12,321 research outputs found
On Nichols algebras over PGL(2,q) and PSL(2,q)
We compute necessary conditions on Yetter-Drinfeld modules over the groups
\mathbf{PGL}(2,q)=\mathbf{PGL}(2,\FF_q) and
\mathbf{PSL}(2,q)=\mathbf{PSL}(2,\FF_q) to generate finite dimensional
Nichols algebras. This is a first step towards a classification of pointed Hopf
algebras with group of group-likes isomorphic to one of these groups.
As a by-product of the techniques developed in this work, we prove that there
is no non-trivial finite-dimensional pointed Hopf algebra over the Mathieu
groups and .Comment: Minor change
Twisted and Nontwisted Bifurcations Induced by Diffusion
We discuss a diffusively perturbed predator-prey system. Freedman and
Wolkowicz showed that the corresponding ODE can have a periodic solution that
bifurcates from a homoclinic loop. When the diffusion coefficients are large,
this solution represents a stable, spatially homogeneous time-periodic solution
of the PDE. We show that when the diffusion coefficients become small, the
spatially homogeneous periodic solution becomes unstable and bifurcates into
spatially nonhomogeneous periodic solutions.
The nature of the bifurcation is determined by the twistedness of an
equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients
decrease. In the nontwisted case two spatially nonhomogeneous simple periodic
solutions of equal period are generated, while in the twisted case a unique
spatially nonhomogeneous double periodic solution is generated through
period-doubling.
Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic
bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex
files. Hard copy of figures available on request from
[email protected]
Spontaneous Charging and Crystallization of Water Droplets in Oil
We study the spontaneous charging and the crystallization of spherical
micron-sized water-droplets dispersed in oil by numerically solving, within a
Poisson-Boltzmann theory in the geometry of a spherical cell, for the density
profiles of the cations and anions in the system. We take into account
screening, ionic Born self-energy differences between oil and water, and
partitioning of ions over the two media. We find that the surface charge
density of the droplet as induced by the ion partitioning is significantly
affected by the droplet curvature and by the finite density of the droplets. We
also find that the salt concentration and the dielectric constant regime in
which crystallization of the water droplets is predicted is enhanced
substantially compared to results based on the planar oil-water interface,
thereby improving quantitative agreement with recent experiments.Comment: 10 pages, 7 figures, submitted for publicatio
On the Response of an OST to a Point-like Heat Source
A new technique of superconducting cavity diagnostics has been introduced by
D. Hartrill at Cornell University, Ithaca, USA. Oscillating Superleak
Transducers (OST) detect the heat transferred from a cavity's quench point via
"Second Sound" through the superfluid He bath, needed to cool the
superconducting cavity. The observed response of an OST is a complex, but
reproducible pattern of oscillations. A small helium evaporation cryostat was
built which allows the investigation of the response of an OST in greater
detail. The distance between a point-like electrical heater and the OST can be
varied. The OST can be mounted either parallel or perpendicular to the plate,
housing the heat source. If the artificial quench-point releases an amount of
energy compatible to a real quench spot on a cavity's surface, the OST signal
starts with a negative pulse, which is usually strong enough to allow automatic
detection. Furthermore, the reflection of the Second Sound on the wall is
observed. A reflection coefficient R = 0.39 +- 0.05 of the glass wall is
measured. This excludes a strong influence of multiple reflections in the
complex OST response. Fourier analyses show three main frequencies, found in
all OST spectra. They can be interpreted as modes of an oscillating circular
membrane.Comment: 10 pages, 16 figure
Towards understanding the variability in biospheric CO2 fluxes:Using FTIR spectrometry and a chemical transport model to investigate the sources and sinks of carbonyl sulfide and its link to CO2
