2,851 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
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
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
Economic evaluation of ASCOT-BPLA: Antihypertensive treatment with an amlodipine-based regimen is cost-effective compared to an atenolol-based regimen
Copyright © 2010 BMJ Publishing Group Ltd & British Cardiovascular Society. Internal or personal use of this material is permitted. However, permission to reprint/republish this material must be obtained from the Publisher.Objective: To compare the cost effectiveness of an amlodipine-based strategy and an atenolol-based strategy in the treatment of hypertension in the UK and Sweden.
Design: A prospective, randomised trial complemented with a Markov model to assess long-term costs and health effects.
Setting: Primary care.
Patients: Patients with moderate hypertension and three or more additional risk factors.
Interventions: Amlodipine 5â10 mg with perindopril 4â8 mg added as needed or atenolol 50â100 mg with bendroflumethiazide 1.25â2.5 mg and potassium added as needed
Main outcome measures: Cost per cardiovascular event and procedure avoided, and cost per quality-adjusted life-year gained.
Results: In the UK, the cost to avoid one cardiovascular event or procedure would be âŹ18â965, and the cost to gain one quality-adjusted life-year would be âŹ21â875. The corresponding figures for Sweden were âŹ13â210 and âŹ16â856.
Conclusions: Compared with the thresholds applied by NICE and in the Swedish National Board of Health and Welfareâs Guidelines for Cardiac Care, an amlodipine-based regimen is cost effective for the treatment of hypertension compared with an atenolol-based regimen in the population studied.The study was supported by the principal funding source, Pfizer, New York, USA
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
Supernova cosmology: legacy and future
The discovery of dark energy by the first generation of high-redshift
supernova surveys has generated enormous interest beyond cosmology and has
dramatic implications for fundamental physics. Distance measurements using
supernova explosions are the most direct probes of the expansion history of the
Universe, making them extremely useful tools to study the cosmic fabric and the
properties of gravity at the largest scales. The past decade has seen the
confirmation of the original results. Type Ia supernovae are among the leading
techniques to obtain high-precision measurements of the dark energy equation of
state parameter, and in the near future, its time dependence. The success of
these efforts depends on our ability to understand a large number of effects,
mostly of astrophysical nature, influencing the observed flux at Earth. The
frontier now lies in understanding if the observed phenomenon is due to vacuum
energy, albeit its unnatural density, or some exotic new physics. Future
surveys will address the systematic effects with improved calibration
procedures and provide thousands of supernovae for detailed studies.Comment: Invited review, Annual Review of Nuclear and Particle Science
(submitted version
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
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