1,677 research outputs found
Comment on "Breakdown of the Internet under Intentional Attack"
We obtain the exact position of the percolation threshold in intentionally
damaged scale-free networks.Comment: 1 page, to appear in Phys. Rev. Let
A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations
The Hartree-Fock equations are modified to directly yield Wannier functions
following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)].
This approach circumvents the a posteriori application of the Wannier
transformation to Bloch functions. I give a novel and rigorous derivation of
the relevant equations by introducing an orthogonalizing potential to ensure
the orthogonality among the resulting functions. The properties of these,
so-called a priori Wannier functions, are analyzed and the relation of the
modified Hartree-Fock equations to the conventional, Bloch-function-based
equations is elucidated. It is pointed out that the modified equations offer a
different route to maximally localized Wannier functions. Their computational
solution is found to involve an effort that is comparable to the effort for the
solution of the conventional equations. Above all, I show how a priori Wannier
functions can be obtained by a modification of the Kohn-Sham equations of
density-functional theory.Comment: 7 pages, RevTeX4, revise
FIBONACCI SUPERLATTICES OF NARROW-GAP III-V SEMICONDUCTORS
We report theoretical electronic structure of Fibonacci superlattices of
narrow-gap III-V semiconductors. Electron dynamics is accurately described
within the envelope-function approximation in a two-band model.
Quasiperiodicity is introduced by considering two different III-V semiconductor
layers and arranging them according to the Fibonacci series along the growth
direction. The resulting energy spectrum is then found by solving exactly the
corresponding effective-mass (Dirac-like) wave equation using tranfer-matrix
techniques. We find that a self-similar electronic spectrum can be seen in the
band structure. Electronic transport properties of samples are also studied and
related to the degree of spatial localization of electronic envelope-functions
via Landauer resistance and Lyapunov coefficient. As a working example, we
consider type II InAs/GaSb superlattices and discuss in detail our results in
this system.Comment: REVTeX 3.0, 16 pages, 8 figures available upon request. To appear in
Semiconductor Science and Technolog
A semi-quantitative scattering theory of amorphous materials
It is argued that topological disorder in amorphous solids can be described
by local strains related to local reference crystals and local rotations. An
intuitive localization criterion is formulated from this point of view. The
Inverse Participation Ratio and the location of mobility edges in band tails is
directly related to the character of the disorder potential in amorphous solid,
the coordination number, the transition integral and the nodes of wave
functions of the corresponding reference crystal. The dependence of the decay
rate of band tails on temperature and static disorder are derived. \textit{Ab
initio} simulations on a-Si and experiments on a-Si:H are compared to these
predictions.Comment: 4 pages, 2 figures, will be submitted to Phys. Rev. Let
Ising Model on Networks with an Arbitrary Distribution of Connections
We find the exact critical temperature of the nearest-neighbor
ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary
degree distribution . We observe an anomalous behavior of the
magnetization, magnetic susceptibility and specific heat, when is
fat-tailed, or, loosely speaking, when the fourth moment of the distribution
diverges in infinite networks. When the second moment becomes divergent,
approaches infinity, the phase transition is of infinite order, and size effect
is anomalously strong.Comment: 5 page
Giant strongly connected component of directed networks
We describe how to calculate the sizes of all giant connected components of a
directed graph, including the {\em strongly} connected one. Just to the class
of directed networks, in particular, belongs the World Wide Web. The results
are obtained for graphs with statistically uncorrelated vertices and an
arbitrary joint in,out-degree distribution . We show that if
does not factorize, the relative size of the giant strongly
connected component deviates from the product of the relative sizes of the
giant in- and out-components. The calculations of the relative sizes of all the
giant components are demonstrated using the simplest examples. We explain that
the giant strongly connected component may be less resilient to random damage
than the giant weakly connected one.Comment: 4 pages revtex, 4 figure
Halting viruses in scale-free networks
The vanishing epidemic threshold for viruses spreading on scale-free networks
indicate that traditional methods, aiming to decrease a virus' spreading rate
cannot succeed in eradicating an epidemic. We demonstrate that policies that
discriminate between the nodes, curing mostly the highly connected nodes, can
restore a finite epidemic threshold and potentially eradicate a virus. We find
that the more biased a policy is towards the hubs, the more chance it has to
bring the epidemic threshold above the virus' spreading rate. Furthermore, such
biased policies are more cost effective, requiring less cures to eradicate the
virus
Generic scale of the "scale-free" growing networks
We show that the connectivity distributions of scale-free growing
networks ( is the network size) have the generic scale -- the cut-off at
. The scaling exponent is related to the exponent
of the connectivity distribution, . We propose the
simplest model of scale-free growing networks and obtain the exact form of its
connectivity distribution for any size of the network. We demonstrate that the
trace of the initial conditions -- a hump at --
may be found for any network size. We also show that there exists a natural
boundary for the observation of the scale-free networks and explain why so few
scale-free networks are observed in Nature.Comment: 4 pages revtex, 3 figure
Electron localization by a magnetic vortex
We study the problem of an electron in two dimensions in the presence of a
magnetic vortex with a step-like profile. Dependending on the values of the
effective mass and gyromagnetic factor of the electron, it may be trapped by
the vortex. The bound state spectrum is obtained numerically, and some limiting
cases are treated analytically.Comment: 8 pages, latex, 4 figure
Epidemic Incidence in Correlated Complex Networks
We introduce a numerical method to solve epidemic models on the underlying
topology of complex networks. The approach exploits the mean-field like rate
equations describing the system and allows to work with very large system
sizes, where Monte Carlo simulations are useless due to memory needs. We then
study the SIR epidemiological model on assortative networks, providing
numerical evidence of the absence of epidemic thresholds. Besides, the time
profiles of the populations are analyzed. Finally, we stress that the present
method would allow to solve arbitrary epidemic-like models provided that they
can be described by mean-field rate equations.Comment: 5 pages, 4 figures. Final version published in PR
- …