1,016 research outputs found
Comparative Evolution of Jupiter and Saturn
We present evolutionary sequences for Jupiter and Saturn, based on new
nongray model atmospheres, which take into account the evolution of the solar
luminosity and partitioning of dense components to deeper layers. The results
are used to set limits on the extent to which possible interior phase
separation of hydrogen and helium may have progressed in the two planets. When
combined with static models constrained by the gravity field, our evolutionary
calculations constrain the helium mass fraction in Jupiter to be between 0.20
and 0.27, relative to total hydrogen and helium. This is in agreement with the
Galileo determination. The helium mass fraction in Saturn's atmosphere lies
between 0.11 and 0.25, higher than the Voyager determination. Based on the
discrepancy between the Galileo and Voyager results for Jupiter, and our
models, we predict that Cassini measurements will yield a higher atmospheric
helium mass fraction for Saturn relative to the Voyager value.Comment: 18 pages, LaTeX, 4 figures. submitted to ``Planetary and Space
Science.'
Conditions for spontaneous homogenization of the Universe
The present-day Universe appears to be homogeneous on very large scales. Yet
when the casual structure of the early Universe is considered, it becomes
apparent that the early Universe must have been highly inhomogeneous. The
current paradigm attempts to answer this problem by postulating the inflation
mechanism However, inflation in order to start requires a homogeneous patch of
at least the horizon size. This paper examines if dynamical processes of the
early Universe could lead to homogenization. In the past similar studies seem
to imply that the set of initial conditions that leads to homogenization is of
measure zero. This essay proves contrary: a set of initial conditions for
spontaneous homogenization of cosmological models can form a set of non-zero
measure.Comment: 7 pages. Fifth Award in the 2010 Gravity Research Foundation essay
competitio
Simultaneous Embeddability of Two Partitions
We study the simultaneous embeddability of a pair of partitions of the same
underlying set into disjoint blocks. Each element of the set is mapped to a
point in the plane and each block of either of the two partitions is mapped to
a region that contains exactly those points that belong to the elements in the
block and that is bounded by a simple closed curve. We establish three main
classes of simultaneous embeddability (weak, strong, and full embeddability)
that differ by increasingly strict well-formedness conditions on how different
block regions are allowed to intersect. We show that these simultaneous
embeddability classes are closely related to different planarity concepts of
hypergraphs. For each embeddability class we give a full characterization. We
show that (i) every pair of partitions has a weak simultaneous embedding, (ii)
it is NP-complete to decide the existence of a strong simultaneous embedding,
and (iii) the existence of a full simultaneous embedding can be tested in
linear time.Comment: 17 pages, 7 figures, extended version of a paper to appear at GD 201
Robust computations with dynamical systems
In this paper we discuss the computational power of Lipschitz
dynamical systems which are robust to in nitesimal perturbations.
Whereas the study in [1] was done only for not-so-natural systems from
a classical mathematical point of view (discontinuous di erential equation
systems, discontinuous piecewise a ne maps, or perturbed Turing
machines), we prove that the results presented there can be generalized
to Lipschitz and computable dynamical systems.
In other words, we prove that the perturbed reachability problem (i.e. the
reachability problem for systems which are subjected to in nitesimal perturbations)
is co-recursively enumerable for this kind of systems. Using
this result we show that if robustness to in nitesimal perturbations is
also required, the reachability problem becomes decidable. This result
can be interpreted in the following manner: undecidability of veri cation
doesn't hold for Lipschitz, computable and robust systems.
