Abstract: We consider two classes of games in which players are the vertices of a directed graph. Initially, nature chooses one player according to some fixed distribution and gives the player a buck. This player passes the buck to one of the player's out-neighbors in the graph. The procedure is repeated indefinitely. In one class of games, each player wants to minimize the asymptotic expected frequency of times that the player receives the buck. In the other class of games, the player wants to maximize it. The PageRank game is a particular case of these maximizing games. We consider deterministic and stochastic versions of the game, depending on how players select the neighbor to which to pass the buck. In both cases, we prove the existence of pure equilibria that do not depend on the initial distribution; this is achieved by showing the existence of a generalized ordinal potential. If the graph on which the game is played admits a Hamiltonian cycle, then this is the outcome of prior-five Nash equilibrium in the minimizing game. For the minimizing game, we then use the price of anarchy and stability to measure fairness of these equilibria.

Abstract: Carbon-based perovskite solar cells (PSCs) have exhibited unprecedented progress in the past decades, however, the deficit of open-circuit voltage and non-radiative recombination losses are the dominating limiting factors in scaling up the devices in view of commercialization. The researchers and scientists recognize the dominating factors and propose different themes to overcome the limiting factors. Among the different solutions, interfacial engineering of PSCs between the interfaces of transporting layer (electron or hole) and perovskite influences the reduction of non-radiative recombination losses with improvement in device efficiency. In this work, one-dimensional (1D) graphitic carbon nitride (g-C3N4) is synthesized through simple pyrolysis using two different mediums (ethanol and ethylene glycol). 1D g-C3N4 is interfaced between electron transport layer and perovskite absorber influences effectively in fine-tuning the work function by aligning the energy level of the fabricated mixed halide PSCs. Nanoscale engineered 1D g-C3N4 interfacial layer supports boosting the power conversion efficiency of the PSCs to 5.20% and 7.14% for tube and layered tube structures at ambient conditions. Further, the interfacial layer aids in improving thermal (tube: similar to 59.80%; layered tube: similar to 74.50%) and photostability (tube: similar to 78.65%; layered tube: similar to 87.25%) characteristics of the fabricated devices for 100 h duration at ambient conditions.

Abstract: A new general formulation for the spatial modeling of combat is presented, where the main drivers are movement attitudes and struggle evolution. This model in its simplest form is represented by a linear set of two coupled partial differential equations for two independent functions of the space and time variables. Even though the problem has a linear shape, non-negative values for the two functions render this problem as nonlinear. In contrast with other attempts, this model ensures stability and theoretical consistency with the original Lanchester Equations, allowing for a better understanding and interpretation of the spatial modeling. As a numerical illustration a simple combat situation is developed. The model is calibrated to simulate different troop movement tactics that allow an invader force to provoke maximum damage at a minimum cost. The analysis provided here reviews the trade-off between spatial grid and time stepping for attrition cases and then extends it to a new method for guaranteeing good numerical behavior when the solution is expected to grow along the time variable. There is a wide variety of spatial problems that could benefit from this analysis. (C) 2011 Elsevier Ltd. All rights reserved.

Abstract: This paper studies vehicle platooning with communication channels subject to random data loss. We focus on homogeneous discrete-time platoons in a predecessor-following topology with a constant time headway policy. We assume that each agent in the platoon sends its current position to the immediate follower through a lossy channel modeled as a Bernoulli process. To reduce the negative effects of data loss over the string stability and performance of the platoon, we use simple strategies that modify the measurement, error, and control signals of the feedback control loop, in each vehicle, when a dropout occurs. Such strategies are based on holding the previous value, dropping to zero, or replacing with a prediction based on a simple linear extrapolation. We performed a simulation-based comparison among a set of different strategies, and found that some strategies are favorable in terms of performance, while some others present improvements for string stabilization. These results strongly suggest that proper design of compensation schemes for the communications of interconnected multi-agent systems plays an important role in their performance and their scalability properties.

Abstract: In underground mining, the design of rock pillars is of crucial importance as these are structures that allow safe mining by maintaining the stability of the surrounding excavations. Pillar design is often a complex task, as it involves estimating the loads at depths and the strength of the rock mass fabric, which depend on the intact strength of the rock and the shape of the pillar in terms of the aspect ratio (width/height). The design also depends on the number, persistence, orientation, and strength of the discontinuities with respect to the orientation and magnitude of the stresses present. Solutions to this engineering problem are based on one or more of the following approaches: empirical design methods, practical experience, and/or numerical modeling. Based on the similarities between masonry structures and rock mass characteristics, an equivalent approach is proposed as the one commonly used in masonry but applied to rock pillar design. Numerical models using different geometric configurations and state of stresses are carried out using a finite difference numerical approach with an adapted masonry model applied to rocks. The results show the capability of the numerical approach to replicate common types of pillar failure modes and stability thresholds as those observed in practice.

Abstract: A two-stage system (partial nitritation (PN) and anammox processes) was used to remove nitrogen from the dewatering liquor originating from the thermal hydrolysis/anaerobic digestion (THP/AD) of municipal WWTP sludge. Two strategies were tested to start up the PN reactor: 1) maintaining a fixed hydraulic retention time (HRT) and increasing the ammonium loading rate (ALR) by decreasing the feeding dilution ratio and 2) feeding undiluted dewatering liquor and gradually decreasing the HRT. With diluted feeding, the reactor performance had destabilization episodes that were statistically correlated with the application of high specific ammonium (> 0.6 g NH4+-N/(g TSS.d)) and organic (> 0.7 g COD/(g TSS.d)) loading rates. The second strategy allowed stable PN reactor operation while treating ALR up to 4.8 g NH4+-N/(L.d) and demonstrating that dilution of THP/AD effluents is not required. The operating conditions promoted the presence of free nitrous acid levels (> 0.14 mg HNO2-N/L) inside the PN reactor that inhibited the proliferation of nitrite oxidizing bacteria.
Batch activity tests showed that the inhibitory effects of organic compounds present in the THP/AD dewatering liquor on the ammonia oxidizing bacteria activity can be removed in the PN reactor. Thus, aerobic pretreatment would not be necessary when two-stage systems are used. The PN reactor effluent was successfully treated by an anammox reactor.
An economic analysis showed that using two-stage systems is advantageous for treating THP/AD dewatering liquor. The implementation of an aerobic pre-treatment unit is recommended for WWTPs capacities higher than 5.10(5) inhabitants equivalent when one-stage systems are used.

Abstract: Retail competition today can be described by three main features: (i) oligopolistic competition, (ii) multi-store settings, and (iii) the presence of large economies of scale. In these markets, firms usually apply a centralized decisions making process in order to take full advantage of economies of scales, e.g. retail distribution centers. In this paper, we model and analyze the stability and chaos of retail competition considering all these issues. In particular, a dynamic multi-market Cournot Nash equilibrium with global economies and diseconomies of scale model is developed. We confirm the non-intuitive hypothesis that retail multi-store competition is more unstable than traditional small business that cover the same demand. The main sources of stability are the scale parameter, the number of markets, and the number of firms. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.