53,452 research outputs found

### Trace functions as Laplace transforms

We study trace functions on the form t\to\tr f(A+tB) where $f$ is a
real function defined on the positive half-line, and $A$ and $B$ are
matrices such that $A$ is positive definite and $B$ is positive
semi-definite. If $f$ is non-negative and operator monotone decreasing, then
such a trace function can be written as the Laplace transform of a positive
measure. The question is related to the Bessis-Moussa-Villani conjecture.
Key words: Trace functions, BMV-conjecture.Comment: Minor change of style, update of referenc

### Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem

We describe the structure of bifurcations in the unbounded classical
Diamagnetic Kepler problem. We conjecture that this system does not have any
stable orbits and that the non-wandering set is described by a complete trinary
symbolic dynamics for scaled energies larger then $\epsilon_c=0.328782\ldots$.Comment: 15 pages PostScript uuencoded with figure

### A fundamental measure theory for the sticky hard sphere fluid

We construct a density functional theory (DFT) for the sticky hard sphere
(SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the
hard sphere fluid [Phys. Rev. Lett. {\bf 63}, 980 (1989)], is based on a set of
weighted densities and an exact result from scaled particle theory (SPT). It is
demonstrated that the excess free energy density of the inhomogeneous SHS fluid
$\Phi_{\text{SHS}}$ is uniquely defined when (a) it is solely a function of the
weighted densities from Kierlik and Rosinberg's version of FMT [Phys. Rev. A
{\bf 42}, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c)
it yields any given direct correlation function (DCF) from the class of
generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J.
Chem. Phys. {\bf 120}, 4742 (2004)]. The resulting DFT is shown to be in very
good agreement with simulation data. In particular, this FMT yields the correct
contact value of the density profiles with no adjustable parameters. Rather
than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT
produces them. Interestingly, although equivalent to Kierlik and Rosinberg's
FMT in the case of hard spheres, the set of weighted densities used for
Rosenfeld's original FMT is insufficient for constructing a DFT which yields
the SHS DCF.Comment: 11 pages, 3 figure

### Alternative method to find orbits in chaotic systems

We present here a new method which applies well ordered symbolic dynamics to
find unstable periodic and non-periodic orbits in a chaotic system. The method
is simple and efficient and has been successfully applied to a number of
different systems such as the H\'enon map, disk billiards, stadium billiard,
wedge billiard, diamagnetic Kepler problem, colinear Helium atom and systems
with attracting potentials. The method seems to be better than earlier applied
methods.Comment: 5 pages, uuencoded compressed tar PostScript fil

### Random Phase Approximation and Extensions Applied to a Bosonic Field Theory

An application of a self-consistent version of RPA to quantum field theory
with broken symmetry is presented. Although our approach can be applied to any
bosonic field theory, we specifically study the $\phi^4$ theory in 1+1
dimensions. We show that standard RPA approach leads to an instability which
can be removed when going to a superior version,i.e. the renormalized RPA. We
present a method based on the so-called charging formula of the many electron
problem to calculate the correlation energy and the RPA effective potential.Comment: 30 pages, LaTeX file, 10 figures included, final version accepted in
EPJ

### Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps

A density functional theory for colloidal dynamics is presented which
includes hydrodynamic interactions between the colloidal particles. The theory
is applied to the dynamics of colloidal particles in an optical trap which
switches periodically in time from a stable to unstable confining potential. In
the absence of hydrodynamic interactions, the resulting density breathing mode,
exhibits huge oscillations in the trap center which are almost completely
damped by hydrodynamic interactions. The predicted dynamical density fields are
in good agreement with Brownian dynamics computer simulations

### The health state preferences and logistical inconsistencies of New Zealanders: a tale of two tariffs

Notwithstanding the proposed use of Cost-Utility Analysis (CUA) to inform health care priority setting in New Zealand, to date there has been no research into New Zealandersâ valuations of health-related quality of life. This paper reports the results of a study of the health state preferences of adult New Zealanders generated from a postal survey to which 1360 people responded (a 50% response rate). The survey employed a self-completed questionnaire in which a selection of health states were described using the EQ-5D health state classification system and respondentsâ valuations were sought using a visual analogue scale (VAS). Close attention is paid to the quality of the data, in particular to the âlogical inconsistenciesâ in respondentsâ valuations. Regression analysis is used to interpolate values over the 245 possible EQ-5D states. Two tariffs of health state preferences, arising from contrasting treatments of the logical inconsistencies, are reported.New Zealand, EuroQol, EQ-5D

### On the nonlocal viscosity kernel of mixtures

In this report we investigate the multiscale hydrodynamical response of a
liquid as a function of mixture composition. This is done via a series of
molecular dynamics simulations where the wave vector dependent viscosity kernel
is computed for three mixtures each with 7-15 different compositions. We
observe that the nonlocal viscosity kernel is dependent on composition for
simple atomic mixtures for all the wave vectors studied here, however, for a
model polymer melt mixture the kernel is independent of composition for large
wave vectors. The deviation from ideal mixing is also studied. Here it is shown
that a Lennard-Jones mixture follows the ideal mixing rule surprisingly well
for a large range of wave vectors, whereas for both the Kob-Andersen mixture
and the polymer melt large deviations are found. Furthermore, for the polymer
melt the deviation is wave vector dependent such that there exists a critical
length scale at which the ideal mixing goes from under-estimating to
over-estimating the viscosity

### Particle ejection during mergers of dark matter halos

Dark matter halos are built from accretion and merging. During merging some
of the dark matter particles may be ejected with velocities higher than the
escape velocity. We use both N-body simulations and single-particle
smooth-field simulations to demonstrate that rapid changes to the mean field
potential are responsible for such ejection, and in particular that dynamical
friction plays no significant role in it. Studying a range of minor mergers, we
find that typically between 5-15% of the particles from the smaller of the two
merging structures are ejected. We also find that the ejected particles
originate essentially from the small halo, and more specifically are particles
in the small halo which pass later through the region in which the merging
occurs.Comment: 18 pages, 12 figures. Accepted for publication in JCA

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