We also show that the perturbed reachability problem is co-r.e. complete
even for C1-systems
A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator
This paper presents a complete algebraic proof of the renormalizability of
the gauge invariant operator to all orders of
perturbation theory in pure Yang-Mills gauge theory, whereby working in the
Landau gauge. This renormalization is far from being trivial as mixing occurs
with other gauge variant operators, which we identify explicitly. We
determine the mixing matrix to all orders in perturbation theory by using
only algebraic arguments and consequently we can uncover a renormalization
group invariant by using the anomalous dimension matrix derived from
. We also present a future plan for calculating the mass of the lightest
scalar glueball with the help of the framework we have set up.Comment: 17 page
A fitter code for Deep Virtual Compton Scattering and Generalized Parton Distributions
We have developped a fitting code based on the leading-twist handbag Deep
Virtual Compton Scattering (DVCS) amplitude in order to extract the Generalized
Parton Distributions (GPD) information from DVCS observables in the valence
region. In a first stage, with simulations and pseudo-data, we show that the
full GPD information can be recovered from experimental data if enough
observables are measured. If only part of these observables are measured,
valuable information can still be extracted, certain observables being
particularly sensitive to certain GPDs. In a second stage, we make a practical
application of this code to the recent DVCS Jefferson Lab Hall A data from
which we can extract numerical constraints for the two GPD Compton Form
Factors.Comment: 15 pages, 8 figure
Implication of the overlap representation for modelling generalized parton distributions
Based on a field theoretically inspired model of light-cone wave functions,
we derive valence-like generalized parton distributions and their double
distributions from the wave function overlap in the parton number conserved
s-channel. The parton number changing contributions in the t-channel are
restored from duality. In our construction constraints of positivity and
polynomiality are simultaneously satisfied and it also implies a model
dependent relation between generalized parton distributions and transverse
momentum dependent parton distribution functions. The model predicts that the
t-behavior of resulting hadronic amplitudes depends on the Bjorken variable
x_Bj. We also propose an improved ansatz for double distributions that embeds
this property.Comment: 15 pages, 8 eps figure
Solving analytic differential equations in polynomial time over unbounded domains
In this paper we consider the computational complexity of solving initial-value problems de ned with analytic ordinary diferential
equations (ODEs) over unbounded domains of Rn and Cn, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of de nition, provided it satis es a very generous bound on its growth, and that the function admits an analytic extension to the complex plane
Riluzole for relapse prevention following intravenous ketamine in treatment-resistant depression:a pilot randomized, placebo-controlled continuation trial
The N-methyl-D-aspartate (NMDA) glutamate receptor antagonist ketamine may have rapid, albeit transient, antidepressant properties. This study in patients with treatment-resistant major depression (TRD) aimed to (1) replicate the acute efficacy of single-close intravenous (i.v.) ketamine; (2) test the efficacy of the glutamate-modulating agent riluzole in preventing post-ketamine relapse; and (3) examine whether pretreatment with lamotrigine would attenuate ketamine's psychotomimetic effects and enhance its antidepressant activity. Twenty-six medication-free patients received open-label i.v. ketamine (0.5 mg/kg over 40 min). Two hours prior to infusion, patients were randomized to lamotrigine (300 mg) or placebo. Seventeen patients (65%,) met response criterion (>= 50% reduction from baseline on the Montgomery-Asberg Depression Rating Scale) 24 h following ketamine. Lamotrigine failed to attenuate the mild, transient side-effects associated with ketamine and did not enhance its antidepressant effects. Fourteen patients (54%) met response criterion 72 h following ketamine and proceeded to participate in a 32-d, randomized, double-blind, placebo-controlled, flexible-dose continuation trial of riluzole (100-200 mg/d). The main outcome measure was time-to-relapse. An interim analysis found no significant differences in time-to-relapse between riluzole and placebo groups [log-rank chi(2) = 0.17, d.f. = 1, p = 0.68], with 80% of patients relapsing on riluzole vs. 50% on placebo. The trial was thus stopped for futility. This pilot study showed that a sub-anaesthetic close of i.v. ketamine is well-tolerated in TRD, and may have rapid and sustained antidepressant properties. Riluzole did not prevent relapse in the first month following ketamine. Further investigation of relapse prevention strategies post-ketamine is necessary
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