1,003 research outputs found
Superdiffusion in a class of networks with marginal long-range connections
A class of cubic networks composed of a regular one-dimensional lattice and a
set of long-range links is introduced. Networks parametrized by a positive
integer k are constructed by starting from a one-dimensional lattice and
iteratively connecting each site of degree 2 with a th neighboring site of
degree 2. Specifying the way pairs of sites to be connected are selected,
various random and regular networks are defined, all of which have a power-law
edge-length distribution of the form with the marginal
exponent s=1. In all these networks, lengths of shortest paths grow as a power
of the distance and random walk is super-diffusive. Applying a renormalization
group method, the corresponding shortest-path dimensions and random-walk
dimensions are calculated exactly for k=1 networks and for k=2 regular
networks; in other cases, they are estimated by numerical methods. Although,
s=1 holds for all representatives of this class, the above quantities are found
to depend on the details of the structure of networks controlled by k and other
parameters.Comment: 10 pages, 9 figure
A new method for hardness determination from depth sensing indentation tests
A new semiempirical formula is developed for the hardness determination of the materials from depth sensing indentation tests. The indentation works measured both during loading and unloading periods are used in the evaluation. The values of the Meyer hardness calculated in this way agree well with those obtained by conventional optical observation, where this latter is possible. While the new hardness formula characterizes well the behavior of the conventional hardness number even for the ideally elastic material, the mean contact pressure generally used in hardness determination differs significantly from the conventional hardness number when the ideally elastic limiting case is being approached
Anomalous diffusion in disordered multi-channel systems
We study diffusion of a particle in a system composed of K parallel channels,
where the transition rates within the channels are quenched random variables
whereas the inter-channel transition rate v is homogeneous. A variant of the
strong disorder renormalization group method and Monte Carlo simulations are
used. Generally, we observe anomalous diffusion, where the average distance
travelled by the particle, []_{av}, has a power-law time-dependence
[]_{av} ~ t^{\mu_K(v)}, with a diffusion exponent 0 \le \mu_K(v) \le 1.
In the presence of left-right symmetry of the distribution of random rates, the
recurrent point of the multi-channel system is independent of K, and the
diffusion exponent is found to increase with K and decrease with v. In the
absence of this symmetry, the recurrent point may be shifted with K and the
current can be reversed by varying the lane change rate v.Comment: 16 pages, 7 figure
On maps preserving connectedness and /or compactness
We call a function -preserving if, for every subspace with property , its image also has property . Of
course, all continuous maps are both compactness- and connectedness-preserving
and the natural question about when the converse of this holds, i.e. under what
conditions is such a map continuous, has a long history.
Our main result is that any non-trivial product function, i.e. one having at
least two non-constant factors, that has connected domain, range, and is
connectedness-preserving must actually be continuous. The analogous statement
badly fails if we replace in it the occurrences of "connected" by "compact". We
also present, however, several interesting results and examples concerning maps
that are compactness-preserving and/or continuum-preserving.Comment: 8 page
Scaling behavior of the contact process in networks with long-range connections
We present simulation results for the contact process on regular, cubic
networks that are composed of a one-dimensional lattice and a set of long edges
with unbounded length. Networks with different sets of long edges are
considered, that are characterized by different shortest-path dimensions and
random-walk dimensions. We provide numerical evidence that an absorbing phase
transition occurs at some finite value of the infection rate and the
corresponding dynamical critical exponents depend on the underlying network.
Furthermore, the time-dependent quantities exhibit log-periodic oscillations in
agreement with the discrete scale invariance of the networks. In case of
spreading from an initial active seed, the critical exponents are found to
depend on the location of the initial seed and break the hyper-scaling law of
the directed percolation universality class due to the inhomogeneity of the
networks. However, if the cluster spreading quantities are averaged over
initial sites the hyper-scaling law is restored.Comment: 9 pages, 10 figure
Two improvements on Tkačenko's addition theorem
summary:We prove that (A) if a countably compact space is the union of countably many subspaces then it is compact; (B) if a compact space is the union of fewer than = \operatorname{cov} (\Cal M) left-separated subspaces then it is scattered. Both (A) and (B) improve results of Tkačenko from 1979; (A) also answers a question that was raised by Arhangel'ski\v{i} and improves a result of Gruenhage
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