597 research outputs found

### Recurrence intervals between earthquakes strongly depend on history

We study the statistics of the recurrence times between earthquakes above a
certain magnitude M$in California. We find that the distribution of the
recurrence times strongly depends on the previous recurrence time$\tau_0$. As
a consequence, the conditional mean recurrence time$\hat \tau(\tau_0)$between
two events increases monotonically with$\tau_0$. For$\tau_0$well below the
average recurrence time$\ov{\tau}, \hat\tau(\tau_0)$is smaller than$\ov{\tau}$, while for$\tau_0>\ov{\tau}$,$\hat\tau(\tau_0)$is greater than$\ov{\tau}$. Also the mean residual time until the next earthquake does not
depend only on the elapsed time, but also strongly on$\tau_0$. The larger$\tau_0$ is, the larger is the mean residual time. The above features should be
taken into account in any earthquake prognosis.Comment: 5 pages, 3 figures, submitted to Physica

### Power-law persistence and trends in the atmosphere: A detailed study of long temperature records

We use several variants of the detrended fluctuation analysis to study the
appearance of long-term persistence in temperature records, obtained at 95
stations all over the globe. Our results basically confirm earlier studies. We
find that the persistence, characterized by the correlation C(s) of temperature
variations separated by s days, decays for large s as a power law, C(s) ~
s^(-gamma). For continental stations, including stations along the coastlines,
we find that gamma is always close to 0.7. For stations on islands, we find
that gamma ranges between 0.3 and 0.7, with a maximum at gamma = 0.4. This is
consistent with earlier studies of the persistence in sea surface temperature
records where gamma is close to 0.4. In all cases, the exponent gamma does not
depend on the distance of the stations to the continental coastlines. By
varying the degree of detrending in the fluctuation analysis we obtain also
information about trends in the temperature records.Comment: 5 pages, 4 including eps figure

### Pore opening effects and transport diffusion in the Knudsen regime in comparison to self- (or tracer-) diffusion

We study molecular diffusion in linear nanopores with different types of
roughness in the so-called Knudsen regime. Knudsen diffusion represents the
limiting case of molecular diffusion in pores, where mutual encounters of the
molecules within the free pore space may be neglected and the time of flight
between subsequent collisions with the pore walls significantly exceeds the
interaction time between the pore wall and the molecules. We present an
extension of a commonly used procedure to calculate transport diffusion
coefficients. Our results show that using this extension, the coefficients of
self- and transport diffusion in the Knudsen regime are equal for all regarded
systems, which improves previous literature data.Comment: 5 pages, 7 figure

### Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated
by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied
for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form
$P_d(r,t)=\rho(r) t^{-1/2} \xi^{-2} f_d(\xi)$, where $\rho(r)\sim r^{2-d}$ is
the density of the chain. Expanding $f_d(\xi)$ in powers of $\xi$, we find that
there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$,
each one characterized by a logarithmic correction in $f_d(\xi)$. Namely, for
$d=2$, $f_2(\xi)\simeq a_2\xi^2\ln\xi+b_2\xi^2$; for $3\le d\le 5$,
$f_d(\xi)\simeq a_d\xi^2+b_d\xi^d$; for $d=6$, $f_6(\xi)\simeq
a_6\xi^2+b_6\xi^6\ln\xi$; for $7\le d\le 9$, $f_d(\xi)\simeq
a_d\xi^2+b_d\xi^6+c_d\xi^d$; for $d=10$, $f_{10}(\xi)\simeq
a_{10}\xi^2+b_{10}\xi^6+c_{10}\xi^{10}\ln\xi$, {\it etc.\/} In particular, for
$d=2$, this implies that the temporal dependence of the probability density of
being close to the origin $Q_2(r,t)\equiv P_2(r,t)/\rho(r)\simeq t^{-1/2}\ln
t$.Comment: LATeX, 10 pages, no figures submitted for publication in PR

