Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic changes which arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptation, v, in several models of such sexual populations and show that v is linear in NU_b only in sufficiently small populations. In large populations, v increases much more slowly as log NU_b. The prefactor of this logarithm, however, increases as the square of the recombination rate. This acceleration of adaptation by recombination implies a strong evolutionary advantage of sex

Scaling function and universal amplitude combinations for self-avoiding polygons

We analyze new data for self-avoiding polygons, on the square and triangular lattices, enumerated by both perimeter and area, providing evidence that the scaling function is the logarithm of an Airy function. The results imply universal amplitude combinations for all area moments and suggest that rooted self-avoiding polygons may satisfy a $q$-algebraic functional equation.Comment: 9 page

Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter

We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight \mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity \mu and the bending rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) . The constant K(J) is found to be the same for both types of polygons, suggesting that self-avoiding polygons should also exhibit the same asymptotic behaviour.Comment: 10 pages, 3 figure

Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: I. Turbulence Statistics

Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256^3 and 512^3 simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li, McKee, & Klein (2006). Our calculations are based on the assumption that the number of ions is conserved, but we show that these results approximately apply to the case of time-dependent ionization in molecular clouds as well. Convergence studies allow us to determine the optimal value of the ionization mass fraction when using the heavy-ion approximation for low Mach number, sub-Alfvenic turbulent systems. We find that ambipolar diffusion steepens the velocity and magnetic power spectra compared to the ideal MHD case. Changes in the density PDF, total magnetic energy, and ionization fraction are determined as a function of the AD Reynolds number. The power spectra for the neutral gas properties of a strongly magnetized medium with a low AD Reynolds number are similar to those for a weakly magnetized medium; in particular, the power spectrum of the neutral velocity is close to that for Burgers turbulence.Comment: 37 pages, 11 figures, 4 table

Crossover from hydrodynamic to acoustic drag on quartz tuning forks in normal and superfluid 4He

We present measurements of the drag forces on quartz tuning forks oscillating at low velocities in normal and superfluid 4He. We have investigated the dissipative drag over a wide range of frequencies, from 6.5 to 600 kHz, by using arrays of forks with varying prong lengths and by exciting the forks in their fundamental and first overtone modes. At low frequencies the behavior is dominated by laminar hydrodynamic drag, governed by the fluid viscosity. At higher frequencies acoustic drag is dominant and is described well by a three-dimensional model of sound emission

Incorporation of Sb5+ into CeO2 : local structural distortion of the fluorite structure from a pentavalent substituent

Hydrothermal crystallisation of CeO2 from aqueous sodium hydroxide solution at 240oC using CeCl3·7H2O in the presence of hydrogen peroxide with addition of either SbCl3 or SbCl5 yields polycrystalline samples of antimony-containing ceria directly from solution. Powder X-ray diffraction shows a contraction of the cubic lattice parameter with increasing Sb content, and also a broadening of Bragg peaks, from which Scherrer analysis yields crystallite domain sizes of 5 - 20 nm. Scanning transmission electron microscopy provides consistent results with observation of highly crystalline particles of a few nm in diameter. X-ray absorption near edge structure spectroscopy at the Ce LIII and Sb K edges reveals the presence of Ce4+ and Sb5+ in the solids. To balance charge the presence of co-included Na is proposed, corroborated by elemental analysis. The general chemical formula of the materials can thus be written as (Ce1 xSbx)1 yNayO2-δ (where x < 0.4 and y ≥ x/3). Sb K-edge extended X-ray absorption fine structure spectroscopy of the substituted ceria samples shows that the local structure of Sb resembles that in NaSbO3, where six-coordinate metal sites are found, but with evidence of a longer interatomic correlation due to surrounding Ce/Sb atoms in the fluorite structure; this implies that the Sb is displaced from the ideal eight-coordinate site of the fluorite structure. This structural distortion gives materials that are unstable under reducing conditions, coupled by the ease of reduction to elemental antimony, which is extruded leading to phase separation

