the need for a full radiative transfer (RT) theory instead of the usual equilibrium diffusion theory used in most nonlinear pulsation codes. Early studies on the importance of RT in the calculation of light curves for Cepheid models showed little effect over diffusion theory. The new opacities though may help to explain the “bump” mass discrepancy problem. For RR Lyrae models the use of RT theory causes some effects both in the color differences (U-B) as well as in the light curves. New opacities help to explain the period ratios for double mode RR Lyrae and beat Cepheids. A new area of research is in the modeling of stars with high luminosity to mass ratios that show tendencies for doubling and transitions to chaos, such as W Virginis and RV Tauri stars. For these stars it has been shown that RT is necessary in calculating their light curves and that the understanding of the shock dynamics depends on the transfer of lines in the pulsating RT dependent atmospheres (Fokin 1991).

Transient Scanning Electron Beam Annealing Methods Used to Study Diffusion and Defects in Implanted Silicon

Rapid thermal annealing of arsenic and boron difluoride implants, such as those used for source/drain regions in CMOS, has been carried out using a scanning electron beam annealer, as part of a study of transient diffusion effects. Three types of e-beam anneal have been performed, with peak temperatures in the range 900-1200°C; the normal isothermal e-beam anneals, together with sub-second fast anneals and ‘dual-pulse’ anneals, in which the sample undergoes an isothermal pre-anneal followed by rapid heating to the required anneal temperature in less than O.5s.The diffusion occuring during these anneal cycles has been modelled using SPS−1D, an implant and diffusion modelling program developed by one of the authors. This has been modified to incorporate simulated temperature vs. time cycles for the anneals. Results are presented applying the usual equilibrium clustering model, a transient point-defect enhancement to the diffusivity proposed recently by Fair and a new dynamic clustering model for arsenic. Good agreement with SIMS measurements is obtained using the dynamic clustering model, without recourse to a transient defect model.Defects remaining in diodes fabricated with the forementioned implants after these anneal cycles have been studied using DLTS techniques. Trap densities for the three types of e-beam anneal are comparable to those for furnace annealed diodes, as are the reverse leakage currents measured (typically 2–5nA for a 0.85mm2 diode at -5V).

Turbulent Shear Flows Over a Step Change in Surface Roughness

A large body of data now exists on the response of turbulent shear flows to sudden or step changes in surface roughness. Authors have used a variety of methods to reduce and present the data; thus a consistent description of these flows has not yet been presented. This paper presents all available data reduced in a uniform way. As there are extremely few Reynolds stress measurements within this large body of data, the analyses presented here are necessarily based on mean velocity profiles. It is shown that the growth rate of the new internal layer for all types of flow both with and without pressure gradient can be described in terms of a single length scale associated with the new wall condition. It is also shown that all mean velocity profiles after a step change in roughness display semi-logarithmic distributions. However, in the region immediately downstream of a step the constant of proportionality (the von Karman constant) has values different from the usual equilibrium value of 0.41. The differences appear to be large with values for the constant ranging between about 0.2 to 0.8.