Modeling of dispersion of air pollutants in the atmosphere is one of the most important and challenging scientific problems. There are several natural and anthropogenic events where passive or chemically active compounds are emitted into the atmosphere. The effect of these chemical species can have serious impacts on our environment and human health. Modeling the dispersion of air pollutants can predict this effect. Therefore, development of various model strategies is a key element for the governmental and scientific communities. We provide here a brief review on the mathematical modeling of the dispersion of air pollutants in the atmosphere. We discuss the advantages and drawbacks of several model tools and strategies, namely Gaussian, Lagrangian, Eulerian and CFD models. We especially focus on several recent advances in this multidisciplinary research field, like parallel computing using graphical processing units, or adaptive mesh refinement.

Helical and helicoidal precipitation patterns emerging in the wake of reaction-diffusion fronts are studied. In our experiments, these chiral structures arise with well defined probabilities PH controlled by conditions such as e.g., the initial concentration of the reagents. We develop a model which describes the observed experimental trends. The results suggest that PH is determined by a delicate interplay among the time-and length-scales related to the front and to the unstable precipitation modes and, furthermore, the noise amplitude also plays a quantifiable role.PACS numbers: 68.35.Ct Helices and helicoids are present from nano-to macroscale (ZnO nanohelices [1], macromolecules and inorganic crystals with a helical structure [2, 3], precipitation helices [4][5][6], fiber geometry of heart walls [7]). Formation of these fascinating structures generally follows two routes. First, templates with chiral symmetry (e.g., oragogel fibers) may exist in the system, and the symmetry is just transcribed to a structure (e.g., inorganic materials [8]) at a larger scale. Second, spontaneous symmetry breaking may occur through the self-assembly of achiral building blocks into a helical/helicoidal structure, as e.g. in case of crystals with chiral morphology [2,9].Theoretically, the symmetry-breaking route is more interesting. Universal aspects may emerge and the robust features of this self-organization process may be important for applications as well. Indeed, control over creating helical structures would make engineering (in particular, the bottom-up design of micro-patterns [10]) more flexible since chiral morphology of materials are known to affect their physical (electronic) properties [6,11].In order to develop insight into the genesis of helices/helicoids, we investigate an emblematic example of pattern formation, namely the formation of precipitation patterns in the wake of reaction-diffusion fronts [12,13]. The motivation for this choice comes from the observation that helicoidal structures have an axis, and the correlations are simple in the plane perpendicular to the axis. This suggests that building the perpendicular correlations in the wake of an advancing planar front may be a simple and natural mechanism of creating helices/helicoids. Additional motivation comes from the existence of a large body of knowledge in the related Liesegang phenomena [12,13]. It allows the use of well-established experimental and theoretical approaches, thus making it easier to develop a novel view on the formation of helical structures.Our main results concern the probabilistic aspects of the symmetry-breaking route. We determine the probability P H of the emergence of single helices/helicoids in Liesegang-type experiments as the conditions such as the initial concentration of inner or outer electrolytes, or the temperature are changed. P H is found to be well reproducible and large (P H > 0.5 for some parameter range). The results are understood by expanding and simulating a model of formation of precipitation patterns [14]...

A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system. However, network states are usually unknown, and only a fraction of the state variables are directly measurable. The observability problem concerns reconstructing the network state from this limited information. Here, we propose a general optimization-based approach for observing the states of nonlinear networks and for optimally selecting the observed variables. Our results reveal several fundamental limitations in network observability, such as the trade-off between the fraction of observed variables and the observation length on one side, and the estimation error on the other side. We also show that, owing to the crucial role played by the dynamics, purely graphtheoretic observability approaches cannot provide conclusions about one's practical ability to estimate the states. We demonstrate the effectiveness of our methods by finding the key components in biological and combustion reaction networks from which we determine the full system state. Our results can lead to the design of novel sensing principles that can greatly advance prediction and control of the dynamics of such networks.

We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size N and power-law exponent γ, while keeping the average degree fixed. We study ensembles generated by three different network construction methods, and we use a greedy algorithm to approximate the MDS. With a structural cutoff imposed on the maximal degree we find linear scaling of the MDS size with respect to N in all three network classes. Without any cutoff (kmax = N – 1) two of the network classes display a transition at γ ≈ 1.9, with linear scaling above, and vanishingly weak dependence below, but in the third network class we find linear scaling irrespective of γ. We find that the partial MDS, which dominates a given z < 1 fraction of nodes, displays essentially the same scaling behavior as the MDS.

A theoretical study of the emergence of helices in the wake of precipitation fronts is presented. The precipitation dynamics is described by the Cahn-Hilliard equation and the fronts are obtained by quenching the system into a linearly unstable state. Confining the process onto the surface of a cylinder and using the pulled-front formalism, our analytical calculations show that there are front solutions that propagate into the unstable state and leave behind a helical structure. We find that helical patterns emerge only if the radius of the cylinder R is larger than a critical value R>R(c), in agreement with recent experiments.

Certain invasive plants may rely on interference mechanisms (allelopathy, e.g.) to gain competitive superiority over native species. But expending resources on interference presumably exacts a cost in another life-history trait, so that the significance of interference competition for invasion ecology remains uncertain. We model ecological invasion when combined effects of preemptive and interference competition govern interactions at the neighborhood scale. We consider three cases. Under "novel weapons," only the initially rare invader exercises interference. For "resistance zones" only the resident species interferes, and finally we take both species as interference competitors. Interference increases the other species' mortality, opening space for colonization. However, a species exercising greater interference has reduced propagation, which can hinder its colonization of open sites. Interference never enhances a rare invader's growth in the homogeneously mixing approximation to our model. But interference can significantly increase an invader's competitiveness, and its growth when rare, if interactions are structured spatially. That is, interference can increase an invader's success when colonization of open sites depends on local, rather than global, species densities. In contrast, interference enhances the common, resident species' resistance to invasion independently of spatial structure, unless the propagation-cost is too great. Increases in background mortality (i.e., mortality not due to interference) always reduce the effectiveness of interference competition.

Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research.A general and robust idea is the parallelization of source codes/programs. Recently, the technological development of graphics hardware created a possibility to use desktop video cards to solve numerically intensive problems. We present a powerful parallel computing framework to solve reaction-diffusion equations numerically using the Graphics Processing Units (GPUs) with CUDA. Four different reaction-diffusion problems, (i) diffusion of chemically inert compound, (ii) Turing pattern formation, (iii) phase separation in the wake of * Corresponding author. Tel.: +36-2090555; fax: +36-1372-2904. a moving diffusion front and (iv) air pollution dispersion were solved, and additionally both the Shared method and the Moving Tiles method were tested. Our results show that parallel implementation achieves typical acceleration values in the order of 5-40 times compared to CPU using a single-threaded implementation on a 2.8 GHz desktop computer.

The Graphics Processing Unit (GPU) is a powerful tool for parallel computing. high speedup with no additional costs to maintain this parallel architecture could result in a wide usage of GPU for diversified environmental applications in the near future.