Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dominance and the maintenance of polymorphism in multiallelic migration-selection models with two demes

The maintenance of genetic variation in a spatially heterogeneous environment has been one of the main research themes in theoretical population genetics. Despite considerable progress in understanding the consequences of spatially structured environments on genetic variation, many problems remain unsolved. One of them concerns the relationship between the number of demes, the degree of dominance, and the maximum number of alleles that can be maintained by selection in a subdivided population. In this work, we study the potential of maintaining genetic variation in a two-deme model with deme-independent degree of intermediate dominance, which includes absence of G x E interaction as a special case. We present a thorough numerical analysis of a two-deme three-allele model, which allows us to identify dominance and selection patterns that harbor the potential for stable triallelic equilibria. The information gained by this approach is then used to construct an example in which existence and asymptotic stability of a fully polymorphic equilibrium can be proved analytically. Noteworthy, in this example the parameter range in which three alleles can coexist is maximized for intermediate migration rates. Our results can be interpreted in a specialist-generalist context and (among others) show when two specialists can coexist with a generalist in two demes if the degree of dominance is deme independent and intermediate. The dominance relation between the generalist allele and the specialist alleles play a decisive role. We also discuss linear selection on a quantitative trait and show that G x E interaction is not necessary for the maintenance of more than two alleles in two demes.

SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

Two Stable Equilibria of the Atlantic Subpolar Gyre

The cyclonic circulation of the Atlantic subpolar gyre is a key mechanism for North Atlantic climate variability on a wide range of time scales. It is generally accepted that it is driven by both cyclonic winds and buoyancy forcing, yet the individual importance and dynamical interactions of the two contributions remain unclear. The authors propose a simplified four-box model representing the convective basin of the Labrador Sea and its shallow and deep boundary current system, the western subpolar gyre. Convective heat loss drives a baroclinic flow of relatively light water around the dense center. Eddy salt flux from the boundary current to the center increases with a stronger circulation, favors the formation of dense waters, and thereby sustains a strong baroclinic flow, approximately 10%–25% of the total. In contrast, when the baroclinic flow is not active, surface waters may be too fresh to convect, and a buoyancy-driven circulation cannot develop. This situation corresponds to a second stable circulation mode. A hysteresis is found for variations in surface freshwater flux and the salinity of the near-surface boundary current. An analytical solution is presented and analyzed.

Hydrothermal phase equilibria in Ln2O3-H2O-CO2 systems : I. The lighter lanthanides

Phase diagrams for Nd2O3-H2O-CO2 and Gd2O3-H2O-CO2 systems at 1500 atm are given along with the results of selected runs in La, Sm and Eu systems. The stable phases in systems of La and Nd, are Ln(OH)CO3-B, Ln2O2CO3-II and LnOOH, in addition to the Ln(OH)3 phase at extremely low partial pressures of CO2 in the system. The systems become more and more complex with decreasing ionic radi and the number of stable carbonate phases increases. Ln2(CO3)3 · 3H2O orthorhombic (tengerate-like phase) is stable from Sm to Gd in addition to the other phases. The Gd(OH)CO3-A (ancylite-like phase) is hydrothermally stable at XCO2 greater-or-equal, slanted 0.5 while its hexagonal polymorph, Gd(OH)CO3-B is stable at low partial pressures of CO2 in the system.

Hydrothermal phase equilibria studies in Ln2O3---H2O systems and synthesis of cubic lanthanide oxides

Phase diagrams for the systems Ln2O3---H2O (Ln = La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Lu and Y) studied at 5000 to 10,000 psi and temperature range of 200–900°C, show that Ln(OH)3 hexagonal and LnOOH monoclinic are the only stable phases from Nd to Ho. The cubic oxide phase (C---Ln2O3) is stable for systems of Er, Tm, Yb and Lu, with no evidence of its equilibrium in the systems of lighter lanthanides. Using strong acids, HNO3 and HCOOH, as mineralisers the cubic oxides could be stabilised from Eu down to Lu. Solid solution phases of CeO2---Y2O3 and Eu2O3---Y2O3 have also been synthesised with HNO3 as mineraliser, since these compounds have promising use as solid electrolyte and phosphor materials respectively.

Thermodynamic properties of Pb2PtO4 and PbPt2O4 and phase equilibria in the system Pb–Pt–O

The compounds Pb2PtO4 and PbPt2O4 were synthesized from an intimate mixture of yellow PbO and Pt metal powders by heating under pure oxygen gas at 973 K for periods up to 600 ks with intermediate grinding and recompacting. Both compounds were found to decompose on heating in pure oxygen to PbO and Pt, apparently in conflict with the requirements for equilibrium phase relations in the ternary system Pb–Pt–O. The oxygen chemical potential corresponding to the three-phase mixtures, Pb2PtO4 + PbO + Pt and PbPt2O4 + PbO + Pt were measured as a function of temperature using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the solid electrolyte and pure oxygen gas at 0.1 MPa pressure as the reference electrode. The standard Gibbs free energies of formation of the ternary oxides were derived from the measurements. Analysis of the results indicated that the equilibrium involving three condensed phases Pb2PtO4 + PbO + Pt is metastable. Under equilibrium conditions, Pb2PtO4 should have decomposed to a mixture of PbO and PbPt2O4. Measurement of the oxygen potential corresponding to this equilibrium decomposition as a function of temperature indicated that decomposition temperature in pure oxygen is 1014(±2) K. This was further confirmed by direct determination of phase relations in the ternary Pb–Pt–O by equilibrating several compositions at 1023 K for periods up to 850 ks and phase identification of quenched samples using X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). Only one ternary oxide PbPt2O4 was stable at 1023 K under equilibrium conditions. Alloys and intermetallic compounds along the Pb–Pt binary were in equilibrium with PbO.

