Multi-armed spirals and multi-pairs antispirals in spatial rock–paper–scissors games

We study the formation of multi-armed spirals and multi-pairs antispirals in spatial rock–paper–scissors games with mobile individuals. We discover a set of seed distributions of species, which is able to produce multi-armed spirals and multi-pairs antispirals with a finite number of arms and pairs based on stochastic processes. The joint spiral waves are also predicted by a theoretical model based on partial differential equations associated with specific initial conditions. The spatial entropy of patterns is introduced to differentiate the multi-armed spirals and multi-pairs antispirals. For the given mobility, the spatial entropy of multi-armed spirals is higher than that of single armed spirals. The stability of the waves is explored with respect to individual mobility. Particularly, we find that both two armed spirals and one pair antispirals transform to the single armed spirals. Furthermore, multi-armed spirals and multi-pairs antispirals are relatively stable for intermediate mobility. The joint spirals with lower numbers of arms and pairs are relatively more stable than those with higher numbers of arms and pairs. In addition, comparing to large amount of previous work, we employ the no flux boundary conditions which enables quantitative studies of pattern formation and stability in the system of stochastic interactions in the absence of excitable media.     

The multi-agent Parrondo’s model based on the network evolution

A multi-agent Parrondo’s model is proposed in the paper. The model includes link A based on the rewiring mechanism (the network evolution) + game B (dependent on the spatial neighbors). Moreover, to produce the paradoxical effect and analyze the “agitating” effect of the network evolution, the dynamic processes of the network evolution + game B are studied. The simulation results and the theoretical analysis both show that the network evolution can make game B which is losing produce the winning paradoxical effect. Furthermore, we obtain the parameter space where the strong or weak Parrondo’s paradox occurs. Each size of the region of the parameter space is larger than the one in the available multi-agent Parrondo’s model of game A + game B. This result shows that the “agitating” effect of rewiring based on the network evolution is better than that of the zero-sum game between individuals.     

Security analysis of the “Ping–Pong” quantum communication protocol in the presence of collective-rotation noise

Environmental noise is inevitable in non-isolated systems. It is, therefore, necessary to analyze the security of the “Ping–Pong” protocol in a noisy environment. An excellent model for collective-rotation noise is introduced, and information theoretical methods are applied to analyze the security of this protocol. If noise level ε   is lower than 11%, an eavesdropper can gain some, but not all, information freely without being detected. Otherwise, the protocol becomes insecure. We conclude that the use of ‘Ping–Pong’ protocol as a quantum secure direct communication (QSDC) protocol is quasi-secure, as declared by the original author when ε?11%$\epsilon ?11\text{\%}$.     

Reputation-based network selection mechanism using game theory

Current and future wireless environments are based on the coexistence of multiple networks supported by various access technologies deployed by different operators. As wireless network deployments increase, their usage is also experiencing a significant growth. In this heterogeneous multi-technology multi-application multi-terminal multi-user environment users will be able to freely connect to any of the available access technologies. Network selection mechanisms will be required in order to keep mobile users “always best connected” anywhere and anytime. In such a heterogeneous environment, game theory techniques can be adopted in order to understand and model competitive or cooperative scenarios between rational decision makers. In this work we propose a theoretical framework for combining reputation-based systems, game theory and network selection mechanism. We define a network reputation factor which reflects the network’s previous behaviour in assuring service guarantees to the user. Using the repeated Prisoner’s Dilemma game, we model the user–network interaction as a cooperative game and we show that by defining incentives for cooperation and disincentives against defecting on service guarantees, repeated interaction sustains cooperation.     

On the role of symmetries in the theory of photonic crystals

We discuss the role of the symmetries in photonic crystals and classify them according to the Cartan–Altland–Zirnbauer scheme. Of particular importance are complex conjugation C$C$ and time-reversal T$T$, but we identify also other significant symmetries. Borrowing the jargon of the classification theory of topological insulators, we show that C$C$ is a “particle–hole-type symmetry” rather than a “time-reversal symmetry” if one considers the Maxwell operator in the first-order formalism where the dynamical Maxwell equations can be rewritten as a Schrödinger equation; The symmetry which implements physical time-reversal is a “chiral-type symmetry”. We justify by an analysis of the band structure why the first-order formalism seems to be more advantageous than the second-order formalism. Moreover, based on the Schrödinger formalism, we introduce a class of effective (tight-binding) models called Maxwell–Harper operators. Some considerations about the breaking of the “particle–hole-type symmetry” in the case of gyrotropic crystals are added at the end of this paper.     

