4,600 research outputs found
Rydberg transition frequencies from the Local Density Approximation
A method is given that extracts accurate Rydberg excitations from LDA density
functional calculations, despite the short-ranged potential. For the case of He
and Ne, the asymptotic quantum defects predicted by LDA are in less than 5%
error, yielding transition frequency errors of less than 0.1eV.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let
Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles
Ensembles of networks are used as null models in many applications. However,
simple null models often show much less clustering than their real-world
counterparts. In this paper, we study a model where clustering is enhanced by
means of a fugacity term as in the Strauss (or "triangle") model, but where the
degree sequence is strictly preserved -- thus maintaining the quenched
heterogeneity of nodes found in the original degree sequence. Similar models
had been proposed previously in [R. Milo et al., Science 298, 824 (2002)]. We
find that our model exhibits phase transitions as the fugacity is changed. For
regular graphs (identical degrees for all nodes) with degree k > 2 we find a
single first order transition. For all non-regular networks that we studied
(including Erdos - Renyi and scale-free networks) we find multiple jumps
resembling first order transitions, together with strong hysteresis. The latter
transitions are driven by the sudden emergence of "cluster cores": groups of
highly interconnected nodes with higher than average degrees. To study these
cluster cores visually, we introduce q-clique adjacency plots. We find that
these cluster cores constitute distinct communities which emerge spontaneously
from the triangle generating process. Finally, we point out that cluster cores
produce pitfalls when using the present (and similar) models as null models for
strongly clustered networks, due to the very strong hysteresis which
effectively leads to broken ergodicity on realistic time scales.Comment: 13 pages, 11 figure
Network dynamics of ongoing social relationships
Many recent large-scale studies of interaction networks have focused on
networks of accumulated contacts. In this paper we explore social networks of
ongoing relationships with an emphasis on dynamical aspects. We find a
distribution of response times (times between consecutive contacts of different
direction between two actors) that has a power-law shape over a large range. We
also argue that the distribution of relationship duration (the time between the
first and last contacts between actors) is exponentially decaying. Methods to
reanalyze the data to compensate for the finite sampling time are proposed. We
find that the degree distribution for networks of ongoing contacts fits better
to a power-law than the degree distribution of the network of accumulated
contacts do. We see that the clustering and assortative mixing coefficients are
of the same order for networks of ongoing and accumulated contacts, and that
the structural fluctuations of the former are rather large.Comment: to appear in Europhys. Let
Efficiency of informational transfer in regular and complex networks
We analyze the process of informational exchange through complex networks by
measuring network efficiencies. Aiming to study non-clustered systems, we
propose a modification of this measure on the local level. We apply this method
to an extension of the class of small-worlds that includes {\it declustered}
networks, and show that they are locally quite efficient, although their
clustering coefficient is practically zero. Unweighted systems with small-world
and scale-free topologies are shown to be both globally and locally efficient.
Our method is also applied to characterize weighted networks. In particular we
examine the properties of underground transportation systems of Madrid and
Barcelona and reinterpret the results obtained for the Boston subway network.Comment: 10 pages and 9 figure
Magnetism and local distortions near carbon impurity in -iron
Local perturbations of crystal and magnetic structure of -iron near
carbon interstitial impurity is investigated by {\it ab initio} electronic
structure calculations. It is shown that the carbon impurity creates locally a
region of ferromagnetic ordering with substantial tetragonal distortions.
Exchange integrals and solution enthalpy are calculated, the latter being in a
very good agreement with experimental data. Effect of the local distortions on
the carbon-carbon interactions in -iron is discussed.Comment: 4 pages 3 figures. Final version, accepted to Phys.Rev. Let
N-representability and stationarity in time-dependent density functional theory
To construct an N-representable time-dependent density-functional theory, a
generalization to the time domain of the Levy-Lieb (LL) constrained search
algorithm is required. That the action is only stationary in the Dirac-Frenkel
variational principle eliminates the possibility of basing the search on the
action itself. Instead, we use the norm of the partial functional derivative of
the action in the Hilbert space of the wave functions in place of the energy of
the LL search. The electron densities entering the formalism are
-representable, and the resulting universal action functional has a unique
stationary point in the density at that corresponding to the solution of the
Schr\"{o}dinger equation. The original Runge-Gross (RG) formulation is subsumed
within the new formalism. Concerns in the literature about the meaning of the
functional derivatives and the internal consistency of the RG formulation are
allayed by clarifying the nature of the functional derivatives entering the
formalism.Comment: 9 pages, 0 figures, Phys. Rev. A accepted. Introduction was expanded,
subsections reorganized, appendix and new references adde
Comment on "On the importance of the free energy for elasticity under pressure"
Marcus et al. (Marcus P, Ma H and Qiu S L 2002 J. Phys.: Condens. Matter 14
L525) claim that thermodynamic properties of materials under pressure must be
computed using the Gibbs free energy , rather than the internal energy .
Marcus et al. state that ``The minima of , but not of , give the
equilibrium structure; the second derivatives of , but not of , with
respect to strains at the equilibrium structure give the equilibrium elastic
constants.'' Both statements are incorrect.Comment: Commen
Systematic corrections to the measured cosmological constant as a result of local inhomogeneity
We calculate the systematic inhomogeneity-induced correction to the
cosmological constant that one would infer from an analysis of the luminosities
and redshifts of Type Ia supernovae, assuming a homogeneous universe. The
calculation entails a post-Newtonian expansion within the framework of second
order perturbation theory, wherein we consider the effects of subhorizon
density perturbations in a flat, dust dominated universe. Within this
formalism, we calculate luminosity distances and redshifts along the past light
cone of an observer. The resulting luminosity distance-redshift relation is fit
to that of a homogeneous model in order to deduce the best-fit cosmological
constant density Omega_Lambda. We find that the luminosity distance-redshift
relation is indeed modified, by a small fraction of order 10^{-5}. When fitting
this perturbed relation to that of a homogeneous universe, we find that the
inferred cosmological constant can be surprisingly large, depending on the
range of redshifts sampled. For a sample of supernovae extending from z=0.02
out to z=0.15, we find that Omega_Lambda=0.004. The value of Omega_Lambda has a
large variance, and its magnitude tends to get larger for smaller redshifts,
implying that precision measurements from nearby supernova data will require
taking this effect into account. However, we find that this effect is likely
too small to explain the observed value of Omega_Lambda=0.7. There have been
previous claims of much larger backreaction effects. By contrast to those
calculations, our work is directly related to how observers deduce cosmological
parameters from astronomical data.Comment: 28 pages, 3 figures, revtex4; v2: corrected comments and the section
on previous work; v3: clarified wording. References adde
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