Hydrothermal phase equilibria in Ln2O3-H2O-CO2 systems for Tm, Yb and Lu

Phase diagrams for Tm2O3-H2O-CO2. Yb2O3-H2O-CO2 and Lu2O3-H2O-CO2 systems at 650 and 1300 bars have been investigated in the temperature range of 100–800°C. The phase diagrams are far more complex than those for the lighter lanthanides. The stable phases are Ln(OH)3, Ln2(CO3)3.3H2O (tengerite phase), orthorhombic-LnOHCO3, hexagonal-Ln2O2CO3. LnOOH and cubic-Ln2O3. Ln(OH)3 is stable only at very low partial pressures of CO2. Additional phases stabilised are Ln2O(OH)2CO3and Ln6(OH)4(CO3)7 which are absent in lighter lanthanide systems. Other phases, isolated in the presence of minor alkali impurities, are Ln6O2(OH)8(CO3)3. Ln4(OH)6(CO3)3 and Ln12O7(OH)10,(CO3)6. The chemical equilibria prevailing in these hydrothermal systems may be best explained on the basis of the four-fold classification of lanthanides.

Use of metastable equilibria for determination of Gibbs energy of solids

Attempts are made to measure activities of both components of a binary alloy (A�B) at 650 K using a solid-state galvanic cell incorporating a new composite solid electrolyte. Since the ionic conductivity of the composite solid electrolyte is three orders of magnitude higher than that of pure CaF2, the cell can be operated at lower temperatures. The alloy phase is equilibrated in separate experiments with flourides of each component and fluorine potential is measured. The mixture of the alloy (A�B) and the fluoride of the more reactive component (BF2) is stable, while (A�B) + AF2 mixture is metastable, Factors governing the possible use of metastable equilibria have been elucidated in this study. In the Co�Ni system, where the difference in Gibbs energies of formation of the fluorides is 21.4 kJ/mol, emf of the cell with metastable phases at the electrode is constant for periods ranging from 90 to 160 ks depending on alloy composition. Subsequently, the emf decreases because of the onset of the displacement reaction. In the Ni�Mn system, measurement of the activity of Ni using metastable equilibria is not fully successful at 650 K because of the large driving force for the displacement reaction (208.8 kJ/mol). Critical factors in the application of metastable equilibria are the driving force for displacement reaction and diffusion coefficients in both the alloy and fluoride solid solution.

Absolutely expedient algorithms for learning Nash equilibria

This paper considers a multi-person discrete game with random payoffs. The distribution of the random payoff is unknown to the players and further none of the players know the strategies or the actual moves of other players. A class of absolutely expedient learning algorithms for the game based on a decentralised team of Learning Automata is presented. These algorithms correspond, in some sense, to rational behaviour on the part of the players. All stable stationary points of the algorithm are shown to be Nash equilibria for the game. It is also shown that under some additional constraints on the game, the team will always converge to a Nash equilibrium.

Phase equilibria in the system CaO-CoO-SiO2 and Gibbs energies of formation of the quaternary oxides CaCoSi2O6, Ca2CoSi2O7, and CaCoSiO4

Phase relations in the pseudoternary system CaO-CoO-SiO2 have been established at 1323 K. Three quaternary oxides were found to be stable: CaCoSi2O6 with clinopyroxene (Cpx), Ca2CoSi2O7 with melilite (Mel), and CaCoSiO4 with olivine (Ol) structures. The Gibbs energies of formation of the quaternary oxides from their component binary oxides were measured using solid-state galvanic cells incorporating yttria-stabilized zirconia as the solid electrolyte in the temperature range of 1000-1324 K. The results can be summarized as follows: CoO (rs) + CaO (rs) + 2SiO(2) (Qtz) --> CaCoSi2O6 (Cpx), Delta G(f)(0) = -117920 + 11.26T (+/-150) J/mol CoO (rs) + 2CaO (rs) + 2SiO(2) (Qtz) --> Ca2CoSi2O7 (Mel), Delta G(f)(0) = -192690 + 2.38T (+/-130) J/mol CoO (rs) + CaO (rs) + SiO2 (Qtz) --> CaCoSiO2 (Ol), Delta G(f)(0) = -100325 + 2.55T (+/-100) J/mol where rs = rock salt (NaCl) structure and Qtz = quartz. The uncertainty limits correspond to twice the standard error estimate. The experimentally observed miscibility gaps along the joins CaO-CoO and CaCoSiO4-Co2SiO4 were used to calculate the excess free energies of mixing for the solid solutions CaxCo1-xO and (CayCo1-y)CoSiO4:Delta G(E) = X(1 - X)[31975X + 26736 (1 - X)] J/mol and Delta G(E) = 23100 (+/-250) Y(1 - Y) J/mol. A T-X phase diagram for the binary CaO-CoO was computed from the thermodynamic information; the diagram agrees with information available in the literature. The computed miscibility gap along the CaCoSiO4-Co2SiO4 join is associated with a critical temperature of 1389 (+/-15) K. Stability fields for the various solid solutions and the quaternary compounds are depicted on chemical-potential diagrams for SiO2, CaO, and CoO at 1323 K.

