3,904 research outputs found
The kernel of newform Dedekind sums
Newform Dedekind sums are a class of crossed homomorphisms that arise from
newform Eisenstein series. We initiate a study of the kernel of these newform
Dedekind sums. Our results can be loosely described as showing that these
kernels are neither "too big" nor "too small." We conclude with an observation
about the Galois action on Dedekind sums that allows for significant
computational efficiency in the numerical calculation of Dedekind sums.Comment: 8+epsilon pages, 2 figure
Simple strong glass forming models: mean-field solution with activation
We introduce simple models, inspired by previous models for froths and
covalent glasses, with trivial equilibrium properties but dynamical behaviour
characteristic of strong glass forming systems. These models are also a
generalization of backgammon or urn models to a non--constant number of
particles, where entropic barriers are replaced by energy barriers, allowing
for the existence of activated processes. We formulate a mean--field version of
the models, which keeps most of the features of the finite dimensional ones,
and solve analytically the out--of--equilibrium dynamics in the low temperature
regime where activation plays an essential role.Comment: 18 pages, 9 figure
Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions
We study analytically the logarithmic corrections to the critical exponents
of the critical behavior of correlation length, susceptibility and specific
heat for the temperature and the finite-size scaling behavior, for a generic
theory at its upper critical dimension (six). We have also computed
the leading correction to scaling as a function of the lattice size. We
distinguish the obtained formulas to the following special cases: percolation,
Lee-Yang (LY) singularities and -component spin glasses. We have compared
our results for the Ising spin glass case with numerical simulations finding a
very good agreement. Finally, and using the results obtained for the Lee-Yang
singularities in six dimensions, we have computed the logarithmic corrections
to the singular part of the free energy for lattice animals in eight
dimensions.Comment: 18 pages. We have extended the computation to lattice animals in
eight dimensions. To be published in Journal of Physics
Study of the phase transition in the 3d Ising spin glass from out of equilibrium numerical simulations
Using the decay of the out equilibrium spin-spin correlation function we
compute the equilibrium Edward-Anderson order parameter in the three
dimensional binary Ising spin glass in the spin glass phase. We have checked
that the Edward-Anderson order parameter computed from out of equilibrium
numerical simulations follows with good precision the critical law as
determined in experiments and in numerical studies at equilibrium. We have also
studied the dependence of the order parameter with the lattice size. Finally we
present a large time study of the scaling of the off-equilibrium
fluctuation-dissipation relations.Comment: 14 pages, 7 Postscript figure
Long distance chiral corrections in B meson amplitudes
We discuss the chiral corrections to f_B and B_B with particular emphasis on
determining the portion of the correction that arises from long distance
physics. For very small pion and kaon masses all of the usual corrections are
truly long distance, while for larger masses the long distance portion
decreases. These chiral corrections have been used to extrapolate lattice
calculations towards the physical region of lighter masses. We show in
particular that the chiral extrapolation is better behaved if only the long
distance portion of the correction is used.Comment: 14 pages, 4 figure
System-of-Systems Considerations in the Notional Development of a Metropolitan Aerial Transportation System
There are substantial future challenges related to sustaining and improving efficient, cost-effective, and environmentally friendly transportation options for urban regions. Over the past several decades there has been a worldwide trend towards increasing urbanization of society. Accompanying this urbanization are increasing surface transportation infrastructure costs and, despite public infrastructure investments, increasing surface transportation "gridlock." In addition to this global urbanization trend, there has been a substantial increase in concern regarding energy sustainability, fossil fuel emissions, and the potential implications of global climate change. A recently completed study investigated the feasibility of an aviation solution for future urban transportation (refs. 1, 2). Such an aerial transportation system could ideally address some of the above noted concerns related to urbanization, transportation gridlock, and fossil fuel emissions (ref. 3). A metro/regional aerial transportation system could also provide enhanced transportation flexibility to accommodate extraordinary events such as surface (rail/road) transportation network disruptions and emergency/disaster relief responses
Fluctuation-dissipation relations in plaquette spin systems with multi-stage relaxation
We study aging dynamics in two non-disordered spin models with multi-spin
interactions, following a sudden quench to low temperature. The models are
relevant to the physics of supercooled liquids. Their low temperature dynamics
resemble those of kinetically constrained models, and obey dynamical scaling,
controlled by zero-temperature critical points. Dynamics in both models are
thermally activated, resulting in multi-stage relaxation towards equilibrium.
We study several two-time correlation and response functions. We find that
equilibrium fluctuation-dissipation relations are generically not satisfied
during the aging regime, but deviations from them are well described by
fluctuation-dissipation ratios, as found numerically in supercooled liquids.
These ratios are purely dynamic objects, containing information about the
nature of relaxation in the models. They are non-universal, and can even be
negative as a result of activated dynamics. Thus, effective temperatures are
not well-defined in these models.Comment: 29 pages, 10 fig
Low T Dynamical Properties of Spin Glasses Smoothly Extrapolate to T=0
We compare ground state properties of 3D Ising Spin Glasses with Gaussian
couplings with results from off-equilibrium numerical simulations at non zero
(but low) temperatures. We find that the non-zero temperature properties of the
system smoothly connect to the T=0 behavior, confirming the point of view that
results established at T=0 typically also give relevant information about the
physics of the system.Comment: 14 pages and 4 ps figure
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