72 research outputs found
The Massive Multi-flavor Schwinger Model
QED with N species of massive fermions on a circle of circumference L is
analyzed by bosonization. The problem is reduced to the quantum mechanics of
the 2N fermionic and one gauge field zero modes on the circle, with nontrivial
interactions induced by the chiral anomaly and fermions masses. The solution is
given for N=2 and fermion masses (m) much smaller than the mass of the U(1)
boson with mass \mu=\sqrt{2e^2/\pi} when all fermions satisfy the same boundary
conditions. We show that the two limits m \go 0 and L \go \infty fail to
commute and that the behavior of the theory critically depends on the value of
mL|\cos\onehalf\theta| where \theta is the vacuum angle parameter. When the
volume is large \mu L \gg 1, the fermion condensate is
-(e^{4\gamma} m\mu^2 \cos^4\onehalf\theta/4\pi^3)^{1/3} or $-2e^\gamma m\mu L
\cos^2 \onehalf\theta /\pi^2 for mL(\mu L)^{1/2} |\cos\onehalf\theta| \gg 1 or
\ll 1, respectively. Its correlation function decays algebraically with a
critical exponent \eta=1 when m\cos\onehalf\theta=0.Comment: 16 pages, latex, uses epsf.sty; replaced with latex src
Conformally flat spacetimes and Weyl frames
We discuss the concepts of Weyl and Riemann frames in the context of metric
theories of gravity and state the fact that they are completely equivalent as
far as geodesic motion is concerned. We apply this result to conformally flat
spacetimes and show that a new picture arises when a Riemannian spacetime is
taken by means of geometrical gauge transformations into a Minkowskian flat
spacetime. We find out that in the Weyl frame gravity is described by a scalar
field. We give some examples of how conformally flat spacetime configurations
look when viewed from the standpoint of a Weyl frame. We show that in the
non-relativistic and weak field regime the Weyl scalar field may be identified
with the Newtonian gravitational potential. We suggest an equation for the
scalar field by varying the Einstein-Hilbert action restricted to the class of
conformally-flat spacetimes. We revisit Einstein and Fokker's interpretation of
Nordstr\"om scalar gravity theory and draw an analogy between this approach and
the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as
viewed in the Weyl frame and address the question of quantizing a conformally
flat spacetime by going to the Weyl frame.Comment: LATEX - 18 page
Variations on the Seventh Route to Relativity
As motivated in the full abstract, this paper further investigates Barbour,
Foster and O Murchadha (BFO)'s 3-space formulation of GR. This is based on
best-matched lapse-eliminated actions and gives rise to several theories
including GR and a conformal gravity theory. We study the simplicity postulates
assumed in BFO's work and how to weaken them, so as to permit the inclusion of
the full set of matter fields known to occur in nature.
We study the configuration spaces of gravity-matter systems upon which BFO's
formulation leans. In further developments the lapse-eliminated actions used by
BFO become impractical and require generalization. We circumvent many of these
problems by the equivalent use of lapse-uneliminated actions, which furthermore
permit us to interpret BFO's formulation within Kuchar's generally covariant
hypersurface framework. This viewpoint provides alternative reasons to BFO's as
to why the inclusion of bosonic fields in the 3-space approach gives rise to
minimally-coupled scalar fields, electromagnetism and Yang--Mills theory. This
viewpoint also permits us to quickly exhibit further GR-matter theories
admitted by the 3-space formulation. In particular, we show that the spin-1/2
fermions of the theories of Dirac, Maxwell--Dirac and Yang--Mills--Dirac, all
coupled to GR, are admitted by the generalized 3-space formulation we present.
Thus all the known fundamental matter fields can be accommodated. This
corresponds to being able to pick actions for all these theories which have
less kinematics than suggested by the generally covariant hypersurface
framework. For all these theories, Wheeler's thin sandwich conjecture may be
posed, rendering them timeless in Barbour's sense.Comment: Revtex version; Journal-ref adde
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
Aliens in Antarctica: Accessing transfer of plant propagules by human visitors to reduce invasion risk
Despite considerable research on biological invasions, key areas remain poorly explored, especially ways to reduce unintentional propagule transfer. The Antarctic represents a microcosm of the situation, with the numbers of established non-native species growing. Information to help reduce potential impacts is therefore critical. We measured the propagule load of seeds, and fragments of bryophytes and lichens (the number of other plant or animal fragments was too low to draw any conclusions) carried in the clothing and gear of visitors to the Antarctic, during the 2007/08 austral summer. Samples were collected from different categories of visitors associated with national research programs and tourism and different categories of clothing and gear, new as well as used. We also collected information about the timing of travel and the regions visitors had travelled to prior to Antarctic travel. Seeds were found in 20% and 45% of tourist and science visitor samples, respectively. For bryophyte and lichen fragments the proportions were 11% and 20%, respectively. Footwear, trousers and bags belonging to field scientists were the highest risk items, especially of those personnel which had previously visited protected areas, parklands/botanic gardens or alpine areas. Tourists who visited rural/agricultural areas prior to travel, and/or travel with national programs or on smaller tourist vessels had the highest probability of transferring plant propagules. Travel either during the boreal or austral autumn months increased the probability of propagule presence. Our assessment is applicable to other areas given evidence of propagule transfer patterns
in those areas that are broadly similar to those documented here. The current work provides a sound evidence base for both self-regulation (e.g. taking care of personal
equipment) and organization-based regulation (e.g. issuing guidelines and holding regular inspections) to reduce propagule transfer of plants to the Antarctic
A Pearson-Dirichlet random walk
A constrained diffusive random walk of n steps and a random flight in Rd,
which can be expressed in the same terms, were investigated independently in
recent papers. The n steps of the walk are identically and independently
distributed random vectors of exponential length and uniform orientation.
