27,670 research outputs found

### Aftershocks in Modern Perspectives: Complex Earthquake Network, Aging, and Non-Markovianity

The phenomenon of aftershocks is studied in view of science of complexity. In
particular, three different concepts are examined: (i) the complex-network
representation of seismicity, (ii) the event-event correlations, and (iii) the
effects of long-range memory. Regarding (i), it is shown the clustering
coefficient of the complex earthquake network exhibits a peculiar behavior at
and after main shocks. Regarding (ii), it is found that aftershocks experience
aging, and the associated scaling holds. And regarding (iii), the scaling
relation to be satisfied by a class of singular Markovian processes is
violated, implying the existence of the long-range memory in processes of
aftershocks.Comment: 28 pages, 6 figures and 1 table. Acta Geophysica, in pres

### Macroscopic thermodynamics of equilibrium characterized by power-law canonical distributions

Macroscopic thermodynamics of equilibrium is constructed for systems obeying
power-law canonical distributions. With this, the connection between
macroscopic thermodynamics and microscopic statistical thermodynamics is
generalized. This is complementary to the Gibbs theorem for the celebrated
exponential canonical distributions of systems in contact with a heat bath.
Thereby, a thermodynamic basis is provided for power-law phenomena ubiquitous
in nature.Comment: 12 page

### Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions

The q-exponential distributions, which are generalizations of the
Zipf-Mandelbrot power-law distribution, are frequently encountered in complex
systems at their stationary states. From the viewpoint of the principle of
maximum entropy, they can apparently be derived from three different
generalized entropies: the Renyi entropy, the Tsallis entropy, and the
normalized Tsallis entropy. Accordingly, mere fittings of observed data by the
q-exponential distributions do not lead to identification of the correct
physical entropy. Here, stabilities of these entropies, i.e., their behaviors
under arbitrary small deformation of a distribution, are examined. It is shown
that, among the three, the Tsallis entropy is stable and can provide an
entropic basis for the q-exponential distributions, whereas the others are
unstable and cannot represent any experimentally observable quantities.Comment: 20 pages, no figures, the disappeared "primes" on the distributions
are added. Also, Eq. (65) is correcte

### B Physics at SLD

We review recent $B$ physics results obtained in polarized $e^+ e^-$
interactions at the SLC by the SLD experiment. The excellent 3-D vertexing
capabilities of SLD are exploited to extract precise \bu and \bd lifetimes,
as well as measurements of the time evolution of $B^0_d - \bar{B^0_d}$ mixing.Comment: 7 pages, 4 figure

### Geometry of escort distributions

Given an original distribution, its statistical and probabilistic attributs
may be scanned by the associated escort distribution introduced by Beck and
Schlogl and employed in the formulation of nonextensive statistical mechanics.
Here, the geometric structure of the one-parameter family of the escort
distributions is studied based on the Kullback-Leibler divergence and the
relevant Fisher metric. It is shown that the Fisher metric is given in terms of
the generalized bit-variance, which measures fluctuations of the crowding index
of a multifractal. The Cramer-Rao inequality leads to the fundamental limit for
precision of statistical estimate of the order of the escort distribution. It
is also quantitatively discussed how inappropriate it is to use the original
distribution instead of the escort distribution for calculating the expectation
values of physical quantities in nonextensive statistical mechanics.Comment: 12 pages, no figure

### Dynamical evolution of clustering in complex network of earthquakes

The network approach plays a distinguished role in contemporary science of
complex systems/phenomena. Such an approach has been introduced into seismology
in a recent work [S. Abe and N. Suzuki, Europhys. Lett. 65, 581 (2004)]. Here,
we discuss the dynamical property of the earthquake network constructed in
California and report the discovery that the values of the clustering
coefficient remain stationary before main shocks, suddenly jump up at the main
shocks, and then slowly decay following a power law to become stationary again.
Thus, the network approach is found to characterize main shocks in a peculiar
manner.Comment: 10 pages, 3 figures, 1 tabl

### Nonextensive thermodynamic relations

The generalized zeroth law of thermodynamics indicates that the physical
temperature in nonextensive statistical mechanics is different from the inverse
of the Lagrange multiplier, beta. This leads to modifications of some of
thermodynamic relations for nonextensive systems. Here, taking the first law of
thermodynamics and the Legendre transform structure as the basic premises, it
is found that Clausius definition of the thermodynamic entropy has to be
appropriately modified, and accordingly the thermodynamic relations proposed by
Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are also to be
rectified. It is shown that the definition of specific heat and the equation of
state remain form invariant. As an application, the classical gas model is
reexamined and, in marked contrast with the previous result obtained by Abe
[Phys. Lett. A 263 (1999) 424: Erratum A 267 (2000) 456] using the unphysical
temperature and the unphysical pressure, the specific heat and the equation of
state are found to be similar to those in ordinary extensive thermodynamics.Comment: 17 pages. The discussion about the Legendre transform structure is
modified and some additional comments are mad

### Scale-invariant statistics of period in directed earthquake network

A new law regarding structure of the earthquake networks is found. The
seismic data taken in California is mapped to a growing directed network. Then,
statistics of period in the network, which implies that after how many
earthquakes an earthquake returns to the initial location, is studied. It is
found that the period distribution obeys a power law, showing the fundamental
difficulty of statistical estimate of period.Comment: 11 pages including 3 figure

### Tsallis Statistics: Averages and a Physical Interpretation of the Lagrange Multiplier $\beta$

Tsallis has proposed a generalisation of the standard entropy, which has
since been applied to a variety of physical systems. In the canonical ensemble
approach that is mostly used, average energy is given by an unnromalised, or
normalised, $q$-expectation value. A Lagrange multiplier $\beta$ enforces the
energy constraint whose physical interpretation, however, is lacking. Here, we
use a microcanonical ensemble approach and find that consistency requires that
only normalised $q$-expectation values are to be used. We then present a
physical interpretation of $\beta$, relating it to a physical temperature. We
derive this interpretation by a different method also.Comment: Latex file. 11 pages. Sections 2 and 3 modified and shortened; an
implicit assumption in Sec 4 is made explicit; a note and a reference added;
other minor changes. To appear in Physics Letters

### Perspectives on Nuclear Structure and Scattering with the Ab Initio No-Core Shell Model

Nuclear structure and reaction theory are undergoing a major renaissance with
advances in many-body methods, strong interactions with greatly improved links
to Quantum Chromodynamics (QCD), the advent of high performance computing, and
improved computational algorithms. Predictive power, with well-quantified
uncertainty, is emerging from non-perturbative approaches along with the
potential for new discoveries such as predicting nuclear phenomena before they
are measured. We present an overview of some recent developments and discuss
challenges that lie ahead. Our focus is on explorations of alternative
truncation schemes in the harmonic oscillator basis, of which our
Japanese--United States collaborative work on the No-Core Monte-Carlo Shell
Model is an example. Collaborations with Professor Takaharu Otsuka and his
group have been instrumental in these developments.Comment: 8 pages, 5 figures, accepted for publication in Proceedings of
Perspectives of the Physics of Nuclear Structure, JPS Conference Proceedings,
Japan (to appear

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