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 π\pi and KK mesons

The charge form factor of $\pi$ and $K$ 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 $CEBAF$ energies, is illustrated. The predictions for the elastic form factor of $\pi$ and $K$ mesons are compared with the results of different relativistic approaches, showing that the measurements of the pion and kaon form factors planned at $CEBAF$ 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 $N$ such points the network is grown by including them one by one according to the serial number into the growing network. The $t$-th point is attached to the $i$-th node of the network using the probability: $\pi_i(t) \sim k_i(t)\ell_{ti}^{\alpha}$ where $k_i(t)$ is the degree of the $i$-th node and $\ell_{ti}$ is the Euclidean distance between the points $t$ and $i$. Here $\alpha$ is a continuously tunable parameter and while for $\alpha=0$ one gets the simple Barab\'asi-Albert network, the case for $\alpha \to -\infty$ corresponds to the spatially continuous version of the well known Scheidegger's river network problem. The modulating parameter $\alpha$ is tuned to study the transition between the two different critical behaviors at a specific value $\alpha_c$ 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 − 1)-fold sumsets A1 + · · · + Ai−1 + 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

Separate muscle bundles of the flexor digitorum superficialis overlying the ulnar nerve

Background: The aim of this study was to elucidate the morphological charac­teristics of the muscle bundles of the flexor digitorum superficialis (FDS) attached to the intermuscular aponeurosis (IMA) and any related structure that could potentially compress the ulnar nerve. Materials and methods: Fifty embalmed limbs of 34 adult cadavers were studied. Results: The FDS arose as multiple separate bundles from the IMA of the lateral surface of the flexor carpi ulnaris in 76% of specimens. Below their origin, these separate bundles became attached continuously as a single mass to form the muscle belly. There were 1, 2, 3, 4 and 5 arising FDS muscle bundles in 28%, 30%, 4%, 10% and 4% of specimens, respectively. The muscle bundles were attached either only superficially (24% of cases) or across the entire width (20% of cases) of the IMA. In 32% of the specimens, bundles arose from the IMA in a combined fashion, being attached to the IMA superficially, deep and across the entire structure. The muscle bundles that arose from the deep part or entire width of the IMA were in contact with the ulnar nerve in 52% of specimens. In 11 (22%) specimens, the deep borders of the lowest muscle bundles close to the ulnar nerve were composed of tendinous fibres that divided from the IMA of the lateral surface of the flexor carpi ulnaris. The distance from the medial epicondyle to the lowest point of the FDS arising from the IMA was 62.0 ± 19.7 mm. Conclusions: The thick tendinous deep border of the lowest muscle bundle of the FDS where it attaches to the IMA is a potential cause of ulnar nerve compression

Production of ZZ Boson Pairs at Photon Linear Colliders

The $ZZ$ pair production rate in high energy $\gamma \gamma$ 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 $ZZ$ final state is possible via photon fusion with backscattered laser photons at a linear $e^+e^-$ collider with energies in the range 600 GeV $< \sqrt{s_{e^+e^-}} <$ 1000 GeV.Comment: 18 pages in REVTEX, Figures available upon request, DOE-ER40757-024,CPP-93-24 and FSU-HEP-93080