Logarithmic corrections of the avalanche distributions of sandpile models at the upper critical dimension

We study numerically the dynamical properties of the BTW model on a square lattice for various dimensions. The aim of this investigation is to determine the value of the upper critical dimension where the avalanche distributions are characterized by the mean-field exponents. Our results are consistent with the assumption that the scaling behavior of the four-dimensional BTW model is characterized by the mean-field exponents with additional logarithmic corrections. We benefit in our analysis from the exact solution of the directed BTW model at the upper critical dimension which allows to derive how logarithmic corrections affect the scaling behavior at the upper critical dimension. Similar logarithmic corrections forms fit the numerical data for the four-dimensional BTW model, strongly suggesting that the value of the upper critical dimension is four.Comment: 8 pages, including 9 figures, accepted for publication in Phys. Rev.

The Bak-Tang-Wiesenfeld sandpile model around the upper critical dimension

We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in different dimensions (D>=6). A finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents, the dynamical exponent, and the dimension of the avalanches. Above the upper critical dimension D_u=4 the exponents equal the known mean field values. An analysis of the area probability distributions indicates that the avalanches are fractal above the critical dimension.Comment: 7 pages, including 9 figures, accepted for publication in Physical Review

Order Parameter and Scaling Fields in Self-Organized Criticality

We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the order parameter and the relevant scaling fields in order to describe the critical behavior in terms of usual concepts of non equilibrium lattice models with steady-states. We point out the inconsistencies of previous mean-field approaches, which lead to different predictions. Numerical simulations confirm the validity of our results beyond mean-field theory.Comment: 4 RevTex pages and 2 postscript figure

How self-organized criticality works: A unified mean-field picture

We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF) models. In analogy with other non-equilibrium critical phenomena, we identify the order parameter with the density of ``active'' sites and the control parameters with the driving rates. Depending on the values of the control parameters, the system is shown to reach a subcritical (absorbing) or super-critical (active) stationary state. Criticality is analyzed in terms of the singularities of the zero-field susceptibility. In the limit of vanishing control parameters, the stationary state displays scaling characteristic of self-organized criticality (SOC). We show that this limit corresponds to the breakdown of space-time locality in the dynamical rules of the models. We define a complete set of critical exponents, describing the scaling of order parameter, response functions, susceptibility and correlation length in the subcritical and supercritical states. In the subcritical state, the response of the system to small perturbations takes place in avalanches. We analyze their scaling behavior in relation with branching processes. In sandpile models because of conservation laws, a critical exponents subset displays mean-field values ($\nu=1/2$ and $\gamma = 1$) in any dimensions. We treat bulk and boundary dissipation and introduce a new critical exponent relating dissipation and finite size effects. We present numerical simulations that confirm our results. In the case of the forest-fire model, our approach can distinguish between different regimes (SOC-FF and deterministic FF) studied in the literature and determine the full spectrum of critical exponents.Comment: 21 RevTex pages, 3 figures, submitted to Phys. Rev.

Sine-Gordon breather form factors and quantum field equations

Using the results of previous investigations on sine-Gordon form factors exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental bose field, general exponentials of it, the energy momentum tensor and all higher currents. Formulae for the asymptotic behavior of bosonic form factors are presented which are motivated by Weinberg's power counting theorem in perturbation theory. It is found that the quantum sine-Gordon field equation holds and an exact relation between the ``bare'' mass and the renormalized mass is obtained. Also a quantum version of a classical relation for the trace of the energy momentum is proven. The eigenvalue problem for all higher conserved charges is solved. All results are compared with perturbative Feynman graph expansions and full agreement is found.Comment: LaTeX, 31 page

Universal scaling behavior of non-equilibrium phase transitions

One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to a given universality class have the same critical exponents, and certain scaling functions become identical near the critical point. It is the aim of this work to demonstrate the usefulness of universal scaling functions for the analysis of non-equilibrium phase transitions. In order to limit the coverage of this article, we focus on a particular class of non-equilibrium critical phenomena, the so-called absorbing phase transitions. These phase transitions arise from a competition of opposing processes, usually creation and annihilation processes. The transition point separates an active phase and an absorbing phase in which the dynamics is frozen. A systematic analysis of universal scaling functions of absorbing phase transitions is presented, including static, dynamical, and finite-size scaling measurements. As a result a picture gallery of universal scaling functions is presented which allows to identify and to distinguish universality classes.Comment: review article, 160 pages, 60 figures include

