Fractal dimension complexity of gravitation fractals in central place theory.

Settlement centers of various types, including cities, produce basins of attraction whose shape can be regular or complexly irregular (from the point of view of geometry). This complexity depends in part on properties of the space surrounding a settlement. This paper demonstrates that by introducing a dynamic approach to space and by including an equation of motion and space resistance, a dramatic change in the stylized static CPT (Central Place Theory) image occurs. As a result of the interplay of gravitational forces, basins of attraction arise around cities, whose boundaries appear to be fractals. This study provides a wealth of spatial fractal complex images which may change the traditional understanding of CPT.

Polymerization and Structure of Opposing Polymer Brushes Studied by Computer Simulations.

A model of the polymerization process during the formation of a pair of polymer brushes was designed and investigated. The obtained system consisted of two impenetrable parallel surfaces with the same number of chains grafted on both surfaces. Coarse-grained chains embedded in nodes of a face-centered cubic lattice with excluded volume interactions were obtained by a 'grafted from' procedure. The structure of synthesized macromolecular systems was also studied. Monte Carlo simulations using the dynamic lattice liquid model were employed using dedicated parallel machine ARUZ in a large size and time scale. The parameters of the polymerization process were found to be crucial for the proper structure of the brush. It was found that for high grafting densities, chains were increasingly compressed, and there is surprisingly little interpenetration of chains from opposite surfaces. It was predicted and confirmed that in a polydisperse sample, the longer chains have unique configurations consisting of a stretched stem and a coiled crown.

Review of Recent Developments of Glass Transition in PVC Nanocomposites.

This review addresses the impact of different nanoadditives on the glass transition temperature (Tg) of polyvinyl chloride (PVC), which is a widely used industrial polymer. The relatively high Tg limits its temperature-dependent applications. The objective of the review is to present the state-of-the-art knowledge on the influence of nanofillers of various origins and dimensions on the Tg of the PVC. The Tg variations induced by added nanofillers can be probed mostly by such experimental techniques as thermomechanical analysis (TMA), dynamic mechanical analysis (DMA), differential scanning calorimetry (DSC), and dielectric thermal analysis (DETA). The increase in Tg is commonly associated with the use of mineral and carbonaceous nanofillers. In this case, a rise in the concentration of nanoadditives leads to an increase in the Tg due to a restraint of the PVC macromolecular chain's mobility. The lowering of Tg may be attributed to the well-known plasticizing effect, which is a consequence of the incorporation of oligomeric silsesquioxanes to the polymeric matrix. It has been well established that the variation in the Tg value depends also on the chemical modification of nanofillers and their incorporation into the PVC matrix. This review may be an inspiration for further investigation of nanofillers' effect on the PVC glass transition temperature.

Dynamics of Opposing Polymer Brushes: A Computer Simulation Study.

Opposing polymer brush systems were synthesized and investigated by molecular modeling. Chains were restricted to a face-centered cubic lattice with the excluded volume interactions only. The system was confined between two parallel impenetrable walls, with the same number of chains grafted to each surface. The dynamic properties of such systems were studied by Monte Carlo simulations based on the dynamic lattice liquid model and using a highly efficient parallel machine ARUZ, which enabled the study of large systems and long timescales. The influence of the surface density and mean polymer length on the system dynamic was discussed. The self-diffusion coefficient of the solvent depended strongly on the degree of polymerization and on the polymer concentration. It was also shown that it is possible to capture changes in solvent mobility that can be attributed to the regions of different polymer densities.

Flux and storage of energy in nonequilibrium stationary states.

Systems kept out of equilibrium in stationary states by an external source of energy store an energy ΔU=U-U_{0}. U_{0} is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine ΔU for two model systems: ideal gas and a Lennard-Jones fluid. ΔU depends not only on the total energy flux, J_{U}, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where the energy flux per unit volume is (i) constant, (ii) proportional to the local temperature, and (iii) proportional to the local density. We show that ΔU/J_{U}=τ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. τ is the characteristic timescale of energy outflow from the system immediately after the shutdown of energy flux. We prove that τ is minimized in stable states of the Rayleigh-Benard cell.

