Environmental Superstatistics

A thermodynamic device placed outdoors, or a local ecosystem, is subject to a variety of different temperatures given by short-tem (daily) and long-term (seasonal) variations. In the long term a superstatistical description makes sense, with a suitable distribution function f(beta) of inverse temperature beta over which ordinary statistical mechanics is averaged. We show that f(beta) is very different at different geographic locations, and typically exhibits a double-peak structure for long-term data. For some of our data sets we also find a systematic drift due to global warming. For a simple superstatistical model system we show that the response to global warming is stronger if temperature fluctuations are taken into account.Comment: 37 figures. Significantly extended version, to appear in Physica A. Added new material in section 6 quantifying the stronger response to global warming if temperature fluctuations are taken into account. Concluding section 7 and several new references adde

Extreme event statistics of daily rainfall: Dynamical systems approach

We analyse the probability densities of daily rainfall amounts at a variety of locations on the Earth. The observed distributions of the amount of rainfall fit well to a q-exponential distribution with exponent q close to q=1.3. We discuss possible reasons for the emergence of this power law. On the contrary, the waiting time distribution between rainy days is observed to follow a near-exponential distribution. A careful investigation shows that a q-exponential with q=1.05 yields actually the best fit of the data. A Poisson process where the rate fluctuates slightly in a superstatistical way is discussed as a possible model for this. We discuss the extreme value statistics for extreme daily rainfall, which can potentially lead to flooding. This is described by Frechet distributions as the corresponding distributions of the amount of daily rainfall decay with a power law. On the other hand, looking at extreme event statistics of waiting times between rainy days (leading to droughts for very long dry periods) we obtain from the observed near-exponential decay of waiting times an extreme event statistics close to Gumbel distributions. We discuss superstatistical dynamical systems as simple models in this context.Comment: 10 pages, 15 figures. Replaced by final version published in J.Phys.

Entropies for severely contracted configuration space

We demonstrate that dual entropy expressions of the Tsallis type apply naturally to statistical-mechanical systems that experience an exceptional contraction of their configuration space. The entropic index $\alpha>1$ describes the contraction process, while the dual index $\alpha ^{\prime }=2-\alpha<1$ defines the contraction dimension at which extensivity is restored. We study this circumstance along the three routes to chaos in low-dimensional nonlinear maps where the attractors at the transitions, between regular and chaotic behavior, drive phase-space contraction for ensembles of trajectories. We illustrate this circumstance for properties of systems that find descriptions in terms of nonlinear maps. These are size-rank functions, urbanization and similar processes, and settings where frequency locking takes place

Incidence of qq-statistics in rank distributions

We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the Lyapunov exponent is negligible or vanishes. The relevant statistical-mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints, and the resulting duality of entropy indexes is seen to portray physically relevant information. While the value of the index $\alpha$ fixes the distribution's power-law exponent, that for the dual index $2-\alpha$ ensures the extensivity of the deformed entropy.Comment: Santa Fe Institute working paper: http://www.santafe.edu/media/workingpapers/14-07-024.pdf. see: http://www.pnas.org/content/early/2014/09/03/1412093111.full.pdf+htm

Distribution of some elements in Veronica scutellata L. from Bolu,Turkey: soil-plant interactions

Veronica scutellata L. occurs in moist and wet habitats, such as ponds, marshes and other wetlands. This study was conducted on this species to examine its mineral element uptake status in terms of interactions between soil and plant. Experimental materials were taken from the Southern coast of Black Sea at coordinates 40º36’N and 31º16’E at an altitude of 1400 m above sea level from Bolu – Turkey; using standard methods and plant (root, stem and leaf parts) and soil mineral element measurements (Al, B, Ca, Cu, Fe, K, Mg, Mn, Na, Ni and Zn) were done. During the study, ICP-OES was employed for the measurement of mineral elements. It was observed that considerable amounts of B, Ca, K, Mg, Mn, Na and Zn are accumulated by the plant

Fewer but poorer: Benevolent partiality in prosocial preferences

A prosocial action typically provides a more sizable benefit when directed at those who have less as opposed to those who have more. However, not all prosocial acts have a direct bearing on socioeconomic disadvantage, nor does disadvantage necessarily imply a greater need for the prosocial outcome. Of interest here, welfare impact may depend on the number of beneficiaries but not on their socioeconomic status. Across four preregistered studies of life-saving decisions, we demonstrate that when allocating resources, many people are benevolently partial. That is, they choose to help the disadvantaged even when this transparently implies sacrificing lives. We suggest that people construct prosocial aid as an opportunity to correct morally aversive inequalities, thusmaking relativelymore disadvantaged recipients amore justifiable target of help. Benevolent partiality is reduced when people reflect beforehand on what aspects they will prioritize in their donation decision