4,311 research outputs found
Studying the scale and q^2 dependence of K^+-->pi^+e^+e^- decay
We extract the K^+-->pi^+e^+e^- amplitude scale at q^2=0 from the recent
Brookhaven E865 high-statistics data. We find that the q^2=0 scale is fitted in
excellent agreement with the theoretical long-distance amplitude. Lastly, we
find that the observed q^2 shape is explained by the combined effect of the
pion and kaon form-factor vector-meson-dominance rho, omega and phi poles, and
a charged pion loop coupled to a virtual photon-->e^+e^- transition.Comment: 8 pages, 3 figure
Partial survival and inelastic collapse for a randomly accelerated particle
We present an exact derivation of the survival probability of a randomly
accelerated particle subject to partial absorption at the origin. We determine
the persistence exponent and the amplitude associated to the decay of the
survival probability at large times. For the problem of inelastic reflection at
the origin, with coefficient of restitution , we give a new derivation of
the condition for inelastic collapse, , and determine
the persistence exponent exactly.Comment: 6 page
Photosynthesis of three dessert banana cultivars along an altitudinal gradient
Poster presented at Tropentag 2011 - Development on the Margin. Bonn (Germany), 3-7 Oct 2011
Casimir Forces between Spherical Particles in a Critical Fluid and Conformal Invariance
Mesoscopic particles immersed in a critical fluid experience long-range
Casimir forces due to critical fluctuations. Using field theoretical methods,
we investigate the Casimir interaction between two spherical particles and
between a single particle and a planar boundary of the fluid. We exploit the
conformal symmetry at the critical point to map both cases onto a highly
symmetric geometry where the fluid is bounded by two concentric spheres with
radii R_- and R_+. In this geometry the singular part of the free energy F only
depends upon the ratio R_-/R_+, and the stress tensor, which we use to
calculate F, has a particularly simple form. Different boundary conditions
(surface universality classes) are considered, which either break or preserve
the order-parameter symmetry. We also consider profiles of thermodynamic
densities in the presence of two spheres. Explicit results are presented for an
ordinary critical point to leading order in epsilon=4-d and, in the case of
preserved symmetry, for the Gaussian model in arbitrary spatial dimension d.
Fundamental short-distance properties, such as profile behavior near a surface
or the behavior if a sphere has a `small' radius, are discussed and verified.
The relevance for colloidal solutions is pointed out.Comment: 37 pages, 2 postscript figures, REVTEX 3.0, published in Phys. Rev. B
51, 13717 (1995
Ways to teach modelling—a 50 year study
This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author’s observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was entirely focused on their learning standards models of a restricted range of phenomena, largely from Newtonian mechanics. This did not develop the numeracy/mathematical literacy that was so clearly important for future citizens. Early explorations started with modelling workshops with high school teachers and mathematics undergraduates, observed and analysed—in some case using video. The theoretical basis of this work has been essentially heuristic, though the Shell Centre studies included, for example, a detailed analysis of formulation processes that has not, as so often, been directly replicated. Recent work has focused on developing a formative assessment approach to teaching modelling that has proved both successful and popular. Finally, the system-level challenges in trying to establish modelling as an integral part of mathematics curricula are briefly discussed
Surface Critical Behavior of Binary Alloys and Antiferromagnets: Dependence of the Universality Class on Surface Orientation
The surface critical behavior of semi-infinite
(a) binary alloys with a continuous order-disorder transition and
(b) Ising antiferromagnets in the presence of a magnetic field is considered.
In contrast to ferromagnets, the surface universality class of these systems
depends on the orientation of the surface with respect to the crystal axes.
There is ordinary and extraordinary surface critical behavior for orientations
that preserve and break the two-sublattice symmetry, respectively. This is
confirmed by transfer-matrix calculations for the two-dimensional
antiferromagnet and other evidence.Comment: Final version that appeared in PRL, some minor stylistic changes and
one corrected formula; 4 pp., twocolumn, REVTeX, 3 eps fig
Local functional models of critical correlations in thin-films
Recent work on local functional theories of critical inhomogeneous fluids and
Ising-like magnets has shown them to be a potentially exact, or near exact,
description of universal finite-size effects associated with the excess
free-energy and scaling of one-point functions in critical thin films. This
approach is extended to predict the two-point correlation function G in
critical thin-films with symmetric surface fields in arbitrary dimension d. In
d=2 we show there is exact agreement with the predictions of conformal
invariance for the complete spectrum of correlation lengths as well as the
detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we
present new numerical predictions for the universal finite-size correlation
length and scaling functions determining the structure of G across the
thin-film. Highly accurate analytical closed form expressions for these
universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let
Conformal off-diagonal boundary density profiles on a semi-infinite strip
The off-diagonal profile phi(v) associated with a local operator (order
parameter or energy density) close to the boundary of a semi-infinite strip
with width L is obtained at criticality using conformal methods. It involves
the surface exponent x_phi^s and displays a simple universal behaviour which
crosses over from surface finite-size scaling when v/L is held constant to
corner finite-size scaling when v/L -> 0.Comment: 5 pages, 1 figure, IOP macros and eps
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