2,948 research outputs found
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 rather than 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 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- 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
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
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,
.As long as the salt content is low and is longer
than the end-to-end distance, the electrostatic persistence length varies only
slowly with . Decreasing the screening length, a controversial
region is entered. We find that the electrostatic persistence length scales as
, in agreement with experiment on flexible
polyelectrolytes, where is a strength parameter measuring the
electrostatic interactions within the polyelectrolyte. For screening lengths
much shorter than the bond length, the 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 in agreement with earlier theories.Comment: 20 pages LaTeX, 9 postscript figure
Isotope Shifts in Beryllium-, Boron-, Carbon-, and Nitrogen-like Ions from Relativistic Configuration Interaction Calculations
Energy levels, normal and specific mass shift parameters as well as
electronic densities at the nucleus are reported for numerous states along the
beryllium, boron, carbon, and nitrogen isoelectronic sequences. Combined with
nuclear data, these electronic parameters can be used to determine values of
level and transition isotope shifts. The calculation of the electronic
parameters is done using first-order perturbation theory with relativistic
configuration interaction wave functions that account for valence, core-valence
and core-core correlation effects as zero-order functions. Results are compared
with experimental and other theoretical values, when available.Comment: 56 pages, 1 figure, Atomic Data and Nuclear Data Tables (2014
Large-scale Multiconfiguration Hartree-fock and Configuration-interaction Calculations of Isotope Shifts and Hyperfine Structures In Boron
A new isotope shift program, part of the multiconfiguration Hartree-Fock (MCHF) atomic structure package, has been written and tested. The program calculates the isotope shift of an atomic level from MCHF or configuration-interaction (CI) wave functions. The program is specially designed to be used with very large CI expansions, for which angular data cannot be stored on disk. To explore the capacity of the program, large-scale isotope shift calculations were performed for the 1s(2)2s(2)2p 2P, 1s(2)2s(2)3s2S, and 1s(2)2s2p2 2D levels in boron. From the isotope shifts of these levels the transition isotope shifts were calculated for the two resonance transitions. The calculated transition isotope shifts are in very good agreement with experimental shifts. As an additional test of the quality of the CI wave functions, the hyperfine structure was calculated for all levels
Large-scale Multiconfiguration Hartree-fock Calculations of Hyperfine-interaction Constants For Low-lying States In Beryllium, Boron, and Carbon
Multiconfiguration Hartree-Fock (MCHF) calculations of hyperfine constants for the 2s2p 3P states of beryllium and the ground states of boron and carbon are reported. The capacity of a recently developed configuration-interaction program [Froese Fischer and Tong (unpublished); Stathopoulos and Froese Fischer (unpublished)], allowing for large configuration expansions, is explored. Using a systematic active-space MCHF approach, combined with large multireference configuration-interaction calculations, it is shown that hyperfine constants can be calculated very accurately. To reliably account for spin-polarization of the Is and 2s shells in boron and carbon, three-particle effects had to be included in a systematic way. The relativistic, finite-nuclear-size- and finite-nuclear-mass-corrected values of the hyperfine constants are compared with experimental values and with the most accurate theoretical values obtained with other methods
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
Constraining dark matter halo properties using lensed SNLS supernovae
This paper exploits the gravitational magnification of SNe Ia to measure
properties of dark matter haloes. The magnification of individual SNe Ia can be
computed using observed properties of foreground galaxies and dark matter halo
models. We model the dark matter haloes of the galaxies as truncated singular
isothermal spheres with velocity dispersion and truncation radius obeying
luminosity dependent scaling laws. A homogeneously selected sample of 175 SNe
Ia from the first 3-years of the Supernova Legacy Survey (SNLS) in the redshift
range 0.2 < z < 1 is used to constrain models of the dark matter haloes
associated with foreground galaxies. The best-fitting velocity dispersion
scaling law agrees well with galaxy-galaxy lensing measurements. We further
find that the normalisation of the velocity dispersion of passive and star
forming galaxies are consistent with empirical Faber-Jackson and Tully-Fisher
relations, respectively. If we make no assumption on the normalisation of these
relations, we find that the data prefer gravitational lensing at the 92 per
cent confidence level. Using recent models of dust extinction we deduce that
the impact of this effect on our results is very small. We also investigate the
brightness scatter of SNe Ia due to gravitational lensing. The gravitational
lensing scatter is approximately proportional to the SN Ia redshift. We find
the constant of proportionality to be B = 0.055 +0.039 -0.041 mag (B < 0.12 mag
at the 95 per cent confidence level). If this model is correct, the
contribution from lensing to the intrinsic brightness scatter of SNe Ia is
small for the SNLS sample.Comment: 11 pages, 7 figures, accepted for publication in MNRA
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
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