Alloy oxide equilibria in the system Ca Al O at 1373 K

The tie lines delineating equilibria between different oxides of the Ca-Al-O system and liquid Ca-Al alloy has been determined at 1373 K. Equilibration of the alloy with two adjacent oxide phases in the CaO-Al2O3 pseudo-binary system was established in a closed cell made of iron. Equilibrium oxide phases were confirmed by x-ray analysis and alloy compositions were determined by chemical analysis. The compound 12CaO.7Al2O3 Ca12Al14O33 was found to be a stable phase in equilibrium with calcium alloys. The experimental diagram is consistent with that calculated from the free energies of formation of the oxide phases and activities in liquid Ca-Al alloys at 1373 K reported in the literature.

Experimental study of phase equilibria in the system Cu-Al-Sn

Phase equilibria in the Cu-rich corner of the ternary system Cu-Al-Sn have been re-investigated. Final equilibrium microstructures of 20 ternary alloy compositions near Cu3Al were used to refine the ternary phase diagram. The microstructures were characterized using optical microscopy (OM), x-ray diffraction (XRD), electron probe microanalysis and transmission electron microscopy. Isothermal sections at 853, 845, 833, 818, 808, 803 and 773 K have been composed. Vertical sections have been drawn at 2 and 3 at% Sn, showing beta(1) as a stable phase. Three-phase fields (alpha + beta + beta(1)) and (beta + beta(1) + gamma(1)) result from beta -> alpha + beta(1) eutectoid and beta + gamma(1) -> beta(1) peritectoid reactions forming metastable beta(1) in the binary Cu-Al. With the lowering of temperature from 853 to 818 K, these three-phase fields are shifted to lower Sn concentrations, with simultaneous shrinkage and shifting of (beta + beta(1)) two-phase field. The three-phase field (alpha + beta + gamma(1)) resulting from the binary reaction beta -> alpha + gamma(1) shifts to higher Sn contents, with associated shrinkage of the beta field, with decreasing temperature. With further reduction of temperature, a new ternary invariant reaction beta + beta(1) -> alpha + gamma(1) is observed at similar to 813 K. The beta disappears completely at 803 K, giving rise to the three-phase field (alpha + beta(1) + gamma(1)). Some general guidelines on the role of ternary additions (M) on the stability of the ordered beta(1) phase are obtained by comparing the results of this study with data in the literature on other systems in the systems group Cu-Al-M.

GRMHD formulation of highly super-Chandrasekhar rotating magnetized white dwarfs: stable configurations of non-spherical white dwarfs

Here we extend the exploration of significantly super-Chandrasekhar magnetized white dwarfs by numerically computing axisymmetric stationary equilibria of differentially rotating magnetized polytropic compact stars in general relativity (GR), within the ideal magnetohydrodynamic regime. We use a general relativistic magnetohydrodynamic (GRMHD) framework that describes rotating and magnetized axisymmetric white dwarfs, choosing appropriate rotation laws and magnetic field profiles (toroidal and poloidal). The numerical procedure for finding solutions in this framework uses the 3 + 1 formalism of numerical relativity, implemented in the open source XNS code. We construct equilibrium sequences by varying different physical quantities in turn, and highlight the plausible existence of super-Chandrasekhar white dwarfs, with masses in the range of 2-3 solar mass, with central (deep interior) magnetic fields of the order of 10(14) G and differential rotation with surface time periods of about 1-10 s. We note that such white dwarfs are candidates for the progenitors of peculiar, overluminous Type Ia supernovae, to which observational evidence ascribes mass in the range 2.1-2.8 solar mass. We also present some interesting results related to the structure of such white dwarfs, especially the existence of polar hollows in special cases.

Formation equilibria of ternary metal complexes with citric acid and glutamine (alanine) in aqueous solution

The species and their formation constants in the ternary, systems were obtained by the Scogs2 software from potentiometric titration data. The Comics software was used to calculate the distribution of species in the ternary systems. MLXH, MLXH2 and MLXH3 are the common species in these systems. The coordination behaviors of the rare earths are very similar and their stability is closely matched. The ternary rare earth complexes are more stable than the corresponding ternary complexes of calcium. The ternary zinc complex with glutamine as the secondary ligand is more stable than the corresponding complexes of rare earths, but the ternary complex with alanine as the secondary ligand shows an inverse trend. The distributions of species in the ternary systems vary with pH changing. A prediction can be made that exogenous rare earths can affect the species of Ca and Zn in human body.