Understanding carbon dioxide (CO2) biospheric processes is of great importance because the terrestrial exchange drives the seasonal and interannual variability of CO2 in the atmosphere. Atmospheric inversions based on CO2 concentration measurements alone can only determine net biosphere fluxes, but not differentiate between photosynthesis (uptake) and respiration (production). Carbonyl sulfide (OCS) could provide an important additional constraint: it is also taken up by plants during photosynthesis but not emitted during respiration, and therefore is a potential means to differentiate between these processes. Solar absorption Fourier Transform InfraRed (FTIR) spectrometry allows for the retrievals of the atmospheric concentrations of both CO2 and OCS from measured solar absorption spectra. Here, we investigate co-located and quasi-simultaneous FTIR measurements of OCS and CO2 performed at five selected sites located in the Northern Hemisphere. These measurements are compared to simulations of OCS and CO2 using a chemical transport model (GEOS-Chem). The coupled biospheric fluxes of OCS and CO2 from the simple biosphere model (SiB) are used in the study. The CO2 simulation with SiB fluxes agrees with the measurements well, while the OCS simulation reproduced a weaker drawdown than FTIR measurements at selected sites, and a smaller latitudinal gradient in the Northern Hemisphere during growing season when comparing with HIPPO (HIAPER Pole-to-Pole Observations) data spanning both hemispheres. An offset in the timing of the seasonal cycle minimum between SiB simulation and measurements is also seen. Using OCS as a photosynthesis proxy can help to understand how the biospheric processes are reproduced in models and to further understand the carbon cycle in the real world
Quantum-classical transition in Scale Relativity
The theory of scale relativity provides a new insight into the origin of
fundamental laws in physics. Its application to microphysics allows us to
recover quantum mechanics as mechanics on a non-differentiable (fractal)
spacetime. The Schrodinger and Klein-Gordon equations are demonstrated as
geodesic equations in this framework. A development of the intrinsic properties
of this theory, using the mathematical tool of Hamilton's bi-quaternions, leads
us to a derivation of the Dirac equation within the scale-relativity paradigm.
The complex form of the wavefunction in the Schrodinger and Klein-Gordon
equations follows from the non-differentiability of the geometry, since it
involves a breaking of the invariance under the reflection symmetry on the
(proper) time differential element (ds - ds). This mechanism is generalized
for obtaining the bi-quaternionic nature of the Dirac spinor by adding a
further symmetry breaking due to non-differentiability, namely the differential
coordinate reflection symmetry (dx^mu - dx^mu) and by requiring invariance
under parity and time inversion. The Pauli equation is recovered as a
non-relativistic-motion approximation of the Dirac equation.Comment: 28 pages, no figur
Family memories in the home: contrasting physical and digital mementos
We carried out fieldwork to characterise and compare physical and digital mementos in the home. Physical mementos are highly valued, heterogeneous and support different types of recollection. Contrary to expectations, we found physical mementos are not purely representational, and can involve appropriating common objects and more idiosyncratic forms. In contrast, digital mementos were initially perceived as less valuable, although participants later reconsidered this. Digital mementos were somewhat limited in function and expression, largely involving representational photos and videos, and infrequently accessed. We explain these digital limitations and conclude with design guidelines for digital mementos, including better techniques for accessing and integrating these into everyday life, allowing them to acquire the symbolic associations and lasting value that characterise their physical counterparts
Obscuration of the Parsec Scale Jets in the Compact Symmetric Object 1946+708
We present results of VLA and VLBA observations of the 1.420 GHz neutral
hydrogen absorption associated with the Compact Symmetric Object 1946+708
(z=0.101). We find significant structure in the gas on parsec scales. The peak
column density in the HI (N_HI~2.2x10^23 cm^-2 (T_s/8000K)) occurs toward the
center of activity of the source, as does the highest velocity dispersion
(FWHM~350 \kms). In addition, we find that the continuum spectra of the various
radio components associated with these jets strongly indicate free-free
absorption. This effect is particularly pronounced toward the core and inner
components of the receding jet, suggesting the presence of a screen local to
the source, perhaps part of an obscuring torus.Comment: revised version, some text added, 1 figure changed; accepted to
Astrophysical Journal, 22 page LaTeX document includes 8 postscript figure
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