Finite-Time Singularity Signature of Hyperinflation

We present a novel analysis extending the recent work of Mizuno et al. [2002] on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of ``inflationary expectation'' or positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time $t_c$. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general nonlinear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time $t_c$, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.Comment: Latex 21 pages including 2 tables and 7 eps figure

Neutrino texture saturating the CP asymmetry

We study a neutrino mass texture which can explain the neutrino oscillation data and also saturate the upper bound of the CP asymmetry $\epsilon_1$ in the leptogenesis. We consider the thermal and non-thermal leptogenesis based on the right-handed neutrino decay in this model. A lower bound of the reheating temperature required for the explanation of the baryon number asymmetry is estimated as $O(10^8)$GeV for the thermal leptogenesis and $O(10^{6})$GeV for the non-thermal one.It can be lower than the upper bound of the reheating temperature imposed by the cosmological gravitino problem. An example of the construction of the discussed texture is also presented.Comment: 23 pages, 6 figure

Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation

We study nonequilibrium phase transitions in a mass-aggregation model which allows for diffusion, aggregation on contact, dissociation, adsorption and desorption of unit masses. We analyse two limits explicitly. In the first case mass is locally conserved whereas in the second case local conservation is violated. In both cases the system undergoes a dynamical phase transition in all dimensions. In the first case, the steady state mass distribution decays exponentially for large mass in one phase, and develops an infinite aggregate in addition to a power-law mass decay in the other phase. In the second case, the transition is similar except that the infinite aggregate is missing.Comment: Major revision of tex

On de-Sitter geometry in crater statistics

The cumulative size-frequency distributions of impact craters on planetary bodies in the solar system appear to approximate a universal inverse square power-law for small crater radii. In this article, we show how this distribution can be understood easily in terms of geometrical statistics, using a de-Sitter geometry of the configuration space of circles on the Euclidean plane and on the unit sphere. The effect of crater overlap is also considered.Comment: 6 pages, 2 figures, accepted by MNRAS. Version 2: title modified, appendix added, some small change

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

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

Phase Transition in the Takayasu Model with Desorption

We study a lattice model where particles carrying different masses diffuse, coalesce upon contact, and also unit masses adsorb to a site with rate $q$ or desorb from a site with nonzero mass with rate $p$. In the limit $p=0$ (without desorption), our model reduces to the well studied Takayasu model where the steady-state single site mass distribution has a power law tail $P(m)\sim m^{-\tau}$ for large mass. We show that varying the desorption rate $p$ induces a nonequilibrium phase transition in all dimensions. For fixed $q$, there is a critical $p_c(q)$ such that if $p<p_c(q)$, the steady state mass distribution, $P(m)\sim m^{-\tau}$ for large $m$ as in the Takayasu case. For $p=p_c(q)$, we find $P(m)\sim m^{-\tau_c}$ where $\tau_c$ is a new exponent, while for $p>p_c(q)$, $P(m)\sim \exp(-m/m^*)$ for large $m$. The model is studied analytically within a mean field theory and numerically in one dimension.Comment: RevTex, 11 pages including 5 figures, submitted to Phys. Rev.

Binary spreading process with parity conservation

Recently there has been a debate concerning the universal properties of the phase transition in the pair contact process with diffusion (PCPD) $2A\to 3A, 2A\to \emptyset$. Although some of the critical exponents seem to coincide with those of the so-called parity-conserving universality class, it was suggested that the PCPD might represent an independent class of phase transitions. This point of view is motivated by the argument that the PCPD does not conserve parity of the particle number. In the present work we pose the question what happens if the parity conservation law is restored. To this end we consider the the reaction-diffusion process $2A\to 4A, 2A\to \emptyset$. Surprisingly this process displays the same type of critical behavior, leading to the conclusion that the most important characteristics of the PCPD is the use of binary reactions for spreading, regardless of whether parity is conserved or not.Comment: RevTex, 4pages, 4 eps figure

Unified View of Scaling Laws for River Networks

Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.Comment: 14 pages, 9 figures, 4 tables (converted to Revtex4, PRE ref added

Coupled-Map Modeling of One-Dimensional Traffic Flow

We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle properly, and the maps are coupled to each other through the headway distance. By simulating the model, we obtain a plot of the flow against the concentration similar to the observed data in real traffic flows. Realistic traffic jam regions are observed in space-time trajectories.Comment: 5 postscript figures available upon reques