Conditioned on the sum of their lengths being equal to a given value l,
closed-form expressions for the distribution of the endpoint of the walk were
obtained altogether for any n for d=1, 2, 4 . Uniform distributions of the
endpoint inside a ball of radius l were evidenced for a walk of three steps in
2D and of two steps in 4D. The previous walk is generalized by considering step
lengths which are distributed over the unit (n-1) simplex according to a
Dirichlet distribution whose parameters are all equal to q, a given positive
value. The walk and the flight above correspond to q=1. For any d >= 3, there
exist, for integer and half-integer values of q, two families of
Pearson-Dirichlet walks which share a common property. For any n, the d
components of the endpoint are jointly distributed as are the d components of a
vector uniformly distributed over the surface of a hypersphere of radius l in a
space Rk whose dimension k is an affine function of n for a given d. Five
additional walks, with a uniform distribution of the endpoint in the inside of
a ball, are found from known finite integrals of products of powers and Bessel
functions of the first kind. They include four different walks in R3 and two
walks in R4. Pearson-Liouville random walks, obtained by distributing the total
lengths of the previous Pearson-Dirichlet walks, are finally discussed.Comment: 33 pages 1 figure, the paper includes the content of a recently
submitted work together with additional results and an extended section on
Pearson-Liouville random walk
The Science of Sungrazers, Sunskirters, and Other Near-Sun Comets
This review addresses our current understanding of comets that venture close to the Sun, and are hence exposed to much more extreme conditions than comets that are typically studied from Earth. The extreme solar heating and plasma environments that these objects encounter change many aspects of their behaviour, thus yielding valuable information on both the comets themselves that complements other data we have on primitive solar system bodies, as well as on the near-solar environment which they traverse. We propose clear definitions for these comets: We use the term near-Sun comets to encompass all objects that pass sunward of the perihelion distance of planet Mercury (0.307 AU). Sunskirters are defined as objects that pass within 33 solar radii of the Sun’s centre, equal to half of Mercury’s perihelion distance, and the commonly-used phrase sungrazers to be objects that reach perihelion within 3.45 solar radii, i.e. the fluid Roche limit. Finally, comets with orbits that intersect the solar photosphere are termed sundivers. We summarize past studies of these objects, as well as the instruments and facilities used to study them, including space-based platforms that have led to a recent revolution in the quantity and quality of relevant observations. Relevant comet populations are described, including the Kreutz, Marsden, Kracht, and Meyer groups, near-Sun asteroids, and a brief discussion of their origins. The importance of light curves and the clues they provide on cometary composition are emphasized, together with what information has been gleaned about nucleus parameters, including the sizes and masses of objects and their families, and their tensile strengths. The physical processes occurring at these objects are considered in some detail, including the disruption of nuclei, sublimation, and ionisation, and we consider the mass, momentum, and energy loss of comets in the corona and those that venture to lower altitudes. The different components of comae and tails are described, including dust, neutral and ionised gases, their chemical reactions, and their contributions to the near-Sun environment. Comet-solar wind interactions are discussed, including the use of comets as probes of solar wind and coronal conditions in their vicinities. We address the relevance of work on comets near the Sun to similar objects orbiting other stars, and conclude with a discussion of future directions for the field and the planned ground- and space-based facilities that will allow us to address those science topics
Learning from multimedia and hypermedia
Computer-based multimedia and hypermedia resources (e.g., the world wide web) have become one of the primary sources of academic information for a majority of pupils and students. In line with this expansion in the field of education, the scientific study of learning from multimedia and hypermedia has become a very active field of research. In this chapter we provide a short overview with regard to research on learning with multimedia and hypermedia. In two review sections, we describe the educational benefits of multiple representations and of learner control, as these are the two defining characteristics of hypermedia. In a third review section we describe recent scientific trends in the field of multimedia/hypermedia learning. In all three review sections we will point to relevant European work on multimedia/hypermedia carried out within the last 5 years, and often carried out within the Kaleidoscope Network of Excellence. According to the interdisciplinary nature of the field this work might come not only from psychology, but also from technology or pedagogy. Comparing the different research activities on multimedia and hypermedia that have dominated the international scientific discourse in the last decade reveals some important differences. Most important, a gap seems to exist between researchers mainly interested in a “serious” educational use of multimedia/ hypermedia and researchers mainly interested in “serious” experimental research on learning with multimedia/hypermedia. Recent discussions about the pros and cons of “design-based research” or “use-inspired basic research” can be seen as a direct consequence of an increasing awareness of the tensions within these two different cultures of research on education
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