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 β\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