Elastic Entropic Forces in Polymer Deformation.

The entropic nature of elasticity of long molecular chains and reticulated materials is discussed concerning the analysis of flows of polymer melts and elastomer deformation in the framework of Frenkel-Eyring molecular kinetic theory. Deformation curves are calculated in line with the simple viscoelasticity models where the activation energy of viscous flow depends on the magnitude of elastic entropic forces of the stretched macromolecules. The interconnections between deformation processes and the structure of elastomer networks, as well as their mutual influence on each other, are considered.

Cities on the Coast and Patterns of Movement between Population Growth and Diffusion.

Sea level rise and high-impact coastal hazards due to on-going and projected climate change dramatically affect many coastal urban areas worldwide, including those with the highest urbanization growth rates. To develop tailored coastal climate services that can inform decision makers on climate adaptation in coastal cities, a better understanding and modeling of multifaceted urban dynamics is important. We develop a coastal urban model family, where the population growth and urbanization rates are modeled in the framework of diffusion over the half-bounded and bounded domains, and apply the maximum entropy principle to the latter case.

Infinite Ergodic Walks in Finite Connected Undirected Graphs.

The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of . As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navigability to the nodes by the different types of ergodic walks; as well as node's fugacity in the course of prospective network expansion or shrinking.

Extreme events and emergency scales.

An event is extreme if its magnitude exceeds the threshold. A choice of a threshold is subject to uncertainty caused by a method, the size of available data, a hypothesis on statistics, etc. We assess the degree of uncertainty by the Shannon's entropy calculated on the probability that the threshold changes at any given time.

Memories of the Future. Predictable and Unpredictable Information in Fractional Flipping a Biased Coin.

Some uncertainty about flipping a biased coin can be resolved from the sequence of coin sides shown already. We report the exact amounts of predictable and unpredictable information in flipping a biased coin. Fractional coin flipping does not reflect any physical process, being defined as a binomial power series of the transition matrix for "integer" flipping.

Exploration-exploitation trade-off features a saltatory search behaviour.

Searching experiments conducted in different virtual environments over a gender-balanced group of people revealed a gender irrelevant scale-free spread of searching activity on large spatio-temporal scales. We have suggested and solved analytically a simple statistical model of the coherent-noise type describing the exploration-exploitation trade-off in humans ('should I stay' or 'should I go'). The model exhibits a variety of saltatory behaviours, ranging from Lévy flights occurring under uncertainty to Brownian walks performed by a treasure hunter confident of the eventual success.