359 research outputs found
Long-term power-law fluctuation in Internet traffic
Power-law fluctuation in observed Internet packet flow are discussed. The
data is obtained by a multi router traffic grapher (MRTG) system for 9 months.
The internet packet flow is analyzed using the detrended fluctuation analysis.
By extracting the average daily trend, the data shows clear power-law
fluctuations. The exponents of the fluctuation for the incoming and outgoing
flow are almost unity. Internet traffic can be understood as a daily periodic
flow with power-law fluctuations.Comment: 10 pages, 8 figure
Heuristic Segmentation of a Nonstationary Time Series
Many phenomena, both natural and human-influenced, give rise to signals whose
statistical properties change under time translation, i.e., are nonstationary.
For some practical purposes, a nonstationary time series can be seen as a
concatenation of stationary segments. Using a segmentation algorithm, it has
been reported that for heart beat data and Internet traffic fluctuations--the
distribution of durations of these stationary segments decays with a power law
tail. A potential technical difficulty that has not been thoroughly
investigated is that a nonstationary time series with a (scale-free) power law
distribution of stationary segments is harder to segment than other
nonstationary time series because of the wider range of possible segment sizes.
Here, we investigate the validity of a heuristic segmentation algorithm
recently proposed by Bernaola-Galvan et al. by systematically analyzing
surrogate time series with different statistical properties. We find that if a
given nonstationary time series has stationary periods whose size is
distributed as a power law, the algorithm can split the time series into a set
of stationary segments with the correct statistical properties. We also find
that the estimated power law exponent of the distribution of stationary-segment
sizes is affected by (i) the minimum segment size, and (ii) the ratio of the
standard deviation of the mean values of the segments, and the standard
deviation of the fluctuations within a segment. Furthermore, we determine that
the performance of the algorithm is generally not affected by uncorrelated
noise spikes or by weak long-range temporal correlations of the fluctuations
within segments.Comment: 23 pages, 14 figure
Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation
One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0,
where in the latter case like particles coagulate on encounters and move as
clusters, are solved exactly with anisotropic hopping rates and assuming
synchronous dynamics. Asymptotic large-time results for particle densities are
derived and discussed in the framework of universality.Comment: 13 pages in plain Te
Exact Solutions of Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation
We report exact results for one-dimensional reaction-diffusion models A+A ->
inert, A+A -> A, and A+B -> inert, where in the latter case like particles
coagulate on encounters and move as clusters. Our study emphasized anisotropy
of hopping rates; no changes in universal properties were found, due to
anisotropy, in all three reactions. The method of solution employed mapping
onto a model of coagulating positive integer charges. The dynamical rules were
synchronous, cellular-automaton type. All the asymptotic large-time results for
particle densities were consistent, in the framework of universality, with
other model results with different dynamical rules, when available in the
literature.Comment: 28 pages in plain TeX + 2 PostScript figure
The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena
The Internet is the most complex system ever created in human history.
Therefore, its dynamics and traffic unsurprisingly take on a rich variety of
complex dynamics, self-organization, and other phenomena that have been
researched for years. This paper is a review of the complex dynamics of
Internet traffic. Departing from normal treatises, we will take a view from
both the network engineering and physics perspectives showing the strengths and
weaknesses as well as insights of both. In addition, many less covered
phenomena such as traffic oscillations, large-scale effects of worm traffic,
and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex
System
Mass-Transport Models with Multiple-Chipping Processes
We study mass-transport models with multiple-chipping processes. The rates of
these processes are dependent on the chip size and mass of the fragmenting
site. In this context, we consider k-chip moves (where k = 1, 2, 3, ....); and
combinations of 1-chip, 2-chip and 3-chip moves. The corresponding mean-field
(MF) equations are solved to obtain the steady-state probability distributions,
P (m) vs. m. We also undertake Monte Carlo (MC) simulations of these models.
The MC results are in excellent agreement with the corresponding MF results,
demonstrating that MF theory is exact for these models.Comment: 18 pages, 4 figures, To appear in European Physical Journal
Demountable Toroidal Field Magnets for Use in a Compact Modular Fusion Reactor
A concept of demountable toroidal field magnets for a compact fusion reactor is discussed. The magnets generate a magnetic field of 9.2 T on axis, in a 3.3 m major radius tokamak. Subcooled YBCO conductors have a critical current density adequate to provide this large magnetic field, while operating at 20 K reduces thermodynamic cooling cost of the resistive electrical joints. Demountable magnets allow for vertical replacement and maintenance of internal components, potentially reducing cost and time of maintenance when compared to traditional sector maintenance. Preliminary measurements of contact resistance of a demountable YBCO electrical joint between are presented
Diffusion-Limited Aggregation Processes with 3-Particle Elementary Reactions
A diffusion-limited aggregation process, in which clusters coalesce by means
of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a
heuristic argument that predicts logarithmic corrections to the mean-field
asymptotic behavior for the concentration of clusters of mass at time ,
, for . The total
concentration of clusters, , decays as at . We also investigate the problem with a localized steady source of
monomers and find that the steady-state concentration scales as
, , and , respectively,
for the spatial dimension equal to 1, 2, and 3. The total number of
clusters, , grows with time as , , and
for = 1, 2, and 3. Furthermore, in three dimensions we
obtain an asymptotic solution for the steady state cluster-mass distribution:
, with the scaling function
and the scaling variable .Comment: 12 pages, plain Te
Communication in networks with hierarchical branching
We present a simple model of communication in networks with hierarchical
branching. We analyze the behavior of the model from the viewpoint of critical
systems under different situations. For certain values of the parameters, a
continuous phase transition between a sparse and a congested regime is observed
and accurately described by an order parameter and the power spectra. At the
critical point the behavior of the model is totally independent of the number
of hierarchical levels. Also scaling properties are observed when the size of
the system varies. The presence of noise in the communication is shown to break
the transition. Despite the simplicity of the model, the analytical results are
a useful guide to forecast the main features of real networks.Comment: 4 pages, 3 figures. Final version accepted in PR
Continuous time random walk with correlated waiting times
Based on the Langevin description of the Continuous Time Random Walk (CTRW),
we consider a generalization of CTRW in which the waiting times between the
subsequent jumps are correlated. We discuss the cases of exponential and slowly
decaying persistent power-law correlations between the waiting times as two
generic examples and obtain the corresponding mean squared displacements as
functions of time. In the case of exponential-type correlations the
(sub)diffusion at short times is slower than in the absence of correlations. At
long times the behavior of the mean squared displacement is the same as in
uncorrelated CTRW. For power-law correlations we find subdiffusion
characterized by the same exponent at all times, which appears to be smaller
than the one in uncorrelated CTRW. Interestingly, in the limiting case of an
extremely long power-law correlations, the (sub)diffusion exponent does not
tend to zero, but is bounded from below by the subdiffusion exponent
corresponding to a short time behavior in the case of exponential correlations
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