20,483 research outputs found
Generalized Bose-Fermi statistics and structural correlations in weighted networks
We derive a class of generalized statistics, unifying the Bose and Fermi
ones, that describe any system where the first-occupation energies or
probabilities are different from subsequent ones, as in presence of thresholds,
saturation, or aging. The statistics completely describe the structural
correlations of weighted networks, which turn out to be stronger than expected
and to determine significant topological biases. Our results show that the null
behavior of weighted networks is different from what previously believed, and
that a systematic redefinition of weighted properties is necessary.Comment: Final version accepted for publication on Physical Review Letter
Strain-stress study of AlxGa1-xN/AlN heterostructures on c-plane sapphire and related optical properties
This work presents a systematic study of stress and strain of AlxGa1-xN/AlN
with composition ranging from GaN to AlN, grown on a c-plane sapphire by
metal-organic chemical vapor deposition, using synchrotron radiation
high-resolution X-ray diffraction and reciprocal space mapping. The c-plane of
the AlxGa1-xN epitaxial layers exhibits compressive strain, while the a-plane
exhibits tensile strain. The biaxial stress and strain are found to increase
with increasing Al composition, although the lattice mismatch between the
AlxGa1-xN and the buffer layer AlN gets smaller. A reduction in the lateral
coherence lengths and an increase in the edge and screw dislocations are seen
as the AlxGa1-xN composition is varied from GaN to AlN, exhibiting a clear
dependence of the crystal properties of AlxGa1-xN on the Al content. The
bandgap of the epitaxial layers is slightly lower than predicted value due to a
larger tensile strain effect on the a-axis compared to the compressive strain
on the c-axis. Raman characteristics of the AlxGa1-xN samples exhibit a shift
in the phonon peaks with the Al composition. The effect of strain is also
discussed on the optical phonon energies of the epitaxial layers. The
techniques discussed here can be used to study other similar materials.Comment: 14 pages, 5 figures, 2 table
On the relation between entanglement and subsystem Hamiltonians
We show that a proportionality between the entanglement Hamiltonian and the
Hamiltonian of a subsystem exists near the limit of maximal entanglement under
certain conditions. Away from that limit, solvable models show that the
coupling range differs in both quantities and allow to investigate the effect.Comment: 7 pages, 2 figures version2: minor changes, typos correcte
Charge form factor of and mesons
The charge form factor of and mesons is evaluated adopting a
relativistic constituent quark model based on the light-front formalism. The
relevance of the high-momentum components of the meson wave function, for
values of the momentum transfer accessible to energies, is illustrated.
The predictions for the elastic form factor of and mesons are
compared with the results of different relativistic approaches, showing that
the measurements of the pion and kaon form factors planned at could
provide information for discriminating among various models of the meson
structure.Comment: 8 pages, latex, 4 figures available as separate .uu fil
A transition from river networks to scale-free networks
A spatial network is constructed on a two dimensional space where the nodes
are geometrical points located at randomly distributed positions which are
labeled sequentially in increasing order of one of their co-ordinates. Starting
with such points the network is grown by including them one by one
according to the serial number into the growing network. The -th point is
attached to the -th node of the network using the probability: where is the degree of the -th node
and is the Euclidean distance between the points and . Here
is a continuously tunable parameter and while for one gets
the simple Barab\'asi-Albert network, the case for
corresponds to the spatially continuous version of the well known Scheidegger's
river network problem. The modulating parameter is tuned to study the
transition between the two different critical behaviors at a specific value
which we numerically estimate to be -2.Comment: 5 pages, 5 figur
Waves of intermediate length through an array of vertical cylinders
We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to construct a mathematical model for waves propagating through a lattice-like array of vertical cylinders, where the macro-scale variation of waves is derived from the dynamics in the micro-scale cells. Assuming infinitesimal waves, periodic lattice configuration, and strong contrast between the lattice spacing and the typical wavelength, the perturbation theory of homogenization (multiple scales) is used to derive the effective equations governing the macro-scale wave dynamics. The constitutive coefficients are computed from the solution of micro-scale boundary-value problem for a finite number of unit cells. Eddy viscosity in a unit cell is determined by balancing the time-averaged rate of dissipation and the rate of work done by wave force on the forest at a finite number of macro stations. While the spirit is similar to RANS scheme, less computational effort is needed. Using one fitting parameter, the theory is used to simulate three existing experiments with encouraging results. Limitations of the present theory are also pointed out.Cornell University (Mary Upson visiting professorship
Percolation in invariant Poisson graphs with i.i.d. degrees
Let each point of a homogeneous Poisson process in R^d independently be
equipped with a random number of stubs (half-edges) according to a given
probability distribution mu on the positive integers. We consider
translation-invariant schemes for perfectly matching the stubs to obtain a
simple graph with degree distribution mu. Leaving aside degenerate cases, we
prove that for any mu there exist schemes that give only finite components as
well as schemes that give infinite components. For a particular matching scheme
that is a natural extension of Gale-Shapley stable marriage, we give sufficient
conditions on mu for the absence and presence of infinite components
A superadditivity and submultiplicativity property for cardinalities of sumsets
For finite sets of integers A1, . . . ,An we study the cardinality of the n-fold
sumset A1 + ¡ ¡ ¡ + An compared to those of (n â 1)-fold sumsets A1 + ¡ ¡ ¡ + Aiâ1 +
Ai+1 + ¡ ¡ ¡ + An. We prove a superadditivity and a submultiplicativity property for
these quantities. We also examine the case when the addition of elements is restricted
to an addition graph between the sets
Production of Boson Pairs at Photon Linear Colliders
The pair production rate in high energy collisions is
evaluated with photons from laser backscattering. We find that searching for
the Standard Model Higgs boson with a mass up to, or slightly larger than, 400
GeV via the final state is possible via photon fusion with backscattered
laser photons at a linear collider with energies in the range 600 GeV
1000 GeV.Comment: 18 pages in REVTEX, Figures available upon request,
DOE-ER40757-024,CPP-93-24 and FSU-HEP-93080
Diameters in preferential attachment models
In this paper, we investigate the diameter in preferential attachment (PA-)
models, thus quantifying the statement that these models are small worlds. The
models studied here are such that edges are attached to older vertices
proportional to the degree plus a constant, i.e., we consider affine PA-models.
There is a substantial amount of literature proving that, quite generally,
PA-graphs possess power-law degree sequences with a power-law exponent \tau>2.
We prove that the diameter of the PA-model is bounded above by a constant
times \log{t}, where t is the size of the graph. When the power-law exponent
\tau exceeds 3, then we prove that \log{t} is the right order, by proving a
lower bound of this order, both for the diameter as well as for the typical
distance. This shows that, for \tau>3, distances are of the order \log{t}. For
\tau\in (2,3), we improve the upper bound to a constant times \log\log{t}, and
prove a lower bound of the same order for the diameter. Unfortunately, this
proof does not extend to typical distances. These results do show that the
diameter is of order \log\log{t}.
These bounds partially prove predictions by physicists that the typical
distance in PA-graphs are similar to the ones in other scale-free random
graphs, such as the configuration model and various inhomogeneous random graph
models, where typical distances have been shown to be of order \log\log{t} when
\tau\in (2,3), and of order \log{t} when \tau>3
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