A Langevin approach to the Log–Gauss–Pareto composite statistical structure

The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.     

Fullerenes in molecular liquids. Solutions in “good” solvents: Another view

Brief review and update information concerning the state of “bare” (unmodified) fullerenes in different solvents, including organosols and hydrosols, is given. The hydrophobic nature of fullerene dispersions in aqueous media is discussed. The possibility of the existence of thermodynamic equilibrium in (fullerene + non-polar solvent) system is questioned. The modern data allow returning to the consideration of C₆₀ (C₇₀, etc.) molecules as colloidal (or sub-colloidal) species, inclined to aggregation. Recent publications support the idea of the solvophobic solvation of fullerene molecules even in “good” solvents. Hence, the solvophobic effect, in concert with the van-der-Waals attraction, seems to be driving forces of permanent (though sometimes very slow) aggregate formation, analogous to coagulation of nano-sized particles of common solvophobic colloidal systems.     

Cycle frequency in standard Rock–Paper–Scissors games: Evidence from experimental economics

The Rock–Paper–Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained to be rather weak. In this work, we performed laboratory experiments on the RPS game and analyzed the social-state evolutionary trajectories of twelve populations of N=6$N=6$ players. We found strong evidence supporting the existence of persistent cycles. The mean cycling frequency was measured to be 0.029±0.009$0.029\pm 0.009$ period per experimental round. Our experimental observations can be quantitatively explained by a simple non-equilibrium model, namely the discrete-time logit dynamical process with a noise parameter. Our work therefore favors the evolutionary game theory over the classical game theory for describing the dynamical behavior of the RPS game.     

Evolution of cooperation among interacting individuals through molecular dynamics simulations

Using molecular dynamics (MD) simulation and evolutionary game theory, we incorporate the spacial structure of individuals into the study of the behaviors of cooperation, by adopting the prisoner's dilemma and snowdrift game as metaphors of cooperation between unrelated individuals. The results show that the introduction of spacial structure enhances cooperation using the strategy of prisoner's dilemma while does not make much changes to the cooperation if the strategy of snowdrift game is used. It is also found that our model is a meta-phase between regular ring graph model and complex network model. And the “activity of players” T^* we introduced makes our simulation much more closer to real world problems.     

Fractional motions

Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.     

Erratum to “Scaling properties of the Baxter–Wu model” [Physica A 390 (2011) 3369–3384]

We detail numerical corrections for the paper “Scaling properties of the Baxter–Wu model”, Velonakis, I.N., Martinos, S.S., Physica A, 390 (2011) 3369–3384.     

Periodic behavior of collapse–revival phenomenon in the full nonlinear interaction between a three-level atom and a single-mode field

In this paper based on a generalization of the Jaynes–Cummings model we solve the dynamical Hamiltonian describing the interaction between a (Λ$\Lambda$ or V-type) three-level atom and a single-mode field in the “full nonlinear regime” and then the analytical form of state vector of the system is explicitly obtained. In this manner, we encountered with “intensity-dependent detuning” as well as “intensity-dependent atom–field coupling” in our two models. Via choosing an appropriate deformation function (which imposes nonlinearity to the system) we consider the influence of Kerr-like medium from which the resonance condition for a selected number of quanta is achieved (selective transition is occurred). Furthermore, by these considerations, we may find the optimum values for atom–field coupling constants which provide a regular periodic behavior of probability amplitudes for the two considered atomic systems. Moreover, to show this periodic time behavior, the temporal evolution of the probability of the allowed atomic transitions as well as the Mandel parameter (as a non-classical sign) is depicted for various circumstances. As is observed, complete revivals may appear in some particular situations.     

Anomalous is ubiquitous

Brownian motion is widely considered the quintessential model of diffusion processes—the most elemental random transport processes in Science and Engineering. Yet so, examples of diffusion processes displaying highly non-Brownian statistics–commonly termed “Anomalous Diffusion” processes–are omnipresent both in the natural sciences and in engineered systems. The scientific interest in Anomalous Diffusion and its applications is growing exponentially in the recent years. In this Paper we review the key statistics of Anomalous Diffusion processes: sub-diffusion and super-diffusion, long-range dependence and the Joseph effect, Lévy statistics and the Noah effect, and 1/f noise. We further present a theoretical model–generalizing the Einstein–Smoluchowski diffusion model–which provides a unified explanation for the prevalence of Anomalous Diffusion statistics. Our model shows that what is commonly perceived as “anomalous” is in effect ubiquitous.     

