6,188 research outputs found
Coarsening Dynamics of Granular Heaplets in Tapped Granular Layers
A semi-continuum model is introduced to study the dynamics of the formation
of granular heaplets in tapped granular layers. By taking into account the
energy dissipation of collisions and screening effects due to avalanches, this
model is able to reproduce qualitatively the pattern of these heaplets. Our
simulations show that the granular heaplets are characterised by an effective
surface tension which depends on the magnitude of the tapping intensity. Also,
we observe that there is a coarsening effect in that the average size of the
heaplets, V grows as the number of taps k increases. The growth law at
intermediate times can be fitted by a scaling function V ~ k^z but the range of
validity of the power law is limited by size effects. The growth exponent z
appears to diverge as the tapping intensity is increased.Comment: 4 pages, 4 figure
A box-covering algorithm for fractal scaling in scale-free networks
A random sequential box-covering algorithm recently introduced to measure the
fractal dimension in scale-free networks is investigated. The algorithm
contains Monte Carlo sequential steps of choosing the position of the center of
each box, and thereby, vertices in preassigned boxes can divide subsequent
boxes into more than one pieces, but divided boxes are counted once. We find
that such box-split allowance in the algorithm is a crucial ingredient
necessary to obtain the fractal scaling for fractal networks; however, it is
inessential for regular lattice and conventional fractal objects embedded in
the Euclidean space. Next the algorithm is viewed from the cluster-growing
perspective that boxes are allowed to overlap and thereby, vertices can belong
to more than one box. Then, the number of distinct boxes a vertex belongs to is
distributed in a heterogeneous manner for SF fractal networks, while it is of
Poisson-type for the conventional fractal objects.Comment: 12 pages, 11 figures, a proceedings of the conference, "Optimization
in complex networks." held in Los Alamo
Nonlocal evolution of weighted scale-free networks
We introduce the notion of globally updating evolution for a class of
weighted networks, in which the weight of a link is characterized by the amount
of data packet transport flowing through it. By noting that the packet
transport over the network is determined nonlocally, this approach can explain
the generic nonlinear scaling between the strength and the degree of a node. We
demonstrate by a simple model that the strength-driven evolution scheme
recently introduced can be generalized to a nonlinear preferential attachment
rule, generating the power-law behaviors in degree and in strength
simultaneously.Comment: 4 pages, 4 figures, final version published in PR
Self-similar disk packings as model spatial scale-free networks
The network of contacts in space-filling disk packings, such as the
Apollonian packing, are examined. These networks provide an interesting example
of spatial scale-free networks, where the topology reflects the broad
distribution of disk areas. A wide variety of topological and spatial
properties of these systems are characterized. Their potential as models for
networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of
higher-dimensional packing
High-pressure spin shifts in the pseudogap regime of superconducting YBa2Cu4O8 as revealed by 17O NMR
A new NMR anvil cell design is used for measuring the influence of high
pressure on the electronic properties of the high-temperature superconductor
YBaCuO above the superconducting transition temperature . It is found that pressure increases the spin shift at all temperatures in
such a way that the pseudo-gap feature has almost disappeared at 63 kbar. This
change of the temperature dependent spin susceptibility can be explained by a
pressure induced proportional decrease (factor of two) of a temperature
dependent component, and an increase (factor of 9) of a temperature independent
component, contrary to the effects of increasing doping. The results
demonstrate that one can use anvil cell NMR to investigate the tuning of the
electronic properties of correlated electronic materials with pressure.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev.
Load distribution in weighted complex networks
We study the load distribution in weighted networks by measuring the
effective number of optimal paths passing through a given vertex. The optimal
path, along which the total cost is minimum, crucially depend on the cost
distribution function . In the strong disorder limit, where , the load distribution follows a power law both in the
Erd\H{o}s-R\'enyi (ER) random graphs and in the scale-free (SF) networks, and
its characteristics are determined by the structure of the minimum spanning
tree. The distribution of loads at vertices with a given vertex degree also
follows the SF nature similar to the whole load distribution, implying that the
global transport property is not correlated to the local structural
information. Finally, we measure the effect of disorder by the correlation
coefficient between vertex degree and load, finding that it is larger for ER
networks than for SF networks.Comment: 4 pages, 4 figures, final version published in PR
Scale-free random branching tree in supercritical phase
We study the size and the lifetime distributions of scale-free random
branching tree in which branches are generated from a node at each time
step with probability . In particular, we focus on
finite-size trees in a supercritical phase, where the mean branching number
is larger than 1. The tree-size distribution exhibits a
crossover behavior when ; A characteristic tree size
exists such that for , and for , , where scales as . For , it follows the conventional
mean-field solution, with .
The lifetime distribution is also derived. It behaves as for , and for when branching step , and for all when . The analytic solutions are
corroborated by numerical results.Comment: 6 pages, 6 figure
Single-shot fluctuations in waveguided high-harmonic generation
For exploring the application potential of coherent soft x-ray (SXR) and
extreme ultraviolet radiation (XUV) provided by high-harmonic generation, it is
important to characterize the central output parameters. Of specific importance
are pulse-to-pulse (shot-to-shot) fluctuations of the high-harmonic output
energy, fluctuations of the direction of the emission (pointing instabilities),
and fluctuations of the beam divergence and shape that reduce the spatial
coherence. We present the first single-shot measurements of waveguided
high-harmonic generation in a waveguided (capillary-based) geometry. Using a
capillary waveguide filled with Argon gas as the nonlinear medium, we provide
the first characterization of shot-to-shot fluctuations of the pulse energy, of
the divergence and of the beam pointing. We record the strength of these
fluctuations vs. two basic input parameters, which are the drive laser pulse
energy and the gas pressure in the capillary waveguide. In correlation
measurements between single-shot drive laser beam profiles and single-shot
high-harmonic beam profiles we prove the absence of drive laser
beam-pointing-induced fluctuations in the high-harmonic output. We attribute
the main source of high-harmonic fluctuations to ionization-induced nonlinear
mode mixing during propagation of the drive laser pulse inside the capillary
waveguide
-free families in the Boolean lattice
For a family of subsets of [n]=\{1, 2, ..., n} ordered by
inclusion, and a partially ordered set P, we say that is P-free
if it does not contain a subposet isomorphic to P. Let be the
largest size of a P-free family of subsets of [n]. Let be the poset with
distinct elements a, b, c, d, a<b, c<d; i.e., the 2-dimensional Boolean
lattice. We show that where . We also prove that the largest -free
family of subsets of [n] having at most three different sizes has at most
2.20711N members.Comment: 18 pages, 2 figure
Shortest paths and load scaling in scale-free trees
The average node-to-node distance of scale-free graphs depends
logarithmically on N, the number of nodes, while the probability distribution
function (pdf) of the distances may take various forms. Here we analyze these
by considering mean-field arguments and by mapping the m=1 case of the
Barabasi-Albert model into a tree with a depth-dependent branching ratio. This
shows the origins of the average distance scaling and allows a demonstration of
why the distribution approaches a Gaussian in the limit of N large. The load
(betweenness), the number of shortest distance paths passing through any node,
is discussed in the tree presentation.Comment: 8 pages, 8 figures; v2: load calculations extende
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