We present the results of Monte Carlo lattice simulations of a model symmetric diblock copolymer wherein a fraction of segments of one block, p, corresponds to ionic species, and the other block does not contain ions. We use experimentally determined Flory−Huggins interaction parameters, χ, to quantify the interactions between ionic and nonionic monomers. Analysis of the experimental data indicate that χ between poly(styrenesulfonate) and polystyrene is about 5, a value that is orders of magnitude larger than that obtained in mixtures of nonionic polymers. Our model predicts that clustering of ionic monomers in the disordered state results in stabilization of the disordered phase and the product p 2 χN is well above the mean-field value of 10.5 at the order−disorder transition (N is the total number of monomers per chain). Network morphologies and hexagonally packed cylinders are observed in the ordered state at large p values while more traditional lamellar phases are found at small values of p.

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This study offers a new perspective on the evolutionary patterns of cities or urban agglomerations. Such developments can range from chaotic to fully ordered. We demonstrate that in a dynamic space of interactive human behaviour cities produce a wealth of gravitational attractors whose size and shape depend on the resistance of space emerging inter alia from transport friction costs. This finding offers original insights into the complex evolution of spatial systems and appears to be consistent with the principles of central place theory known from the spatial sciences and geography. Our approach is dynamic in nature and forms a generalisation of hierarchical principles in geographic space.

The dynamics of spatial hierarchical processes displays fascinating images of the evolution of attraction basins of towns. Assuming in the present paper a random character of such complex processes, gravitational modeling is employed to depict changes in the nature of fuzzy boundaries between attraction basins in a hexagonal world, i.e. the geographical pattern central in the renowned and influential Christaller–Lösch central place theory in geography. The paper presents various interesting stylized maps of such stochastic processes. Our findings demonstrate that the collective behavior of actors in geographic space shows a white noise pattern that mirrors a fuzzy gravitation towards large population concentrations. These results support the validity of the conventional central place theory.

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Using self-consistent field theory (SCFT) in spherical unit cells of various dimensionalities, D, a phase diagram of a diblock, A-b-B, is calculated in 5 dimensional space, d=5. This is an extension of a previuos work for d=4. The phase diagram is parameterized by the chain composition, f , and incompatibility between A and B, quantified by the product χN . We predict 5 stable nanophases: layers, cylinders, 3D spherical cells, 4D spherical cells, and 5D spherical cells. In the strong segregation limit, that is for large χN , the order-order transition compositions are determined by the strong segregation theory (SST) in its simplest form. While the predictions of the SST theory are close to the corresponding SCFT extrapolations for d = 4, the extrapolations for d = 5 significantly differ from them. We find that the S 5 nanophase is stable in a narrow strip between ordered S 4 nanophase and the disordered phase. The calculated order-disorder transition lines depend weakly on d, as expected. *

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In recent years, numerous Polish cities and municipalities have become involved in the creation of bike-sharing systems. Although the contribution of bike-sharing to creating sustainable transport caused some controversy in the literature, the positive role of cycling in promoting low-emission mobility and a healthy lifestyle is widely acknowledged. As part of the European Union’s sustainable transport agenda, some Polish local governments have obtained funding from structural funds for the implementation of bicycle-sharing schemes. This article presents an overview of selected systems, as well as a preliminary analysis of their users’ activity based on data obtained through a Web API. Although the scope of the data was limited in time due to the shutdown of the systems caused by the COVID-19 pandemic shortly after their spring reactivation, some patterns could be observed. In particular, users activity was more evenly distributed over time in larger cities (over 300 thousand of residents), whereas in smaller cities alternating periods of high and low activity was observed.