Lévy-like movement patterns of metastatic cancer cells revealed in microfabricated systems and implicated in vivo.

Metastatic cancer cells differ from their non-metastatic counterparts not only in terms of molecular composition and genetics, but also by the very strategy they employ for locomotion. Here, we analyzed large-scale statistics for cells migrating on linear microtracks to show that metastatic cancer cells follow a qualitatively different movement strategy than their non-invasive counterparts. The trajectories of metastatic cells display clusters of small steps that are interspersed with long "flights". Such movements are characterized by heavy-tailed, truncated power law distributions of persistence times and are consistent with the Lévy walks that are also often employed by animal predators searching for scarce prey or food sources. In contrast, non-metastatic cancerous cells perform simple diffusive movements. These findings are supported by preliminary experiments with cancer cells migrating away from primary tumors in vivo. The use of chemical inhibitors targeting actin-binding proteins allows for "reprogramming" the Lévy walks into either diffusive or ballistic movements.

Communication: Molecular-level description of constrained chain topologies in multiblock copolymer gel networks.

Network characteristics in physical gels composed of solvated block copolymers varying in molecular design are examined here by dynamic rheology and computer simulations. In two triblock copolymer series, one with chain length (N) varied at constant copolymer composition (f) and the other with f varied at constant N, we discern the dependence of equilibrium network metrics on both N and f. Increasing the block number in a linear multiblock series at constant N and f escalates conformational complexity, which dominates network connectivity classified according to a midblock conformation index.

Complex Phase Behavior and Network Characteristics of Midblock-Solvated Triblock Copolymers as Physically Cross-Linked Soft Materials.

In the presence of a midblock-selective solvent, triblock copolymers not only self-organize but also form a molecular network. Thermoplastic elastomer gels constitute examples of such materials and serve as sealants and adhesives, as well as ballistic, microfluidic, and electroactive media. We perform Monte Carlo and dissipative particle dynamics simulations to investigate the phase behavior and network characteristics of these materials. Of particular interest is the existence of a truncated octahedral morphology that resembles the atomic arrangement of various inorganic species. Both simulation approaches quantify the midblock bridges responsible for network development and thus provide a detailed molecular picture of these composition-tunable soft materials.

Incipient microphase separation in short chain perfluoropolyether-block-poly(ethylene oxide) copolymers.

Incipient microphase separation is observed by wide angle X-ray scattering (WAXS) in short chain multiblock copolymers consisting of perfluoropolyether (PFPE) and poly(ethylene oxide) (PEO) segments. Two PFPE-PEO block copolymers were studied; one with dihydroxyl end groups and one with dimethyl carbonate end groups. Despite having a low degree of polymerization (N ∼ 10), these materials exhibited significant scattering intensity, due to disordered concentration fluctuations between their PFPE-rich and PEO-rich domains. The disordered scattering intensity was fit to a model based on a multicomponent random phase approximation to determine the value of the interaction parameter, χ, and the radius of gyration, Rg. Over the temperature range 30-90 °C, the values of χ were determined to be very large (∼2-2.5), indicating a high degree of immiscibility between the PFPE and PEO blocks. In PFPE-PEO, due to the large electron density contrast between the fluorinated and non-fluorinated block and the high value of χ, disordered scattering was detected at intermediate scattering angles, (q ∼ 2 nm-1) for relatively small polymer chains. Our ability to detect concentration fluctuations was enabled by both a relatively large value of χ and significant scattering contrast.

Self-Organisation in Spatial Systems-From Fractal Chaos to Regular Patterns and Vice Versa.

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.

Dual modes of self-assembly in superstrongly segregated bicomponent triblock copolymer melts.

