Wake effect in doped graphene due to moving external charge

We use the dielectric-response formalism to evaluate the induced density of charge carriers in supported graphene due to an external moving charged particle in terms of its velocity and distance from graphene for several equilibrium charge carrier densities due to graphene doping. We show that, when the particle speed exceeds a threshold value, an oscillatory wake effect develops in the induced charge density trailing the particle. Strong effects are observed in the wake pattern due to finite size of the graphene–substrate gap, as well as due to strong coupling effects, and plasmon damping of graphene?s π electrons.     

Thermodynamic potentials and thermodynamic relations in nonextensive thermodynamics

The generalized Gibbs free energy and enthalpy are derived in the framework of nonextensive thermodynamics by using the concept of the physical temperature and the physical pressure. Some relations of the thermodynamical potentials are changed due to the difference between the physical temperature and the inverse of Lagrange multiplier. We derive the thermodynamical relation between the heat capacities at a constant volume and at a constant pressure using the generalized thermodynamical potential. We find that it has a different form from the traditional one in Gibbs thermodynamics. But, the expressions of the heat capacities in this framework using the generalized thermodynamical potentials are still the same as the traditional one.     

Integrating neighborhoods in the evaluation of fitness promotes cooperation in the spatial prisoner’s dilemma game

A fundamental question of human society is the evolution of cooperation. Many previous studies explored this question via setting spatial background, where players obtain their payoffs by playing game with their nearest neighbors. Another undoubted fact is that the environment plays an important role in the individual development. Inspired by these phenomena, we reconsider the definition of individual fitness which integrates the environment, denoted by the average payoff of all individual neighbors, with the traditional individual payoffs by introducing a selection parameter u. Tuning u equal to zero returns the traditional version, while increasing u bears the influence of environment. We find that considering the environment, i.e., integrating neighborhoods in the evaluation of fitness, promotes cooperation. If we enhance the value of u, the invasion of defection could be resisted better. We also provide quantitative explanations and complete phase diagrams presenting the influence of the environment on the evolution of cooperation. Finally, the universality of this mechanism is testified for different neighborhood sizes, different topology structures and different game models. Our work may shed light on the emergence and persistence of cooperation in our life.     

Evolution of cooperation among mobile agents with heterogenous view radii

In this paper, we study cooperative behavior among mobile agents; the agents have heterogenous view radii and they play the prisoner’s dilemma game with those being within their vision fields. It is found that the cooperation level is remarkably promoted when the heterogeneity of view radii is considered, and the degree distribution of the system is investigated to explain this interesting phenomenon. Moreover, we report that the cooperative behavior is best favored by low density, moderate view radius, and small moving speed. Our findings may be helpful in understanding cooperative behavior in natural and social systems consisting of mobile agents.     

Tunable I-shaped metamaterial by loading varactor diode for reconfigurable antenna

A tunable metamaterial by employing I-shaped metamaterial with loaded varactor diode is presented in this paper and the phase of emitting wave modulated by the varactor diode is demonstrated. We have proved that the energy loss is relatively low when the working frequency is chosen to be away from the resonance frequency of the I-shaped metamaterial. By using the metamaterial, a pattern reconfigurable antenna is designed based on arrayed antennas theory. Simulations results show that the radiation pattern can be tuned to different angles by properly arranging the linear phase difference of adjacent regions.     

Reliability measures for two-part partition of states for aggregated Markov repairable systems

Three models for the aggregated stochastic processes based on an underlying continuous-time Markov repairable system are developed in which two-part partition of states is used. Several availability measures such as interval availability, instantaneous availability and steady-state availability are presented. Some of these availabilities are derived by using Laplace transforms, which are more compact and concise. Other reliability-distributions for these three models are given as well.     

Reciprocal supply chain with intention

The traditional hypothesis of “rationality” is far from perfect. Models of fairness solely based on consequence cannot explain why the same consequence of an action is perceived and reciprocated differently. A reciprocity model which accounts for both consequence and its underlying intention is presented in this paper to illustrate the effect of intention in a traditional dyadic channel where one supplier plays a Stackelberg-like game with one retailer. This research aims to investigate how reciprocity may affect the members’ decisions and the channel’s coordination. In this study, two scenarios are discussed: (1) the retailer has a preference for reciprocity while the supplier does not and (2) both the retailer and the supplier have a preference for reciprocity. Results for acrimonious supply chain (γμ>1$\gamma \mu >1$) and harmonious supply chain (γμ?1$\gamma \mu ?1$) are analyzed. Furthermore, we derive equilibria under the two scenarios and prove the existence and the uniqueness of the equilibria. The results show that intention plays an important role in decision making of the supply chain and will significantly change the equilibria. Moreover, an acrimonious supply chain can be coordinated with a simple wholesale-price contract under certain conditions, which can never happen in a traditional channel. A harmonious supply chain, however, cannot be coordinated in any way.     

Solving the logit-based stochastic user equilibrium problem with elastic demand based on the extended traffic network model

This paper proposes a novel extended traffic network model to solve the logit-based stochastic user equilibrium (SUE) problem with elastic demand. In this model, an extended traffic network is established by properly adding dummy nodes and links to the original traffic network. Based on the extended traffic network, the logit-based SUE problem with elastic demand is transformed to the SUE problem with fixed demand. Such problem is then further converted to a linearly constrained convex programming and addressed by a predictor–corrector interior point algorithm with polynomial complexity. A numerical example is provided to compare the proposed model with the method of successive averages (MSA). The numerical results indicate that the proposed model is more efficient and has a better convergence than the MSA.     

Congruences of multipartition functions modulo powers of primes

Let p _r (n) denote the number of r-component multipartitions of n, and let S _γ,λ be the space spanned by η(24z) ^γ ?(24z), where η(z) is the Dedekind’s eta function and ?(z) is a holomorphic modular form in \(M_{\lambda}(\mathrm{SL}_{2}(\mathbb{Z}))\) . In this paper, we show that the generating function of \(p_{r}(\frac{m^{k} n +r}{24})\) with respect to n is congruent to a function in the space S _γ,λ modulo m ^k . As special cases, this relation leads to many well known congruences including the Ramanujan congruences of p(n) modulo 5,7,11 and Gandhi’s congruences of p ₂(n) modulo 5 and p ₈(n) modulo 11. Furthermore, using the invariance property of S _γ,λ under the Hecke operator \(T_{\ell^{2}}\) , we obtain two classes of congruences pertaining to the m ^k -adic property of p _r (n).     

Orlicz mixed quermassintegrals

The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy-Kubota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established for this new Orlicz mixed quermassintegrals.