A Variational Approach to the Structure and Thermodynamics of Linear Polyelectrolytes with Coulomb and Screened Coulomb Interactions

A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between {\em all}monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as $N^3$ rather than $N^4$ as expected in a more naive approach. The method has the additional advantage that in contrast to Monte Carlo calculations the entropy is easily computed. An analysis of the high and low temperature limits is given. Also, the variational formulation is shown to respect the appropriate virial identities.The accuracy of the approximations introduced are tested against Monte Carlo simulations for problem sizes ranging from $N=20$ to 1024. Very good accuracy is obtained for chains with unscreened Coulomb interactions. The addition of salt is described through a screened Coulomb interaction, for which the accuracy in a certain parameter range turns out to be inferior to the unscreened case. The reason is that the harmonic variational Ansatz becomes less efficient with shorter range interactions. As a by-product a very efficient Monte Carlo algorithm was developed for comparisons, providing high statistics data for very large sizes -- 2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on low-$T$ approximations to end-end and monomer-monomer separations. It is argued that the former increases faster than linearly with the number of bonds.Comment: 40 pages LaTeX, 13 postscript figure

The Electrostatic Persistence Length Calculated from Monte Carlo, Variational and Perturbation Methods

Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. For the flexible model the electrostatic persistence length shows roughly three regimes in its dependence on the Debye-H\"{u}ckel screening length, $\kappa^{-1}$.As long as the salt content is low and $\kappa^{-1}$ is longer than the end-to-end distance, the electrostatic persistence length varies only slowly with $\kappa^{-1}$. Decreasing the screening length, a controversial region is entered. We find that the electrostatic persistence length scales as $sqrt{\xi_p}/\kappa$, in agreement with experiment on flexible polyelectrolytes, where $\xi_p$ is a strength parameter measuring the electrostatic interactions within the polyelectrolyte. For screening lengths much shorter than the bond length, the $\kappa^{-1}$ dependence becomes quadratic in the variational calculation. The simulations suffer from numerical problems in this regime, but seem to give a relationship half-way between linear and quadratic. A low temperature expansion only reproduces the first regime and a high temperature expansion, which treats the electrostatic interactions as a perturbation to a Gaussian chain, gives a quadratic dependence on the Debye length. For a sufficiently stiff chain, the persistence length varies quadratically with $\kappa^{-1}$ in agreement with earlier theories.Comment: 20 pages LaTeX, 9 postscript figure

Delensing Gravitational Wave Standard Sirens with Shear and Flexion Maps

Supermassive black hole binary systems (SMBHB) are standard sirens -- the gravitational wave analogue of standard candles -- and if discovered by gravitational wave detectors, they could be used as precise distance indicators. Unfortunately, gravitational lensing will randomly magnify SMBHB signals, seriously degrading any distance measurements. Using a weak lensing map of the SMBHB line of sight, we can estimate its magnification and thereby remove some uncertainty in its distance, a procedure we call "delensing." We find that delensing is significantly improved when galaxy shears are combined with flexion measurements, which reduce small-scale noise in reconstructed magnification maps. Under a Gaussian approximation, we estimate that delensing with a 2D mosaic image from an Extremely Large Telescope (ELT) could reduce distance errors by about 30-40% for a SMBHB at z=2. Including an additional wide shear map from a space survey telescope could reduce distance errors by 50%. Such improvement would make SMBHBs considerably more valuable as cosmological distance probes or as a fully independent check on existing probes.Comment: 9 pages, 4 figures, submitted to MNRA

A Variational Approach for Minimizing Lennard-Jones Energies

A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, {\it rotors}, and consists in the iterative solution of a set of deterministic equations with annealing in temperature. The singular short-distance behaviour of the Lennard-Jones potential is adiabatically switched on in order to obtain stable convergence. As testbeds for the approach two distinct ensembles of molecules are used, characterized by a roughly dense-packed ore a more elongated ground state. For the latter, problems are generated from natural frequencies of occurrence of amino acids and phenomenologically determined potential parameters; they seem to represent less disorder than was previously assumed in synthetic protein studies. For the dense-packed problems in particular, the variational algorithm clearly outperforms a gradient descent method in terms of minimal energies. Although it cannot compete with a careful simulating annealing algorithm, the variational approach requires only a tiny fraction of the computer time. Issues and results when applying the method to polyelectrolytes at a finite temperature are also briefly discussed.Comment: 14 pages, uuencoded compressed postscript fil

Detailed Abundances for the Old Population near the Galactic Center: I. Metallicity distribution of the Nuclear Star Cluster

