Operation regimes and slower-is-faster effect in the controlof traffic intersections

The efficiency of traffic flows in urban areas is known to crucially depend on signal operation. Here, elements of signal control are discussed, based on the minimization of overall travel times or vehicle queues. Interestingly, we find different operation regimes, some of which involve a “slower-is-faster effect”, where a delayed switching reduces the average travel times. These operation regimes characterize different ways of organizing traffic flows in urban road networks. Besides the optimize-one-phase approach, we discuss the procedure and advantages of optimizing multiple phases as well. To improve the service of vehicle platoons and support the self-organization of “green waves”, it is proposed to consider the price of stopping newly arriving vehicles.     

Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network

We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperators and sustainable cooperation. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary Prisoner's Dilemma game on a variant of Newman-Watts small-world network, whose heterogeneity can be tuned by a parameter. It is found that optimal cooperation level exists at some intermediate topological heterogeneity for different temptations to defect. That is, frequency of cooperators peaks at a certain specific value of degree heterogeneity — neither the most heterogeneous case nor the most homogeneous one would favor the cooperators. Besides, the average degree of networks and the adopted update rule also affect the cooperation level.     

Anticipative control of switched queueing systems

The relevant dynamics of a queueing process can be anticipated by taking future arrivals into account. If the transport from one queue to another is associated with transportation delays, as it is typical for traffic or productions networks, future arrivals to a queue are known over some time horizon and, thus, can be used for an anticipative control of the corresponding flows. A queue is controlled by switching its outflow between “on” and “off” similar to green and red traffic lights, where switching to “on” requires a non-zero setup time. Due to the presence of both continuous and discrete state variables, the queueing process is described as a hybrid dynamical system. From this formulation, we derive one observable of fundamental importance: the green time required to clear the queue. This quantity allows to detect switching time points for serving platoons without delay, i.e., in a “green wave” manner. Moreover, we quantify the cost of delaying the start of a service period or its termination in terms of additional waiting time. Our findings may serve as a basis for strategic control decisions.     

Mathematical modeling in biology: A critical assessment

Summary  The molecular revolution and the development of biology-derived industry have led in the last fifty years to an unprecedented “leap forward” of life sciences in terms of experimental data. Less success has been achieved in the organisation of such data and in the consequent development of adequate explanatory and predictive theories and models. After a brief historical excursus inborn difficulties of mathematisation of biological objects and processes derived from the complex dynamics of life are discussed along with the logical tools (simplification, choice of observation points etc.) used to overcome them. “Autistic”, monodisciplinary attitudes towards biological modeling of mathematicians, physicists, biologists aimed in each case at the use of the tools of other disciplines to solve “selfish” problems are also taken into account and a warning against derived dangers (reification of monodisciplinary metaphors, lack of falsification etc.) is given. Finally “top-down” (deductive) and “bottom up” (inductive) heuristic interactive approaches to mathematisation are critically discussed with the help of a serie of examples.     

Cooperation in the spatial public goods game with the second-order reputation evaluation

The existence of reputation can significantly promote the level of cooperation within the human population. In the recent years, most of the researches were based on binary image score or first-order evaluation standard. In this paper, we propose a second-order reputation evaluation model, in which the individual's image score will change not only in accordance with his own strategy, but also the reputation value of neighbors. Individuals try to enhance their reputation to cooperate with the surrounding high-reputation individuals, and then becomes an influential individual in the population. The existence of this mechanism renders the individuals who at the edge of the clusters formed by the cooperators to rapidly accumulate their reputation values through the adoption of cooperative strategy, and then the cooperative strategy can be spread widely and rapidly in the whole population. Through extensive numerical simulations, it is clearly indicated that the population cooperation behavior will be obviously improved when the individual's influence factor becomes smaller or the reputation step length increases. The current results are further conducive to understanding the emergence of cooperation in many real world systems.     

Promoting cooperation in social dilemmas via simple coevolutionary rules

We study the evolution of cooperation in structured populations within popular models of social dilemmas, whereby simple coevolutionary rules are introduced that may enhance players abilities to enforce their strategy on the opponent. Coevolution thus here refers to an evolutionary process affecting the teaching activity of players that accompanies the evolution of their strategies. Particularly, we increase the teaching activity of a player after it has successfully reproduced, yet we do so depending on the disseminated strategy. We separately consider coevolution affecting either only the cooperators or only the defectors, and show that both options promote cooperation irrespective of the applied game. Opposite to intuitive reasoning, however, we reveal that the coevolutionary promotion of players spreading defection is, in the long run, more beneficial for cooperation than the likewise promotion of cooperators. We explain the contradictive impact of the two considered coevolutionary rules by examining the differences between resulting heterogeneities that segregate participating players, and furthermore, demonstrate that the influential individuals completely determine the final outcome of the games. Our findings are immune to changes defining the type of considered social dilemmas and highlight that the heterogeneity of players, resulting in a positive feedback mechanism, is a fundamental property promoting cooperation in groups of selfish individuals.     

Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks

In human societies the probability of strategy adoption from a given person may be affected by the personal features. Now we investigate how an artificially imposed restricted ability to reproduce, overruling ones fitness, affects an evolutionary process. For this purpose we employ the evolutionary prisoner's dilemma game on different complex graphs. Reproduction restrictions can have a facilitative effect on the evolution of cooperation that sets in irrespective of particularities of the interaction network. Indeed, an appropriate fraction of less fertile individuals may lead to full supremacy of cooperators where otherwise defection would be widespread. By studying cooperation levels within the group of individuals having full reproduction capabilities, we reveal that the recent mechanism for the promotion of cooperation is conceptually similar to the one reported previously for scale-free networks. Our results suggest that the diversity in the reproduction capability, related to inherently different attitudes of individuals, can enforce the emergence of cooperative behavior among selfish competitors.     

Shiva diagrams for composite-boson many-body effects: how they work

The purpose of this paper is to show how the diagrammatic expansion in fermion exchanges of scalar products of N-composite-boson (“coboson”) states can be obtained in a practical way. The hard algebra on which this expansion is based, will be given in an independent publication. Due to the composite nature of the particles, the scalar products of N-coboson states do not reduce to a set of Kronecker symbols, as for elementary bosons, but contain subtle exchange terms between two or more cobosons. These terms originate from Pauli exclusion between the fermionic components of the particles. While our many-body theory for composite bosons leads to write these scalar products as complicated sums of products of “Pauli scatterings” between two cobosons, they in fact correspond to fermion exchanges between any number P of quantum particles, with 2 ≤P≤N. These P-body exchanges are nicely represented by the so-called “Shiva diagrams”, which are topologically different from Feynman diagrams, due to the intrinsic many-body nature of the Pauli exclusion from which they originate. These Shiva diagrams in fact constitute the novel part of our composite-exciton many-body theory which was up to now missing to get its full diagrammatic representation. Using them, we can now “see” through diagrams the physics of any quantity in which enters N interacting excitons — or more generally N composite bosons —, with fermion exchanges included in an exact — and transparent — way.     

The exciton many-body theory extended to any kind of composite bosons

We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between N excitons can be treated exactly through a set of dimensionless “Pauli scatterings” between two excitons. Many-body effects with free excitons turn out to be rather simple because these excitons are the exact one-pair eigenstates of the semiconductor Hamiltonian, in the absence of localized traps. They consequently form a complete orthogonal basis for one-pair states. As essentially all quantum particles known as bosons are composite bosons, it is highly desirable to extend this free exciton many-body theory to other kinds of “cobosons” — a contraction for composite bosons — the physically relevant ones being possibly not the exact one-pair eigenstates of the system Hamiltonian. The purpose of this paper is to derive the “Pauli scatterings” and the “interaction scatterings” of these cobosons in terms of their wave functions and the interactions which exist between the fermions from which they are constructed. It is also explained how to calculate many-body effects in such a very general composite boson system.     

Negative index materials with gain media for fast modulation

Negative index materials (NIM) enable subwavelength resolution and are promising for applications in integrated optical systems, since the mode volume is small. Most promising NIM systems essentially use noble metals (Ag, Au) with material losses much lower than in other metals, but still rather hefty, like in metal–dielectric–metal “fishnets”. Therefore, we perform extensive finite-difference time-domain modeling of NIM “fishnets” in combination with gain medium, InGaAsP multiple quantum wells in the present work. The signal recovery is weak, which is related to weak overlap between the radiation field and the gain medium. The signal modulation speed may be very large, in a picosecond range.     

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, “weak” or “strong”, interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular ,are found to be robust against these perturbations. Received: 7 October 1997 / Accepted: 19 November 1997     

Cooperative dynamics of snowdrift game on spatial distance-dependent small-world networks

We investigate the evolution of cooperative behaviors of small-world networking agents in a snowdrift game mode, where two agents (nodes) are connected with probability depending on their spatial Euclidean lattice distance in the power-law form controlled by an exponent α. Extensive numerical simulations indicate that the game dynamics crucially depends on the spatial topological structure of underlying networks with different values of the exponent α. Especially, in the distance-independent case of α=0, the small-world connectivity pattern contributes to an enhancement of cooperation compared with that in regular lattices, even for the case of having a high cost-to-benefit ratio r. However, with the increment of α>0, when r≥0.4, the spatial distance-dependent small-world (SDSW) structure tends to inhibit the evolution of cooperation in the snowdrift game.     