Scaling prediction for self-avoiding polygons revisited

We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the bicritical point. We also consider the shape of the critical curve near the bicritical point, which describes the crossover to the branched polymer phase. Our recently conjectured expression for the scaling function of rooted self-avoiding polygons is further supported. For (unrooted) self-avoiding polygons, the analysis reveals the presence of an additional additive term with a new universal amplitude. We conjecture the exact value of this amplitude.Comment: 17 pages, 3 figure

Incorporation of square-planar Pd2+ in fluorite CeO2 : hydrothermal preparation, local structure, redox properties and stability

The direct hydrothermal crystallisation at 240 °C of Pd2+-containing ceria is investigated to study the extent to which precious metal dopants may be introduced into the cubic fluorite lattice. Samples of composition Ce1−xPdxO2−δ, where 0 ≤ x ≤ 0.15 can be produced in which Pd is included within the CeO2 structure to give a linear lattice expansion. Attempts to produce higher Pd2+-substitution result in the formation of PdO as a secondary phase. Ce and Pd were determined to be in the +4 and +2 oxidation states, respectively, by X-ray absorption near edge structure, suggesting oxide deficiency as the mechanism of charge balance. Extended X-ray absorption fine structure (EXAFS) analysis at the Pd K-edge reveals that Pd2+ has local square-planar coordination, as expected, and that a structural model can fitted in which the average fluorite structure is maintained, but with Pd2+ sitting in the square faces of oxide ions present in the local cubic geometry of Ce. This model, consistent with previous modelling studies, gives an excellent fit to the EXAFS spectra, and explains the observed lattice expansion. Transmission electron microscopy analysis shows that Pd is well dispersed in the nanocrystalline ceria particles, and in situ powder XRD shows that upon heating in air the samples remain stable up to 800 °C. H2-TPR shows that Pd-substitution leads to low temperature (<200 °C) reduction of the oxide, which increases in magnitude with increasing Pd-substitution. On prolonged heating, however, the Pd is lost from the ceria lattice to give dispersed Pd metal, suggesting an inherent instability of Pd-doped CeO2

Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers

It is shown that a recently conjectured form for the critical scaling function for planar self-avoiding polygons weighted by their perimeter and area also follows from an exact renormalization group flow into the branched polymer problem, combined with the dimensional reduction arguments of Parisi and Sourlas. The result is generalized to higher-order multicritical points, yielding exact values for all their critical exponents and exact forms for the associated scaling functions.Comment: 5 pages; v2: factors of 2 corrected; v.3: relation with existing theta-point results clarified, some references added/update

Ce(OH)2Cl and lanthanide-substituted variants as precursors to redox-active CeO2 materials

The cerium(III) hydroxide chloride Ce(OH)2Cl crystallises directly as a polycrystalline powder from a solution of CeCl3·7H2O in poly(ethylene) glycol (Mn = 400) heated at 240 °C and is found to be isostructural with La(OH)2Cl, as determined from high-resolution synchrotron powder X-ray diffraction (P21/m, a = 6.2868(2) Å, b = 3.94950(3) Å, c = 6.8740(3) Å, β = 113.5120(5)°). Replacement of a proportion of the cerium chloride in synthesis by a second lanthanide chloride yields a set of materials Ce1−xLnx(OH)2Cl for Ln = La, Pr, Gd, Tb. For La the maximum value of x is 0.2, with an isotropic expansion of the unit cell, but for the other lanthanides a wider composition range is possible, and the lattice parameters show an isotropic contraction with increasing x. Thermal decomposition of the hydroxide chlorides at 700 °C yields mixed-oxides Ce1−xLnxO2−δ that all have cubic fluorite structures with either expanded (Ln = La, Gd) or contracted (Ln = Pr, Tb) unit cells compared to CeO2. Scanning electron microscopy shows a shape memory effect in crystal morphology upon decomposition, with clusters of anisotropic sub-micron crystallites being seen in the precursor and oxide products. The Pr- and Tb-substituted oxides contain the substituent in a mixture of +3 and +4 oxidation states, as seen by X-ray absorption near edge structure spectroscopy at the lanthanide LIII edges. The mixed oxide materials are examined using temperature programmed reduction in 10%H2 in N2, which reveals redox properties suitable for heterogeneous catalysis, with the Pr-substituted materials showing the greatest reducibility at lower temperature