32,718 research outputs found
Semiclassical collision theory. Multidimensional Bessel uniform approximation
A multidimensional Bessel uniform approximation for the semiclassical S matrix is derived for the case of four real stationary phase points. A formula is also developed for the particular case when four stationary phase points may be considered to be well separated in pairs. The latter equation is then used in the treatment of two real and two complex stationary phase points
Semiclassical collision theory. Application of multidimensional uniform approximations to the atom-rigid-rotor system
The multidimensional Bessel and Airy uniform approximations developed earlier in this series for the semiclassical S matrix are applied to the atom rigid−rotor system. The need is shown for (a) using a geoemetrical criterion for determining whether a stationary phase point (s.p.pt) is a maximum, minimum, or saddle point; (b) choosing a proper quadrilateral configuration of the s.p.pts. with the phases as nearly equal as possible; and (c) choosing a unit cell to favor near−separation of variables. (a) and (b) apply both to the Airy and to the Bessel uniform approximations, and (c) to the Bessel. The use of a contour plot both to understand and to facilitate the search in new cases is noted. The case of real and complex−valued stationary phase points is also considered, and the Bessel uniform−in−pairs approximation is applied. Comparison is made with exact quantum results. As in the one−dimensional case, the Bessel is an improvement over the Airy for ’’k = 0’’ transitions, while for other transitions they give similar results. Comparison in accuracy with the results of the integral method is also given. As a whole, the agreement can be considered to be reasonable. The improvement of the present over various more approximate results is shown
Integrability of irrotational silent cosmological models
We revisit the issue of integrability conditions for the irrotational silent
cosmological models. We formulate the problem both in 1+3 covariant and 1+3
orthonormal frame notation, and show there exists a series of constraint
equations that need to be satisfied. These conditions hold identically for
FLRW-linearised silent models, but not in the general exact non-linear case.
Thus there is a linearisation instability, and it is highly unlikely that there
is a large class of silent models. We conjecture that there are no spatially
inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate
further issues that await clarification.Comment: Minor corrections and improvements; 1 new reference; to appear Class.
Quantum Grav.; 16 pages Ioplpp
Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
In this paper we give a complete analysis of the phase transitions in the
mean-field Blume-Emery-Griffiths lattice-spin model with respect to the
canonical ensemble, showing both a second-order, continuous phase transition
and a first-order, discontinuous phase transition for appropriate values of the
thermodynamic parameters that define the model. These phase transitions are
analyzed both in terms of the empirical measure and the spin per site by
studying bifurcation phenomena of the corresponding sets of canonical
equilibrium macrostates, which are defined via large deviation principles.
Analogous phase transitions with respect to the microcanonical ensemble are
also studied via a combination of rigorous analysis and numerical calculations.
Finally, probabilistic limit theorems for appropriately scaled values of the
total spin are proved with respect to the canonical ensemble. These limit
theorems include both central-limit-type theorems when the thermodynamic
parameters are not equal to critical values and non-central-limit-type theorems
when these parameters equal critical values.Comment: 33 pages, revtex
Birkhoff Theorem and Matter
Birkhoff's theorem for spherically symmetric vacuum spacetimes is a key
theorem in studying local systems in general relativity theory. However
realistic local systems are only approximately spherically symmetric and only
approximately vacuum. In a previous paper, we showed the theorem remains
approximately true in an approximately spherically symmetric vacuum space time.
In this paper we prove the converse case: the theorem remains approximately
true in a spherically symmetric, approximately vacuum space time.Comment: 7 pages, Revtex
Generalized canonical ensembles and ensemble equivalence
This paper is a companion article to our previous paper (J. Stat. Phys. 119,
1283 (2005), cond-mat/0408681), which introduced a generalized canonical
ensemble obtained by multiplying the usual Boltzmann weight factor of the canonical ensemble with an exponential factor involving a continuous
function of the Hamiltonian . We provide here a simplified introduction
to our previous work, focusing now on a number of physical rather than
mathematical aspects of the generalized canonical ensemble. The main result
discussed is that, for suitable choices of , the generalized canonical
ensemble reproduces, in the thermodynamic limit, all the microcanonical
equilibrium properties of the many-body system represented by even if this
system has a nonconcave microcanonical entropy function. This is something that
in general the standard () canonical ensemble cannot achieve. Thus a
virtue of the generalized canonical ensemble is that it can be made equivalent
to the microcanonical ensemble in cases where the canonical ensemble cannot.
