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We examine the long-term behavior of nonintegrable, energy-conserved, 1D systems of macroscopic grains interacting via a contact-only generalized Hertz potential and held between stationary walls. Existing dynamical studies showed the absence of energy equipartitioning in such systems, hence their long-term dynamics was described as quasi-equilibrium. Here, we show that these systems do in fact reach thermal equilibrium at sufficiently long times, as indicated by the calculated heat capacity. This phase is described by equilibrium statistical mechanics, opening up the possibility that the machinery of nonequilibrium statistical mechanics may be used to understand the behavior of these systems away from equilibrium.

Shortest path plays an important role in the study of complex networks. But in real transportation systems, choosing the shortest path may not be the best way for the drivers. Based on the traffic equilibrium theory, we generalize the concept of shortest path. Flux distribution is also investigated by using the generalized concept on various types of complex networks. We find that the flux differs little in all the edges of lattice while in small-world and scale-free networks, the flux distribution follows a power law, and in the random network, the flux distribution has an exponential tail. We consider lattice may be the optimal topology in design a transportation network.

In this paper, we present two epidemic models with a nonlinear incidence and transfer from infectious to recovery. For epidemic models, the basic reproductive number is calculated. A dynamic system based on threshold, using LaSalle’s invariance principle and Lyapunov function, is structured completely by the basic reproductive number. By studying the SIR and SIRS models under the nonlinear condition, the general validity of the method is verified.

In this study, two polymeric resins with different pore sizes were synthesized to study comparative adsorption of reactive black KNB dye. Styrene-divinylbenzene copolymer resin NG-8 has an average pore size of 3.82 nm, about half of that of polydivinylbenzene resin NG-7 (6.90 nm). NG-8 also has a surface acidity about 4 times that of NG-7, resulting in a much more negative surface of the former resin as compared to the latter at pH 6.05. Equilibrium adsorption of KNB was significantly influenced by the surface functionality of the resins, as evidenced by the observations that NG-8 adsorbed constantly less KNB than NG-7 and that the presence of CaCl₂ enhanced the adsorption by both resins. The intra-particle diffusion appears to be the primary rate-limiting process. While the pores of both resins are accessible to KNB, the slower adsorption by NG-8 than by NG-7 suggests that the smaller pores of NG-8 further retard the intra-particle diffusion of KNB.

The interaction between iron(II) tetrasulfophthalocyanine ([Fe^IITSPc]⁴⁺) and histamine results in the oxidation of the central metal by oxygen in the former, with the formation of a complex denoted as [(His)Fe^IIITSPc]³⁻ (where His = histamine). The rate constant for the formation of the complex is k_f = 2.41 × 10⁻²dm³.mol⁻¹.s⁻¹ and an equilibrium constant of 6.3 dm³.mol^-1 was obtained. The oxidation state of the central metal of [Fe^IITSPc]⁴⁻ before and after the coordination of histamine is confirmed by spectroelectrochemistry. Further electrochemical oxidation of this [(His)Fe^IIITsPc]³⁻ derivative results in a metal-based process proposed to involve an Fe^IV phthalocyanine species.

We consider jamming in wireless networks in the framework of zero-sum games with linearized Shannon capacity utility function. The base station has to distribute the power fairly among the users in the presence of a jammer. The jammer in turn tries to distribute its power among the channels to produce as much harm as possible. This game can also be viewed as a minimax problem against the nature. We show that the game has the unique equilibrium and investigate its properties and also we developed an efficient algorithm which allows to find the optimal strategies in finite number of steps.