Spatio-temporal scaling

These principles ensure correct hydrodynamic behavior of DPD fluid. The advantage of DPD over other methods lies in the possibility of matching the scale of discrete-particle simulation to the dominant spatio-temporal scales of the entire system. For example, in MD simulation the timescales associated with evolution of heavy colloidal particles are many orders of magnitude larger than the temporal evolution of solvent particles. If the solvent molecules are coarse-grained into DPD droplets, they evolve much more slowly and are able to match the time scales close to those associated with the colloidal particles. 

For complex fluids, the gap in the spatio-temporal scales between the smallest microstructures and the largest structures is much smaller than for simple fluids. Dzwinel and Yuen (2000b) have shown that by using moderate number of particles, we can simulate in two dimensions multiresolution structures ranging frommicellar arrays to the large colloidal agglomerates. 

Kahru, M., Nommann, S., 1990. The phytoplankton spring bloom in the Baltic Sea in 1985, 1986 multitude of spatio-temporal scales. Continental Shelf Research, 10, 329-354. 

Different behaviour at different spatio-temporal scales, ranging from small-scale concentration fluctuations in the turbulence inertial range to large-scale air movements in synoptic events affecting the entire troposphere. 

This is referred to as the scaling paradigm (Fig. 2). The scaling is of utmost importance given the fact that most environmental problems occur at the larger spatio-temporal scales, while most characterization techniques and well-validated modelling concepts are only operational at the lower scale. 

The distribution and fate of PAHs in the atmosphere has been the subject of numerous studies covering a wide range of spatio-temporal scales and relevant sources (references in Finlayson-Pitts and Pitts 2000 Prevedouros et al. 2005 Tsapakis and Stephanou 2005 Lammel et al. 2009a Balasubramanian and He 2010). Most studies focused on occurrence of the parent PAHs, while nitro-PAHs gained interest in the chemistry of nitrogen oxides rich atmospheres (Finlayson-Pitts and Pitts 2000) and alkylated and partly oxygenated PAHs had significantly less been addressed so far (e.g. Albinet et al. 2008). 

The issue of spatio-temporal scaling is far from resolved but we postulate that from an evolutionary viewpoint at local geographic scales where dispersal limitations are minimal, environmental heterogeneity is the major driver of diversity over time. Across larger distances the effects of dispersal limitation become more... 

Under many practical situations such as in biological systems, above-mentioned two self-organization principles are not always distinguishable so clearly. Contrary, they often play their roles in different spatio-temporal scales to bring about highly complicated structures in open systems. A biological system is a good but not the only example we can find it in a very simple system as well. 

Capillary network and porous material in the mesoscale can be viewed as a complex system consisting of two mutually interacting constituents, namely, the colloidal suspension and the wall material. The complexity of these components is connected mainly with the development of multiple spatio-temporal scales involved in a proper description of their physical, chemical, and geometrical properties. In the case of colloidal suspension, the multiple scales come from ... 

The other way for simulating systems over wider spatio-temporal scales consists of employing heterogeneous hybridized cross-scale models. 

Common primitives, particles, defined by a set of attributes whose physical meaning is different depending which spatio-temporal scale is currently being considered. 

On the other hand, the LBG method can capture both mesoscopic and macroscopic scales even larger than those that can be modeled by discrete-particle methods. This advantage is due to computational simplicity of the method, which comes from coarse-grained discretization of both the space and time and drastic simplification of collision rules between particles. We can look at the validity of these simplifications by comparing them with more realistic discrete-particles simulation. We regard both DPD and LBG as being complementary computational tools for modeling the slow dynamics in porous media over wide spatio-temporal scales. 

The entire biosphere is today subjected to the consequences of human activities and to their combined impacts on the enviromnent and biodiversity. These impacts often translate into modifications of the chemical properties of the enviromnent which are notably observed in the most remote areas of the globe (contamination by organic pollutants persisting in polar regions, acidification and anoxia of deep water of certain oceanic regions, eutrophication and/or soil erosion). Despite this, the concepts and tools to imderstand the impacts of these multiple abiotic constraints at different spatio-temporal scales, on diversified communities and in interactions are missing. 

---