Molecular Diffusion and DNP Enhancement in Aqueous Char Suspensions

The heterogeneous¹H dynamic nuclear polarization (DNP) effect is studied at low magnetic fields for a system consisting of several newly synthesized carbon chars suspended in water. By using Fourier Transform pulsed-field-gradient spin–echo NMR spectroscopy, several different self-diffusion coefficients have been observed in aqueous char suspensions, corresponding to regions of differing water mobility in the porous structure. Proton spin–lattice relaxation data generally confirm the results of molecular diffusion measurements. Through utilization of the Torrey model, the influence of “cage effects” on DNP enhancement in porous media is discussed. Results suggest that short-range nuclear–electronic interactions in pores have a dominant effect on DNP enhancement in char suspensions.     

Doves and hawks in economics revisited: An evolutionary quantum game theory based analysis of financial crises

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as a consequence of the financial crisis, it would be desirable to change the “rules of the game” in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the well-known hawk-dove game by a quantum approach, we can show that dependent on entanglement, evolutionary stable strategies also can emerge, which are not predicted by the classical evolutionary game theory and where the total economic population uses a non-aggressive quantum strategy.     

Entanglement,superselection rules and supersymmetric quantum mechanics

In this paper we show that the energy eigenstates of supersymmetric quantum mechanics (SUSYQM) with non-definite “fermion” number are entangled states. They are “physical states” of the model provided that observables with odd number of spin variables are allowed in the theory like it happens in the Jaynes–Cummings model. Those states generalize the so-called “spin-spring” states of the Jaynes–Cummings model which have played an important role in the study of entanglement.     

Stable loosely-coupled-type algorithm for fluid–structure interaction in blood flow

We introduce a novel loosely coupled-type algorithm for fluid–structure interaction between blood flow and thin vascular walls. This algorithm successfully deals with the difficulties associated with the “added mass effect”, which is known to be the cause of numerical instabilities in fluid–structure interaction problems involving fluid and structure of comparable densities. Our algorithm is based on a time-discretization via operator splitting which is applied, in a novel way, to separate the fluid sub-problem from the structure elastodynamics sub-problem. In contrast with traditional loosely-coupled schemes, no iterations are necessary between the fluid and structure sub-problems; this is due to the fact that our novel splitting strategy uses the “added mass effect” to stabilize rather than to destabilize the numerical algorithm. This stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub-problem. The stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable. Due to the crucial role played by the kinematic lateral boundary condition, the proposed algorithm is named the “kinematically coupled scheme”.     

The rock–paper–scissors game

Rock–Paper–Scissors (RPS), a game of cyclic dominance, is not merely a popular children’s game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no background in game theory, this paper introduces the concepts of Nash equilibrium and evolutionarily stable strategy, and reviews some recent theoretical and empirical efforts on the non-equilibrium properties of the iterated RPS, including collective cycling, conditional response patterns and microscopic mechanisms that facilitate cooperation. We also introduce several dynamical processes to illustrate the applications of RPS as a simplified model of species competition in ecological systems and price cycling in economic markets.     

Exact vortex solitons in a quasi-two-dimensional Bose–Einstein condensate with spatially inhomogeneous cubic–quintic nonlinearity

The exact vortex soliton solutions of the quasi-two-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities are constructed by similarity transformation. It is demonstrated that spatially inhomogeneous cubic–quintic nonlinearity can support exact vortex solitons in which there are two quantum numbers S and m. The radius structures and density distributions of these vortex solitons are studied, and it is shown that the number of ring structure of the vortex solitons increases by one with increasing the “radial quantum number” m by one.     

A possible scenario of the Pioneer anomaly in the framework of Finsler geometry

The weak field approximation of geodesics in Randers–Finsler space is investigated. We show that a Finsler structure of Randers space corresponds to the constant and sunward anomalous acceleration demonstrated by the Pioneer 10 and 11 data. The additional term in the geodesic equation acts as “electric force”, which provides the anomalous acceleration.