While ABC triblock copolymers are known to form a plethora of dual-mode (i.e., order-on-order) nanostructures, bicomponent ABA triblock copolymers normally self-assemble into single morphologies at thermodynamic incompatibility levels up to the strong-segregation regime. In this study, we employ on-lattice Monte Carlo simulations to examine the phase behavior of molecularly asymmetric A(1)BA(2) copolymers possessing chemically identical endblocks differing significantly in length. In the limit of superstrong segregation, interstitial micelles composed of the minority A(2) endblock are observed to arrange into two-dimensional hexagonal arrays along the midplane of B-rich lamellae in compositionally symmetric (50:50 A:B) copolymers. Simulations performed here establish the coupled molecular-asymmetry and incompatibility conditions under which such micelles form, as well as the temperature dependence of their aggregation number. Beyond an optimal length of the A(2) endblock, the propensity for interstitial micelles to develop decreases, and the likelihood for colocation of both endblocks in the A(1)-rich lamellae increases. Interestingly, the strong-segregation theory of Semenov developed to explain the formation of free micelles by diblock copolymers accurately predicts the onset of interstitial micelles confined at nanoscale dimensions between parallel lamellae.

Communication: Molecular-level insights into asymmetric triblock copolymers: network and phase development.

Molecularly asymmetric triblock copolymers progressively grown from a parent diblock copolymer can be used to elucidate the phase and property transformation from diblock to network-forming triblock copolymer. In this study, we use several theoretical formalisms and simulation methods to examine the molecular-level characteristics accompanying this transformation, and show that reported macroscopic-level transitions correspond to the onset of an equilibrium network. Midblock conformational fractions and copolymer morphologies are provided as functions of copolymer composition and temperature.

Why Cells are Microscopic: A Transport-Time Perspective.

Physical-chemical reasoning is used to demonstrate that the sizes of both prokaryotic and eukaryotic cells are such that they minimize the times needed for the macromolecules to migrate throughout the cells and interact/react with one another. This conclusion does not depend on a particular form of the crowded-medium diffusion model, as thus points toward a potential optimization principle of cellular organisms. In eukaryotes, size optimality renders the diffusive transport as efficient as active transport - in this way, the cells can conserve energetic resources that would otherwise be expended in active transport.

Great expectations: can artificial molecular machines deliver on their promise?

The development and fabrication of mechanical devices powered by artificial molecular machines is one of the contemporary goals of nanoscience. Before this goal can be realized, however, we must learn how to control the coupling/uncoupling to the environment of individual switchable molecules, and also how to integrate these bistable molecules into organized, hierarchical assemblies that can perform significant work on their immediate environment at nano-, micro- and macroscopic levels. In this tutorial review, we seek to draw an all-important distinction between artificial molecular switches which are now ten a penny-or a dime a dozen-in the chemical literature and artificial molecular machines which are few and far between despite the ubiquitous presence of their naturally occurring counterparts in living systems. At the single molecule level, a prevailing perspective as to how machine-like characteristics may be achieved focuses on harnessing, rather than competing with, the ineluctable effects of thermal noise. At the macroscopic level, one of the major challenges inherent to the construction of machine-like assemblies lies in our ability to control the spatial ordering of switchable molecules-e.g., into linear chains and then into muscle-like bundles-and to influence the cross-talk between their switching kinetics. In this regard, situations where all the bistable molecules switch synchronously appear desirable for maximizing mechanical power generated. On the other hand, when the bistable molecules switch "out of phase," the assemblies could develop intricate spatial or spatiotemporal patterns. Assembling and controlling synergistically artificial molecular machines housed in highly interactive and robust architectural domains heralds a game-changer for chemical synthesis and a defining moment for nanofabrication.

An apparent critical point in binary mixtures: experimental and simulation study.

We report the experimental and simulation studies for the system of nitrobenzene-cyclododecane, showing an apparent critical point, which lies in their metastable, experimentally inaccessible state, below their melting point, affecting physical and chemical properties of this system in the stable liquid phase. The nonlinear dielectric effect (NDE) was measured in the mixture of nitrobenzene with cyclododecane. The mixture has been found to show an apparent critical point which lies below the melting point, manifested as anomalous NDE behavior in the vicinity of the critical concentrations in the stable liquid phase. The melting temperature of this system was estimated using the differential scanning calorimetry method. For such a system, we also performed Monte Carlo (MC) simulations that aimed to analyze the kinds of phase transitions observed and the conditions of their occurrence in Lennard-Jones mixture. The enthalpy, configurational energy, and radial distribution function have been estimated by the MC simulation method in the N-P-T system. Immiscibility conditions according to the approach by Schoen and Hoheisel [Mol. Phys. 57, 65 (1986)] are also discussed.