The case of quadratic -functions is discussed in detail; it leads to the
so-called Gaussian ensemble.Comment: 8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title
changed, references updated, new paragraph added, minor differences with
published versio
Dark Matter in SuperGUT Unification Models
After a brief update on the prospects for dark matter in the constrained
version of the MSSM (CMSSM) and its differences with models based on minimal
supergravity (mSUGRA), I will consider the effects of unifying the
supersymmetry-breaking parameters at a scale above M_{GUT}. One of the
consequences of superGUT unification, is the ability to take vanishing scalar
masses at the unification scale with a neutralino LSP dark matter candidate.
This allows one to resurrect no-scale supergravity as a viable phenomenological
model.Comment: 12 pages, 16 figures, To be published in the Proceedings of the 6th
DSU Conference, Leon, Mexico, ed. D. Delepin
Numerical evaluation of one-loop QCD amplitudes
We present the publicly available program NGluon allowing the numerical
evaluation of primitive amplitudes at one-loop order in massless QCD. The
program allows the computation of one-loop amplitudes for an arbitrary number
of gluons. The focus of the present article is the extension to one-loop
amplitudes including an arbitrary number of massless quark pairs. We discuss in
detail the algorithmic differences to the pure gluonic case and present cross
checks to validate our implementation. The numerical accuracy is investigated
in detail.Comment: Talk given at ACAT 2011 conference in London, 5-9 Septembe
Local freedom in the gravitational field
In a cosmological context, the electric and magnetic parts of the Weyl
tensor, E_{ab} and H_{ab}, represent the locally free curvature - i.e. they are
not pointwise determined by the matter fields. By performing a complete
covariant decomposition of the derivatives of E_{ab} and H_{ab}, we show that
the parts of the derivative of the curvature which are locally free (i.e. not
pointwise determined by the matter via the Bianchi identities) are exactly the
symmetrised trace-free spatial derivatives of E_{ab} and H_{ab} together with
their spatial curls. These parts of the derivatives are shown to be crucial for
the existence of gravitational waves.Comment: New results on gravitational waves included; new references added;
revised version (IOP style) to appear Class. Quantum Gra
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Developmental changes in the germinability, desiccation tolerance, hardseededness, and longevity of individual seeds of Trifolium ambiguum
Background and Aims: Using two parental clones of outcrossing Trifolium ambiguum as a potential model system, we examined how during seed development the maternal parent, number of seeds per pod, seed position within the pod, and pod position within the inflorescence influenced individual seed fresh weight, dry weight, water content, germinability, desiccation tolerance, hardseededness, and subsequent longevity of individual seeds.
Methods: Near simultaneous, manual reciprocal crosses were carried out between clonal lines for two experiments. Infructescences were harvested at intervals during seed development. Each individual seed was weighed and then used to determine dry weight or one of the physiological behaviour traits.
Key Results: Whilst population mass maturity was reached at 33–36 days after pollination (DAP), seed-to-seed variation in maximum seed dry weight, when it was achieved, and when maturation drying commenced, was considerable. Individual seeds acquired germinability between 14 and 44 DAP, desiccation tolerance between 30 and 40 DAP, and the capability to become hardseeded between 30 and 47 DAP. The time for viability to fall to 50 % (p50) at 60 % relative humidity and 45 °C increased between 36 and 56 DAP, when the seed coats of most individuals had become dark orange, but declined thereafter. Individual seed f. wt at harvest did not correlate with air-dry storage survival period. Analysing survival data for cohorts of seeds reduced the standard deviation of the normal distribution of seed deaths in time, but no sub-population showed complete uniformity of survival period.
Conclusions: Variation in individual seed behaviours within a developing population is inherent and inevitable. In this outbreeder, there is significant variation in seed longevity which appears dependent on embryo genotype with little effect of maternal genotype or architectural factors
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