Measuring Lyapunov exponents of large chaotic systems with global coupling by time series analysis

Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we develop a method to overcome this difficulty, valid for highly symmetric systems such as systems with global coupling for which the dimensionality of recurrence analysis can be reduced drastically. We test our method numerically with two globally coupled systems, namely, logistic maps and limit-cycle oscillators with global coupling. The evaluated exponent values are successfully compared with the true ones obtained by the standard numerical method. We also describe a few techniques to improve the accuracy of the proposed method.Comment: 6 pages, 4 figure

A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces

The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we i) pay debts to heroic predecessors, ii) highlight additional, experimentally relevant aspects of the recently solved 1+1 KPZ problem, iii) use an expanding substrates formalism to gain access to the 3d radial KPZ equation and, lastly, iv) examining extremal paths on disordered hierarchical lattices, set our gaze upon the fate of $d$=$\infty$ KPZ. Clearly, there remains ample unexplored territory within the realm of KPZ and, for the hearty, much work to be done, especially in higher dimensions, where numerical and renormalization group methods are providing a deeper understanding of this iconic equation.Comment: Mini-review, mixed w/ new results. 18 pages, 6 figures. Journal of Statistical Physics, in press; v2: corrects typos, adds ref

Scaling of hysteresis loops at phase transitions into a quasiabsorbing state

Models undergoing a phase transition to an absorbing state weakly broken by the addition of a very low spontaneous nucleation rate are shown to exhibit hysteresis loops whose width $\Delta\lambda$ depends algebraically on the ramp rate $r$. Analytical arguments and numerical simulations show that $\Delta\lambda \sim r^{\kappa}$ with $\kappa = 1/(\beta'+1)$, where $\beta'$ is the critical exponent governing the survival probability of a seed near threshold. These results explain similar hysteresis scaling observed before in liquid crystal convection experiments. This phenomenon is conjectured to occur in a variety of other experimental systems.Comment: 4 pages, 4 figures, 1 tabl

Mid-infrared luminosity as an indicator of the total infrared luminosity of galaxies

The infrared (IR) emission plays a crucial role for understanding the star formation in galaxies hidden by dust. We first examined four estimators of the IR luminosity of galaxies, L_fir (Helou et al. 1988), L_tir (Dale et al. 2001), revised version of L_tir (Dale & Helou 2002) (we denote L_tir2), and L_ir (Sanders & Mirabel 1996) by using the observed SEDs of well-known galaxies. We found that L_ir provides excellent estimates of the total IR luminosity for a variety of galaxy SEDs. The performance of L_tir2 was also found to be very good. Using L_ir, we then statistically analyzed the IRAS PSCz galaxy sample (Saunders et al. 2000) and found useful formulae relating the MIR monochromatic luminosities [L(12um) and L(25um)], and L_ir. For this purpose we constructed a subsample of 1420 galaxies with all IRAS four band (12, 25, 60, and 100um) flux densities. We found linear relations between L_ir and MIR luminosities, L(12um) and L(25um). The prediction error with 95-% confidence level is a factor of 4-5. Hence, these formulae are useful for the estimation of the total IR luminosity only from 12um or 25um observations. We further tried to make an `interpolation' formula for galaxies at 0<z<1. For this purpose we construct the formula of the relation between 15-um luminosity and the total IR luminosity. We conclude that the 15-um formula can be used as an estimator of the total IR luminosity from 24um observation of galaxies at z \simeq 0.6.Comment: A&A in press, 8 pages, 9 figures, numerical errors correcte

Statistics of circular interface fluctuations in an off-lattice Eden model

Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of the height (radius) fluctuations are numerically determined and compared with the recent theoretical developments as well as the author's experimental result on growing interfaces in turbulent liquid crystal [K. A. Takeuchi and M. Sano, arXiv:1203.2530]. We focus in particular on analytically unsolved properties such as the temporal correlation function and the persistence probability in space and time. Good agreement with the experiment is found in characteristic quantities for them, which implies that the geometry-dependent universality of the KPZ class holds here as well, but otherwise a few dissimilarities are also found. Finite-time corrections in the cumulants of the distribution are also studied and shown to decay as $t^{-2/3}$ for the mean, in contrast to $t^{-1/3}$ reported for all the previously known cases.Comment: 15 pages, 10 figures; reference updated (v2,v3); minor changes in text (v3

Strategic vs Non-Strategic Motivations of Sanctioning

We isolate strategic and non-strategic motivations of sanctioning in a repeated public goods game. In two experimental treatments, subjects play the public goods game with the possibility to sanction others. In the STANDARD sanctions treatment, each subject learns about the sanctions received in the same round as they were assigned, but in the SECRET sanctions treatment, sanctions are announced only after the experiment is finished, removing in this way all strategic reasons to punish. We find that sanctioning is similar in both treatments, giving support for nonstrategic explanations of sanctions (altruistic punishment). Interestingly, contributions to the public good in both treatments with sanctioning are higher than when the public goods game is played without any sanctioning, irrespective of announcing the sanctions to their receivers during the play of the game, or only after the game is finished. The mere knowledge that sanctions might be assigned increases cooperation: subjects correctly expect that nonstrategic sanctioning takes place against freeriders.altruistic punishment;nonstrategic sanctions;strategic sanctions;public goods;economic experiment

Crossover from Growing to Stationary Interfaces in the Kardar-Parisi-Zhang Class

This Letter reports on how the interfaces in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) class undergo, in the course of time, a transition from the flat, growing regime to the stationary one. Simulations of the polynuclear growth model and experiments on turbulent liquid crystal reveal universal functions of the KPZ class governing this transition, which connect the distribution and correlation functions for the growing and stationary regimes. This in particular shows how interfaces realized in experiments and simulations actually approach the stationary regime, which is never attained unless a stationary interface is artificially given as an initial condition.Comment: 5 pages, 3 figures; improved introduction and other minor/stylistic changes (v2