Pharmaceutical pollution of the world's rivers

Environmental exposure to active pharmaceutical ingredients (APIs) can have negative effects on the health of ecosystems and humans. While numerous studies have monitored APIs in rivers, these employ different analytical methods, measure different APIs, and have ignored many of the countries of the world. This makes it difficult to quantify the scale of the problem from a global perspective. Furthermore, comparison of the existing data, generated for different studies/regions/continents, is challenging due to the vast differences between the analytical methodologies employed. Here, we present a global-scale study of API pollution in 258 of the world's rivers, representing the environmental influence of 471.4 million people across 137 geographic regions. Samples were obtained from 1,052 locations in 104 countries (representing all continents and 36 countries not previously studied for API contamination) and analyzed for 61 APIs. Highest cumulative API concentrations were observed in sub-Saharan Africa, south Asia, and South America. The most contaminated sites were in low- to middle-income countries and were associated with areas with poor wastewater and waste management infrastructure and pharmaceutical manufacturing. The most frequently detected APIs were carbamazepine, metformin, and caffeine (a compound also arising from lifestyle use), which were detected at over half of the sites monitored. Concentrations of at least one API at 25.7% of the sampling sites were greater than concentrations considered safe for aquatic organisms, or which are of concern in terms of selection for antimicrobial resistance. Therefore, pharmaceutical pollution poses a global threat to environmental and human health, as well as to delivery of the United Nations Sustainable Development Goals

Removal efficiency of pharmaceuticals in a full scale constructed wetland in East Ukraine

Pharmaceuticals in surface water are a threat to drinking water supplies. The removal of 12 pharmaceuticals was investigated in a full scale constructed wetland processing hospital wastewaters in East Ukraine. Passive integrative samplers POCIS were used to monitor target compounds in the wastewater inlet and outlet at the beginning of the constructed wetland operation in 2012 and three years later in 2015. Pharmaceuticals were effectively removed; however, their removal efficiency differed among the compounds and years of the operation. An increase of removal efficiency was observed for androstenedione, carbamazepine, caffeine, diclofenac, estrone, ibuprofen, paracetamol, propranolol and triclosan with greater water residence time and an increase in macrophyte cover. Removal patterns of pharmaceuticals were discussed based on specific physical chemical properties of molecules, changes in the operational conditions of the constructed wetland and inlet pollutant concentrations. Further research is needed to fully understand how the maturation of constructed wetlands influences the removal of emerging contaminants from wastewater

Multi-tracing of recharge seasonality and contamination in groundwater:a tool for urban water resource management

Abstract In this study, sources of recharge and contamination in urban groundwater and in groundwater underneath a forest in the same aquifer were determined and compared. Data on hydro-chemical parameters and stable isotopes of water were collected in urban and forest springs in the Kharkiv region, Ukraine, over a period of 12 months. Groundwater transit time and precipitation contribution were calculated using hydrogeological data and stable isotopes of water to delineate groundwater recharge conditions. Hydro-chemical data, stable isotopes and emerging contaminants were used to trace anthropogenic groundwater recharge and approximate sewage and tap water contributions to the aquifer. The results indicated that each spring had unique isotopic signatures that could be explained by recharge conditions, groundwater residence time, and specific mixing patterns with sewage and water leaks. Elevated nitrate content, stable isotopes of nitrate, and the presence of emerging pollutants (mainly illicit drugs) in most of the urban springs confirmed mixing of urban groundwater with sewage leaks. These leaks amounted to up to 25% of total recharge and exhibited seasonal variations in some springs. Overall, the results show that urban groundwater receives variable seasonal contributions of anthropogenic components that increase the risk to the environment and human health, and reduce its usability for drinking water production. The multi-tracing approach presented can be useful for other cities worldwide that have similar problems of poor water management and inadequate sewage and water supply infrastructure