6,241 research outputs found
Quantum Effects in Matter-Wave Diffraction
Advances in micro-technology of the last years have made it possible to carry
optics textbooks experiments over to atomic and molecular beams, such as
diffraction by a double slit or transmission grating. The usual wave-optical
approach gives a good qualitative description of these experiments. However,
small deviations therefrom and sophisticated quantum mechanics yield new
surprising insights on the size of particles and on their interaction with
surfaces.Comment: 6 pages, 3 Postscript figures. To appear in the Proceedings of
Quantum Theory and Symmetry, Cracow, July 2001, edited by E. Kapuscik and A.
Horzela, World Scientifi
Tree modules
After stating several tools which can be used to construct indecomposable
tree modules for quivers without oriented cycles, we use these methods to
construct indecomposable tree modules for every imaginary Schur root. These
methods also give a recipe for the construction of tree modules for every root.
Moreover, we give several examples illustrating the results.Comment: Typos corrected; references added; deleted former Lemma 3.13 which is
not neede
Perspective: network-guided pattern formation of neural dynamics
The understanding of neural activity patterns is fundamentally linked to an
understanding of how the brain's network architecture shapes dynamical
processes. Established approaches rely mostly on deviations of a given network
from certain classes of random graphs. Hypotheses about the supposed role of
prominent topological features (for instance, the roles of modularity, network
motifs, or hierarchical network organization) are derived from these
deviations. An alternative strategy could be to study deviations of network
architectures from regular graphs (rings, lattices) and consider the
implications of such deviations for self-organized dynamic patterns on the
network. Following this strategy, we draw on the theory of spatiotemporal
pattern formation and propose a novel perspective for analyzing dynamics on
networks, by evaluating how the self-organized dynamics are confined by network
architecture to a small set of permissible collective states. In particular, we
discuss the role of prominent topological features of brain connectivity, such
as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the
notion of network-guided pattern formation with numerical simulations and
outline how it can facilitate the understanding of neural dynamics
Generalization of the noise model for time-distance helioseismology
In time-distance helioseismology, information about the solar interior is
encoded in measurements of travel times between pairs of points on the solar
surface. Travel times are deduced from the cross-covariance of the random wave
field. Here we consider travel times and also products of travel times as
observables. They contain information about e.g. the statistical properties of
convection in the Sun. The basic assumption of the model is that noise is the
result of the stochastic excitation of solar waves, a random process which is
stationary and Gaussian. We generalize the existing noise model (Gizon and
Birch 2004) by dropping the assumption of horizontal spatial homogeneity. Using
a recurrence relation, we calculate the noise covariance matrices for the
moments of order 4, 6, and 8 of the observed wave field, for the moments of
order 2, 3 and 4 of the cross-covariance, and for the moments of order 2, 3 and
4 of the travel times. All noise covariance matrices depend only on the
expectation value of the cross-covariance of the observed wave field. For
products of travel times, the noise covariance matrix consists of three terms
proportional to , , and , where is the duration of the
observations. For typical observation times of a few hours, the term
proportional to dominates and , where the are arbitrary travel times. This
result is confirmed for travel times by Monte Carlo simulations and
comparisons with SDO/HMI observations. General and accurate formulae have been
derived to model the noise covariance matrix of helioseismic travel times and
products of travel times. These results could easily be generalized to other
methods of local helioseismology, such as helioseismic holography and ring
diagram analysis
Relation between directed polymers in random media and random bond dimer models
We reassess the relation between classical lattice dimer models and the
continuum elastic description of a lattice of fluctuating polymers. In the
absence of randomness we determine the density and line tension of the polymers
in terms of the bond weights of hard-core dimers on the square and the
hexagonal lattice. For the latter, we demonstrate the equivalence of the
canonical ensemble for the dimer model and the grand-canonical description for
polymers by performing explicitly the continuum limit. Using this equivalence
for the random bond dimer model on a square lattice, we resolve a previously
observed discrepancy between numerical results for the random dimer model and a
replica approach for polymers in random media. Further potential applications
of the equivalence are briefly discussed.Comment: 6 pages, 3 figure
Star formation and molecular hydrogen in dwarf galaxies: a non-equilibrium view
We study the connection of star formation to atomic (HI) and molecular
hydrogen (H) in isolated, low metallicity dwarf galaxies with
high-resolution ( = 4 M, = 100) SPH
simulations. The model includes self-gravity, non-equilibrium cooling,
shielding from an interstellar radiation field, the chemistry of H
formation, H-independent star formation, supernova feedback and metal
enrichment. We find that the H mass fraction is sensitive to the adopted
dust-to-gas ratio and the strength of the interstellar radiation field, while
the star formation rate is not. Star formation is regulated by stellar
feedback, keeping the gas out of thermal equilibrium for densities 1
cm. Because of the long chemical timescales, the H mass remains out
of chemical equilibrium throughout the simulation. Star formation is
well-correlated with cold ( T 100 K ) gas, but this dense and cold
gas - the reservoir for star formation - is dominated by HI, not H. In
addition, a significant fraction of H resides in a diffuse, warm phase,
which is not star-forming. The ISM is dominated by warm gas (100 K T
K) both in mass and in volume. The scale height of the
gaseous disc increases with radius while the cold gas is always confined to a
thin layer in the mid-plane. The cold gas fraction is regulated by feedback at
small radii and by the assumed radiation field at large radii. The decreasing
cold gas fractions result in a rapid increase in depletion time (up to 100
Gyrs) for total gas surface densities 10
Mpc, in agreement with observations of dwarf galaxies in the
Kennicutt-Schmidt plane.Comment: Accepted for publication in MNRAS. Changes (including a pamameter
study in Appendix C) highlighte
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