The transport of liquid and solutes in porous media over widely different time and length scales, ranging from specific interactions with the surface (and the associated interfacial dynamics) to the effective pore diffusion through hierarchical porosity, is central to many environmental and technological processes. This interplay between surface functionality and hierarchical porosity requires, on the one hand, a detailed molecular-level picture of sorption, reaction, and mobility, and realistic geometrical models of hierarchically porous media on the other, to establish (and apply) quantitative morphology– functionality–transport relationships for the tailored preparation of ever more selective and efficient materials for storage, separation, and catalysis.

The structure, dynamics, and mobility of binary solvents and solute molecules at adsorbent surfaces play an important role in adsorption, catalysis, and separation. When investigating chemical systems, information gained by experimental data is often limited to the macroscopic view. Molecular dynamics (MD) simulations allow new insights on molecular processes and offer the possibility to study the molecular-level picture at solid-liquid interfaces in detail.

Experimental studies of the aging of BrB-2 beryllium bronze in a constant magnetic field (PMF) show a noticeable “negative” magnetoplastic effect (MPE), which consists in reducing the ductility of the alloy and increasing the microhardness to 30% [1]. In some cases, the using a accompanied by the formation of structural formations — coherent scattering blocks — with a size of less than 100 nm [2], which we have identified as the nano-magnetoplastic effect (NMPE). It is of interest to search for optimal aging regimes that lead to the greatest effects of MPE and NMPE, and to establish the physical mechanisms of these effects.

The resistance perceived by guest molecules upon entering or leaving a microporous host material (the “surface barrier”) is known to often surpass the influence of diffusion in its interior on the overall rate of molecular uptake and release [1, 2]. Our knowledge of the relevant mechanisms of surface permeation, however, is still rather limited. This is related to the difficulties in its direct measurement which, given the “nanoscopic” extension of the relevant space scale, notably exceed the difficulties which do exist with already the diffusion measurement. A question discussed in this context refers to the possibility that the resistance perceived by the molecules on entering the pore space may differ from that perceived upon leaving [3-5].

Two types of host systems for one-dimensional molecular arrangements are considered, namely zeolites containing one- and twodimensional arrays of channels of sub-nanometre dimension and porous silicon with channel diameters in the range of a few nanometres. After a discussion of the potential of zeolites as host systems, in particular for molecular arrangements under the conditions of single-file diffusion and of molecular traffic control, actual diffusion measurements by means of pulsed-field gradient NMR and interference/IR microscopy are shown to reveal substantial differences between the real and ideal zeolite structure. In contrast, porous silicon with onedimensional channel arrays is successfully exploited as a host system allowing the experimental observation of such most important features of molecular confinement like hysteresis in mesoscalic systems and surface diffusion. Thus, the attainable experimental insight offers promising conditions for a comparison of the results with those of the theoretical treatment of the observed phenomena.

We construct classical stochastic mass transport processes for stationary states which are chosen to factorize over pairs of sites of an undirected, connected, but otherwise arbitrary graph. For the special topology of a ring we derive static properties such as the critical point of the transition between the liquid and the condensed phase, the shape of the condensate and its scaling with the system size. It turns out that the shape is not universal, but determined by the interplay of local and ultralocal interactions. In two dimensions the effect of anisotropic interactions of hopping rates can be treated analytically, since the partition function allows a dimensional reduction to an effective one-dimensional zero-range process. Here we predict the onset, shape and scaling of the condensate on a square lattice. We indicate further extensions in the outlook.

Graph theoretical approaches have become a powerful tool for investigating the architecture and dynamics of complex networks. The topology of network graphs revealed small-world properties for very different real systems among these neuronal networks. In this study, we observed the early development of mouse retinal ganglion cell (RGC) networks in vitro using timelapse video microscopy. By means of a time-resolved graph theoretical analysis of the connectivity, shortest path length and the edge length, we were able to discover the different stages during the network formation. Starting from single cells, at the first stage neurons connected to each other ending up in a network with maximum complexity. In the further course, we observed a simplification of the network which manifested in a change of relevant network parameters such as the minimization of the path length. Moreover, we found that RGC networks self-organized as small-world networks at both stages; however, the optimization occurred only in the second stage.

In this lecture, I will report on a model aiming at studying the dynamics and spreading of riots. It involves an epidemiological approach for the dynamics with a diffusion interaction term. I will discuss this model in the setting of the French riots of 2005 and compare its outcome with a rather detailed set of data for these riots. I will also describe a more general class of reaction-diffusion systems that are relevant in this context.

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