Inhomogeneous sandpile model: Crossover from multifractal scaling to finite size scaling

We study an inhomogeneous sandpile model in which two different toppling rules are defined. For any site only one rule is applied corresponding to either the Bak, Tang and Wiesenfeld model {[}P.Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. \textbf{59}, 381 (1987){]} or the Manna two-state sandpile model {[}S. S. Manna, J. Phys. A \textbf{24}, L363 (1991){]}. A parameter $c$ is introduced which describes a density of sites which are randomly deployed and where the stochastic Manna rules are applied. The results show that the avalanche area exponent $\tau_{a}$, avalanche size exponent $\tau_{s}$, and capacity fractal dimension $D_{s}$ depend on the density $c$. A crossover from multifractal scaling of the Bak, Tang, and Wiesenfeld model ($c=0$) to finite size scaling was found. The critical density $c$ is found to be in the interval $0<c<0.01$. These results demonstrate that local dynamical rules are important and can change the global properties of the model.Comment: 17 pages, 6 figure

Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models

Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K. Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C. Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each one of these models belongs to a distinct universality class.Comment: 18 pages of text, RevTeX, additional 8 figures in 12 PS file

Rejoinder

Rejoinder of "Estimating Random Effects via Adjustment for Density Maximization" by C. Morris and R. Tang [arXiv:1108.3234]Comment: Published in at http://dx.doi.org/10.1214/11-STS349REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discussion of "Estimating Random Effects via Adjustment for Density Maximization" by C. Morris and R. Tang

Discussion of "Estimating Random Effects via Adjustment for Density Maximization" by C. Morris and R. Tang [arXiv:1108.3234]Comment: Published in at http://dx.doi.org/10.1214/11-STS349A the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Pair correlation function of short-ranged square-well fluids

We have performed extensive Monte Carlo simulations in the canonical (NVT) ensemble of the pair correlation function for square-well fluids with well widths $\lambda-1$ ranging from 0.1 to 1.0, in units of the diameter $\sigma$ of the particles. For each one of these widths, several densities $\rho$ and temperatures $T$ in the ranges $0.1\leq\rho\sigma^3\leq 0.8$ and $T_c(\lambda)\lesssim T\lesssim 3T_c(\lambda)$, where $T_c(\lambda)$ is the critical temperature, have been considered. The simulation data are used to examine the performance of two analytical theories in predicting the structure of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and B. C.-Y. Lu, J. Chem. Phys. {\bf 100}, 3079, 6665 (1994)] and the non-perturbative model proposed by two of us [S. B. Yuste and A. Santos, J. Chem. Phys. {\bf 101}, 2355 (1994)]. It is observed that both theories complement each other, as the latter theory works well for short ranges and/or moderate densities, while the former theory does for long ranges and high densities.Comment: 10 pages, 10 figure

Asymptotics for kk-crank of kk-colored partitions

In this paper, we obtain asymptotic formulas for $k$-crank of $k$-colored partitions. Let $M_k(a, c; n)$ denote the number of $k$-colored partitions of $n$ with a $k$-crank congruent to $a$ mod $c$. For the cases $k=2,3,4$, Fu and Tang derived several inequality relations for $M_k(a, c; n)$ using generating functions. We employ the Hardy-Ramanujan Circle Method to extend the results of Fu and Tang. Furthermore, additional inequality relations for $M_k(a, c; n)$ have been established, such as logarithmic concavity and logarithmic subadditivity.Comment: 40 pages. arXiv admin note: text overlap with arXiv:1311.4344 by other author

Detection and attribution of an anomaly in terrestrial photosynthesis in Europe during the COVID-19 lockdown

Carbon dioxide (CO2) uptake by plant photosynthesis, referred to as gross primary production (GPP) at the ecosystem level, is sensitive to environmental factors, including pollutant exposure, pollutant uptake, and changes in the scattering of solar shortwave irradiance (SWin) - the energy source for photosynthesis. The 2020 spring lockdown due to COVID-19 resulted in improved air quality and atmospheric transparency, providing a unique opportunity to assess the impact of air pollutants on terrestrial ecosystem functioning. However, detecting these effects can be challenging as GPP is influenced by other meteorological drivers and management practices. Based on data collected from 44 European ecosystem-scale CO2 flux monitoring stations, we observed significant changes in spring GPP at 34 sites during 2020 compared to 2015-2019. Among these, 14 sites showed an increase in GPP associated with higher SWin, 10 sites had lower GPP linked to atmospheric and soil dryness, and seven sites were subjected to management practices. The remaining three sites exhibited varying dynamics, with one experiencing colder and rainier weather resulting in lower GPP, and two showing higher GPP associated with earlier spring melts. Analysis using the regional atmospheric chemical transport model (LOTOS-EUROS) indicated that the ozone (O-3) concentration remained relatively unchanged at the research sites, making it unlikely that O-3 exposure was the dominant factor driving the primary production anomaly. In contrast, SWin increased by 9.4 % at 36 sites, suggesting enhanced GPP possibly due to reduced aerosol optical depth and cloudiness. Our findings indicate that air pollution and cloudiness may weaken the terrestrial carbon sink by up to 16 %. Accurate and continuous ground-based observations are crucial for detecting and attributing subtle changes in terrestrial ecosystem functioning in response to environmental and anthropogenic drivers

Extension of a theorem of Duffin and Schaeffer

Let $r_1,\ldots,r_s:\mathbb{Z}_{n\geqslant 0}\to\mathbb{C}$ be linearly recurrent sequences whose associated eigenvalues have arguments in $\pi\mathbb{Q}$ and let $F(z):=\sum_{n\geqslant 0}f(n)z^n$, where $f(n)\in\{r_1(n),\ldots,$ $r_s(n)\}$ for each $n\geqslant 0$. We prove that if $F(z)$ is bounded in a sector of its disk of convergence, it is a rational function. This extends a very recent result of Tang and Wang, who gave the analogous result when the sequence $f(n)$ takes on values of finitely many polynomials.Comment: 2 page