7,329 research outputs found
Non mean-field behavior of the contact process on scale-free networks
We present an analysis of the classical contact process on scale-free
networks. A mean-field study, both for finite and infinite network sizes,
yields an absorbing-state phase transition at a finite critical value of the
control parameter, characterized by a set of exponents depending on the network
structure. Since finite size effects are large and the infinite network limit
cannot be reached in practice, a numerical study of the transition requires the
application of finite size scaling theory. Contrary to other critical phenomena
studied previously, the contact process in scale-free networks exhibits a
non-trivial critical behavior that cannot be quantitatively accounted for by
mean-field theory.Comment: 5 pages, 4 figures, published versio
Optimization of Network Robustness to Waves of Targeted and Random Attack
We study the robustness of complex networks to multiple waves of simultaneous
(i) targeted attacks in which the highest degree nodes are removed and (ii)
random attacks (or failures) in which fractions and respectively of
the nodes are removed until the network collapses. We find that the network
design which optimizes network robustness has a bimodal degree distribution,
with a fraction of the nodes having degree k_2= (\kav - 1 +r)/r and the
remainder of the nodes having degree , where \kav is the average
degree of all the nodes. We find that the optimal value of is of the order
of for
Mechanical properties of wood-derived silicon carbide aluminum-alloy composites as a function of temperature
The mechanical behavior [i.e., stiffness, strength, and toughness (K_(IC))] of SiC Al–Si–Mg metal–ceramic composites (50:50 by volume) was studied at temperatures ranging from 25 to 500 °C. The SiC phase was derived from wood precursors, which resulted in an interconnected anisotropic ceramic that constrained the pressure melt-infiltrated aluminum alloy. The composites were made using SiC derived from two woods (sapele and beech) and were studied in three orthogonal orientations. The mechanical properties and corresponding deformation micromechanisms were different in the longitudinal (LO) and transverse directions, but the influence of the precursor wood was small. The LO behavior was controlled by the rigid SiC preform and the load transfer from the metal to the ceramic. Moduli in this orientation were lower than the Halpin–Tsai predictions due to the nonlinear and nonparallel nature of the Al-filled pores. The LO K_(IC) agreed with the Ashby model for the K_(IC) contribution of ductile inclusions in a brittle ceramic
Heterogeneous pair approximation for voter models on networks
For models whose evolution takes place on a network it is often necessary to
augment the mean-field approach by considering explicitly the degree dependence
of average quantities (heterogeneous mean-field). Here we introduce the degree
dependence in the pair approximation (heterogeneous pair approximation) for
analyzing voter models on uncorrelated networks. This approach gives an
essentially exact description of the dynamics, correcting some inaccurate
results of previous approaches. The heterogeneous pair approximation introduced
here can be applied in full generality to many other processes on complex
networks.Comment: 6 pages, 6 figures, published versio
Extremal dynamics on complex networks: Analytic solutions
The Bak-Sneppen model displaying punctuated equilibria in biological
evolution is studied on random complex networks. By using the rate equation and
the random walk approaches, we obtain the analytic solution of the fitness
threshold to be 1/(_f+1), where _f=/ (=) in the quenched
(annealed) updating case, where is the n-th moment of the degree
distribution. Thus, the threshold is zero (finite) for the degree exponent
\gamma 3) for the quenched case in the thermodynamic limit. The
theoretical value x_c fits well to the numerical simulation data in the
annealed case only. Avalanche size, defined as the duration of successive
mutations below the threshold, exhibits a critical behavior as its distribution
follows a power law, P_a(s) ~ s^{-3/2}.Comment: 6 pages, 2 figure
Surface phase transitions in one-dimensional channels arranged in a triangular cross-sectional structure: Theory and Monte Carlo simulations
Monte Carlo simulations and finite-size scaling analysis have been carried
out to study the critical behavior in a submonolayer lattice-gas of interacting
monomers adsorbed on one-dimensional channels arranged in a triangular
cross-sectional structure. The model mimics a nanoporous environment, where
each nanotube or unit cell is represented by a one-dimensional array. Two kinds
of lateral interaction energies have been considered: , interaction
energy between nearest-neighbor particles adsorbed along a single channel and
, interaction energy between particles adsorbed across
nearest-neighbor channels. For and , successive planes are
uncorrelated, the system is equivalent to the triangular lattice and the
well-known
ordered phase is found at low temperatures and a coverage, , of 1/3
. In the more general case ( and ), a
competition between interactions along a single channel and a transverse
coupling between sites in neighboring channels allows to evolve to a
three-dimensional adsorbed layer. Consequently, the and structures "propagate" along the
channels and new ordered phases appear in the adlayer. The Monte Carlo
technique was combined with the recently reported Free Energy Minimization
Criterion Approach (FEMCA), to predict the critical temperatures of the
order-disorder transformation. The excellent qualitative agreement between
simulated data and FEMCA results allow us to interpret the physical meaning of
the mechanisms underlying the observed transitions.Comment: 24 pages, 6 figure
Localization transition on complex networks via spectral statistics
The spectral statistics of complex networks are numerically studied.
The features of the Anderson metal-insulator transition are found to be
similar for a wide range of different networks. A metal-insulator transition as
a function of the disorder can be observed for different classes of complex
networks for which the average connectivity is small. The critical index of the
transition corresponds to the mean field expectation. When the connectivity is
higher, the amount of disorder needed to reach a certain degree of localization
is proportional to the average connectivity, though a precise transition cannot
be identified. The absence of a clear transition at high connectivity is
probably due to the very compact structure of the highly connected networks,
resulting in a small diameter even for a large number of sites.Comment: 6 pages, expanded introduction and referencess (to appear in PRE
Constraining the cosmic radiation density due to lepton number with Big Bang Nucleosynthesis
The cosmic energy density in the form of radiation before and during Big Bang
Nucleosynthesis (BBN) is typically parameterized in terms of the effective
number of neutrinos N_eff. This quantity, in case of no extra degrees of
freedom, depends upon the chemical potential and the temperature characterizing
the three active neutrino distributions, as well as by their possible
non-thermal features. In the present analysis we determine the upper bounds
that BBN places on N_eff from primordial neutrino--antineutrino asymmetries,
with a careful treatment of the dynamics of neutrino oscillations. We consider
quite a wide range for the total lepton number in the neutrino sector, eta_nu=
eta_{nu_e}+eta_{nu_mu}+eta_{nu_tau} and the initial electron neutrino asymmetry
eta_{nu_e}^in, solving the corresponding kinetic equations which rule the
dynamics of neutrino (antineutrino) distributions in phase space due to
collisions, pair processes and flavor oscillations. New bounds on both the
total lepton number in the neutrino sector and the nu_e -bar{nu}_e asymmetry at
the onset of BBN are obtained fully exploiting the time evolution of neutrino
distributions, as well as the most recent determinations of primordial 2H/H
density ratio and 4He mass fraction. Note that taking the baryon fraction as
measured by WMAP, the 2H/H abundance plays a relevant role in constraining the
allowed regions in the eta_nu -eta_{nu_e}^in plane. These bounds fix the
maximum contribution of neutrinos with primordial asymmetries to N_eff as a
function of the mixing parameter theta_13, and point out the upper bound N_eff
< 3.4. Comparing these results with the forthcoming measurement of N_eff by the
Planck satellite will likely provide insight on the nature of the radiation
content of the universe.Comment: 17 pages, 9 figures, version to be published in JCA
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