The Origins of the Field Concept in Physics

The term, “field,” made its first appearance in physics as a technical term in the mid-nineteenth century. But the notion of what later came to be called a field had been a long time in gestation. Early discussions of magnetism and of the cause of the ocean tides had long ago suggested the idea of a “zone of influence” surrounding certain bodies. Johannes Kepler's mathematical rendering of the orbital motion of Mars encouraged him to formulate what he called “a true theory of gravity” involving the notion of attraction. Isaac Newton went on to construct an eminently effective dynamics, with attraction as its primary example of force. Was his a field theory? Historians of science disagree. Much depends on whether a theory consistent with the notion of action at a distance ought qualify as a “field” theory. Roger Boscovich and Immanuel Kant later took the Newtonian concept of attraction in new directions. It was left to Michael Faraday to propose the “physical existence” of lines of force and to James Clerk Maxwell to add as criterion the presence of energy as the ontological basis for a full-blown “field theory” of electromagnetic phenomena.     

Retrieval of the quasi-optimal signal activating the excitable systems using preceding noise samples

We propose a method for obtaining a signal leading to the activation of an excitable dynamic system for a signal energy close to minimal. The efficiency of this technique, which is based on recording and processing of noise samples preceding the activation was tested using the FitzHugh–Nagumo, Hodgkin–Huxley, and Luo–Rudy models as examples. It is shown that the proposed procedure gives good results when the noise intensity is smaller than or close to the system activation energy. The criteria of “low” and “high” intensities of fluctuations are proposed. The method of increasing the stability of the excitable system with respect to “low-intensity” noise by filtering or another way of suppression of the spectral components that make the main contribution to the energetically optimal activation signal is justified. The relation between eigenvalues of the linearized system of the Hamiltonian equations, which describe the optimal trajectories and the activation signal, and eigenvalues of the excitable system linearized near the initial equilibroum state is found.     

Funnels in energy landscapes

Local minima and the saddle points separating them in the energy landscape are known to dominate the dynamics of biopolymer folding. Here we introduce a notion of a “folding funnel” that is concisely defined in terms of energy minima and saddle points, while at the same time conforming to a notion of a “folding funnel” as it is discussed in the protein folding literature.     

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (“grey body”) and of an amplifying medium (“random laser”) are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold. Received 8 August 2000     

Elastic Green's function of icosahedral quasicrystals

The elastic theory of quasicrystals considers, in addition to the “normal” displacement field, three “phason” degrees of freedom. We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling between the phonons and phasons is small. Received: 18 December 1997 / Accepted: 6 March 1998     

Interface-induced dephasing of Mie plasmon polaritons

Surface and, in particular, interface effects influence all physical and chemical properties of nanostructured matter. Mie surface plasmon polaritons (MPPs) in metallic nanoparticles are excellent and sensitive sensors for optical investigation of these effects of realistic particles since their lifetimes due to dephasing (decoherence) effects and their resonance energies drastically depend upon the chemistry and topology of their surfaces/interfaces. A survey is given over some results of our own long term research on MPPs which started, in fact, as early as 1969. Theoretical models and experiments concerning the A parameter, the δ n parameter, MPP phase decoherence and static and dynamic interface charge transfer effects (“chemical interface damping”) are briefly summarized. The effect of radiation damping is disregarded throughout: we assume the particle sizes to be small enough to justify this simplification, which makes it easier to draw conclusions from the MPPs on nanomaterial properties. Obviously, there is a wide field for future research concerning particle interfaces on the basis of Mie’s theory. On the other hand, all of these effects have to be incorporated into Mie’s theory to obtain a “modern” version which is reliable on a quantitative level to describe experimental data.     

Cooperation and community structure in social networks

Situations of conflict giving rise to social dilemmas are widespread in society. One way of studying these important phenomena is by using simplified models of individual behavior under conflicting situations such as evolutionary game theory. Starting from the observation that individuals interact through networks of acquaintances, we study the evolution of cooperation on model and real social networks through well known paradigmatic games. Using a new payoff scheme which leaves replicator dynamics invariant, we find that cooperation is sustainable in such networks, even in the difficult case of the prisoner’s dilemma. The evolution and stability of cooperation implies the condensation of game strategies into the existing community structures of the social network in which clusters of cooperators survive thanks to their higher connectivity towards other fellow cooperators.