We report the first high spectral resolution study of 17 M giants kinematically confirmed to lie within a few parsecs of the Galactic Center, using R=24,000 spectroscopy from Keck/NIRSPEC and a new linelist for the infrared K band. We consider their luminosities and kinematics, which classify these stars as members of the older stellar population and the central cluster. We find a median metallicity of =-0.16 and a large spread from approximately -0.3 to +0.3 (quartiles). We find that the highest metallicities are [Fe/H]<+0.6, with most of the stars being at or below the Solar iron abundance. The abundances and the abundance distribution strongly resembles that of the Galactic bulge rather than disk or halo; in our small sample we find no statistical evidence for a dependence of velocity dispersion on metallicity.Comment: 18 pages, 14 figures, accepted for publication in A

Absence of Conventional Spin-Glass Transition in the Ising Dipolar System LiHo_xY_{1-x}F_4

The magnetic properties of single crystals of LiHo_xY_{1-x}F_4 with x=16.5% and x=4.5% were recorded down to 35 mK using a micro-SQUID magnetometer. While this system is considered as the archetypal quantum spin glass, the detailed analysis of our magnetization data indicates the absence of a phase transition, not only in a transverse applied magnetic field, but also without field. A zero-Kelvin phase transition is also unlikely, as the magnetization seems to follow a non-critical exponential dependence on the temperature. Our analysis thus unmasks the true, short-ranged nature of the magnetic properties of the LiHo_xY_{1-x}F_4 system, validating recent theoretical investigations suggesting the lack of phase transition in this system.Comment: 5 pages, 4 figure

Evidence against anomalous compositions for giants in the Galactic Nuclear Star Cluster

Very strong Sc I lines have been found recently in cool M giants in the Nuclear Star Cluster in the Galactic Center. Interpreting these as anomalously high scandium abundances in the Galactic Center would imply a unique enhancement signature and chemical evolution history for nuclear star clusters, and a potential test for models of chemical enrichment in these objects. We present high resolution K-band spectra (NIRSPEC/Keck II) of cool M giants situated in the solar neighborhood and compare them with spectra of M giants in the Nuclear Star Cluster. We clearly identify strong Sc I lines in our solar neighborhood sample as well as in the Nuclear Star Cluster sample. The strong Sc I lines in M giants are therefore not unique to stars in the Nuclear Star Cluster and we argue that the strong lines are a property of the line formation process that currently escapes accurate theoretical modeling. We further conclude that for giant stars with effective temperatures below approximately 3800 K these Sc I lines should not be used for deriving the scandium abundances in any astrophysical environment until we better understand how these lines are formed. We also discuss the lines of vanadium, titanium, and yttrium identified in the spectra, which demonstrate a similar striking increase in strength below 3500 K effective temperature.Comment: 11 pages, 6 figures, accepted for publication in Ap

Extended calculations of energy levels, radiative properties, AJA_{J}, BJB_{J} hyperfine interaction constants, and Land\'e gJg_{J}-factors for nitrogen-like \mbox{Ge XXVI}

Employing two state-of-the-art methods, multiconfiguration Dirac--Hartree--Fock and second-order many-body perturbation theory, highly accurate calculations are performed for the lowest 272 fine-structure levels arising from the $2s^{2} 2p^{3}$, $2s 2p^{4}$, $2p^{5}$, $2s^{2} 2p^{2} 3l$~($l=s,p,d$), $2s 2p^{3}3l$ ($l=s,p,d$), and $2p^{4} 3l$ ($l=s,p,d$) configurations in nitrogen-like Ge XXVI. Complete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Land\'e $g_{J}$-factors, and E1, E2, M1, M2 line strengths, oscillator strengths, and transition rates among these 272 levels are provided. Comparisons are made between the present two data sets, as well as with other available experimental and theoretical values. The present data are accurate enough for identification and deblending of emission lines involving the $n=3$ levels, and are also useful for modeling and diagnosing fusion plasmas

Extended Calculations of Spectroscopic Data: Energy Levels, Lifetimes and Transition rates for O-like ions from Cr XVII to Zn XXIII

Employing two state-of-the-art methods, multiconfiguration Dirac--Hartree--Fock and second-order many-body perturbation theory, the excitation energies and lifetimes for the lowest 200 states of the $2s^2 2p^4$, $2s 2p^5$, $2p^6$, $2s^2 2p^3 3s$, $2s^2 2p^3 3p$, $2s^2 2p^3 3d$, $2s 2p^4 3s$, $2s 2p^4 3p$, and $2s 2p^4 3d$ configurations, and multipole (electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2)) transition rates, line strengths, and oscillator strengths among these states are calculated for each O-like ion from Cr XVII to Zn XXIII. Our two data sets are compared with the NIST and CHIANTI compiled values, and previous calculations. The data are accurate enough for identification and deblending of new emission lines from the sun and other astrophysical sources. The amount of data of high accuracy is significantly increased for the $n = 3$ states of several O-like ions of astrophysics interest, where experimental data are very scarce