### Volcanic forcing improves Atmosphere-Ocean Coupled General Circulation Model scaling performance

Recent Atmosphere-Ocean Coupled General Circulation Model (AOGCM) simulations
of the twentieth century climate, which account for anthropogenic and natural
forcings, make it possible to study the origin of long-term temperature
correlations found in the observed records. We study ensemble experiments
performed with the NCAR PCM for 10 different historical scenarios, including no
forcings, greenhouse gas, sulfate aerosol, ozone, solar, volcanic forcing and
various combinations, such as it natural, anthropogenic and all forcings. We
compare the scaling exponents characterizing the long-term correlations of the
observed and simulated model data for 16 representative land stations and 16
sites in the Atlantic Ocean for these scenarios. We find that inclusion of
volcanic forcing in the AOGCM considerably improves the PCM scaling behavior.
The scenarios containing volcanic forcing are able to reproduce quite well the
observed scaling exponents for the land with exponents around 0.65 independent
of the station distance from the ocean. For the Atlantic Ocean, scenarios with
the volcanic forcing slightly underestimate the observed persistence exhibiting
an average exponent 0.74 instead of 0.85 for reconstructed data.Comment: 4 figure

### Long term persistence in the sea surface temperature fluctuations

We study the temporal correlations in the sea surface temperature (SST)
fluctuations around the seasonal mean values in the Atlantic and Pacific
oceans. We apply a method that systematically overcome possible trends in the
data. We find that the SST persistence, characterized by the correlation $C(s)$
of temperature fluctuations separated by a time period $s$, displays two
different regimes. In the short-time regime which extends up to roughly 10
months, the temperature fluctuations display a nonstationary behavior for both
oceans, while in the asymptotic regime it becomes stationary. The long term
correlations decay as $C(s) \sim s^{-\gamma}$ with $\gamma \sim 0.4$ for both
oceans which is different from $\gamma \sim 0.7$ found for atmospheric land
temperature.Comment: 14 pages, 5 fiure

### Supremacy distribution in evolving networks

We study a supremacy distribution in evolving Barabasi-Albert networks. The
supremacy $s_i$ of a node $i$ is defined as a total number of all nodes that
are younger than $i$ and can be connected to it by a directed path. For a
network with a characteristic parameter $m=1,2,3,...$ the supremacy of an
individual node increases with the network age as $t^{(1+m)/2}$ in an
appropriate scaling region. It follows that there is a relation $s(k) \sim
k^{m+1}$ between a node degree $k$ and its supremacy $s$ and the supremacy
distribution $P(s)$ scales as $s^{-1-2/(1+m)}$. Analytic calculations basing on
a continuum theory of supremacy evolution and on a corresponding rate equation
have been confirmed by numerical simulations.Comment: 4 pages, 4 figure

### Percolation of randomly distributed growing clusters: Finite Size Scaling and Critical Exponents

We study the percolation properties of the growing clusters model. In this
model, a number of seeds placed on random locations on a lattice are allowed to
grow with a constant velocity to form clusters. When two or more clusters
eventually touch each other they immediately stop their growth. The model
exhibits a discontinuous transition for very low values of the seed
concentration $p$ and a second, non-trivial continuous phase transition for
intermediate $p$ values. Here we study in detail this continuous transition
that separates a phase of finite clusters from a phase characterized by the
presence of a giant component. Using finite size scaling and large scale Monte
Carlo simulations we determine the value of the percolation threshold where the
giant component first appears, and the critical exponents that characterize the
transition. We find that the transition belongs to a different universality
class from the standard percolation transition.Comment: 5 two-column pages, 6 figure

### Nonlinear Volatility of River Flux Fluctuations

We study the spectral properties of the magnitudes of river flux increments,
the volatility. The volatility series exhibits (i) strong seasonal periodicity
and (ii) strongly power-law correlations for time scales less than one year. We
test the nonlinear properties of the river flux increment series by randomizing
its Fourier phases and find that the surrogate volatility series (i) has almost
no seasonal periodicity and (ii) is weakly correlated for time scales less than
one year. We quantify the degree of nonlinearity by measuring (i) the amplitude
of the power spectrum at the seasonal peak and (ii) the correlation power-law
exponent of the volatility series.Comment: 5 revtex pages, 6 page

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