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ABSTRACT
According to Mulder’s theory, the zombies will eventually fall on each other and make love. However, be it for love or evil, the cold hard reality remains that the actions of the undead, just as those of the living, are also structured by... more
According to Mulder’s theory, the zombies will eventually fall on each other and make love. However, be it for love or evil, the cold hard reality remains that the actions of the undead, just as those of the living, are also structured by simple constraints of social or spatiotemporal nature. In this chapter, we improve upon the standard zombie outbreak model by considering the underlying social network of the living and the horde behaviour of the undead. This model is then further improved by considering the adaptive nature of social interactions: people usually tend to avoid contact with zombies. Doing so captures the coevolution of the human social network and of the zombie outbreak, which encourages humans to naturally barricade themselves in groups of survivors to better fight the undead menace. And then? Better stack goods, arm yourself and be patient, for the undead hordes are there to stay; hopefully dancing and making love.
An operational definition of chaos is helpful to appreciate Dyson’s assertion. In our presentation, deterministic chaos has a technical and precise meaning and despite a lack of a universal definition, most researchers would agree that it... more
An operational definition of chaos is helpful to appreciate Dyson’s assertion. In our presentation, deterministic chaos has a technical and precise meaning and despite a lack of a universal definition, most researchers would agree that it could be described as follows: Chaos is a long-term aperiodic behavior of a dynamical system that possesses the property of sensitivity to initial conditions. – long-term aperiodic behavior means that regularity (periodicity or quasi-periodicity) of the motion is absent. – dynamical system indicates that determinism is present and that the source of the irregularity is inherent to that determinism and not to be found in a stochastic component. – sensitivity to initial conditions implies that a very small deviation in the initial conditions is sufficient to create large deviations in the future states (the so-called “butterfly effect”), i.e. despite the presence of determinism, practical long-term predictability is lost. This is the type of motion that Dyson had in mind. It is not new of course and it is clear that Maxwell and Boltzmann, the founders of statistical physics, were acutely aware of the property of sensitivity to initial conditions and its consequences. Not before Poincaré [2] could one ascertain the existence of this property in a system with few degrees of freedom, namely the reduced 3-body problem. It was not until 1990 however that Ott, Grebogi and Yorke (OGY) [3] addressed the question of control of chaos and described the theoretical steps necessary to achieve this goal. This method was very much in the spirit of von Neumann who imagined as early as 1950, that ‘ ‘ every unstable motion could be nudged into a stable motion by small pushes and pulls applied at the right places” [1]. The theoretical OGY work was rapidly followed by experimental verification [3]: von Neumann’s dream had become reality. This brief report describes some practical implementations for the recovery of order from chaos. Our examples are from the realm of conservative (Hamiltonian) systems. They are chosen because they have been much less studied than their dissipative counterparts, because their mixed (regular and chaotic) phase space offers new challenges to the standard control schemes and because of the growing evidence that the mere existence of Hamiltonian chaos [4] may shed new light on the foundations of statistical physics [5]. The stabilization of their chaotic behavior offers new grounds for a fascinating adventure. Many reviews on the control of chaos have appeared in the last few years and the reader may wish to consult the partial list given in [6].
Experimental studies of the production and transport of projectile excited states in solid carbon targets have been performed for Ar17+ and Kr35+ at high velocity (respectively vp=23 and 35.6 a.u.). A range of target thickness from single... more
Experimental studies of the production and transport of projectile excited states in solid carbon targets have been performed for Ar17+ and Kr35+ at high velocity (respectively vp=23 and 35.6 a.u.). A range of target thickness from single collision condition to equilibrium has been investigated. Charge state distributions, nl populations of core and Rydberg projectile states, as well as the population of fine structure substates (nlj) are determined. Theoretical predictions have been developed both in a collisional and a dynamical screening picture, using quantum as well as classical descriptions for the transport of projectile excited states. Discussions based on a comparison between experimental results and the different types of calculations are presented.
The authors have measured total cross sections for electron transfer between 400 MeV bare Fe 26+ ions and He, N 2, Ne and Ar targets, corresponding to intermediate to high reduced velocities, 1< or= nu/nu i, f< or= 10 (nu is the... more
The authors have measured total cross sections for electron transfer between 400 MeV bare Fe 26+ ions and He, N 2, Ne and Ar targets, corresponding to intermediate to high reduced velocities, 1< or= nu/nu i, f< or= 10 (nu is the incident projectile velocity and nu i, f are the ...
An approximate analytic form is given for the second Born approximation to the amplitude for charge transfer from an initial n'l'm to a final nlm hydrogenic one-electron state. This amplitude contains the correct... more
An approximate analytic form is given for the second Born approximation to the amplitude for charge transfer from an initial n'l'm to a final nlm hydrogenic one-electron state. This amplitude contains the correct double-scattering form at asymptotically high velocities and the cross section for charge transfer may be obtained by a single numerical integration. The transfer 1s to nlm is presented as a particular example and analytic forms for the asymptotic cross section are derived in this case.
Page 297. ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 30 CONTINUUM DISTORTED WAVE METHODS IN ION-ATOM COLLISIONS DERRICKS. F. CROTHERS Department of Applied Mathematics ...
Explicit expressions for capture of an electron to and from arbitrary hydrogenic states are presented for various multiple-scattering approaches, namely approximate forms of the strong-potential Born (SPB) and impulse approximations (IA)... more
Explicit expressions for capture of an electron to and from arbitrary hydrogenic states are presented for various multiple-scattering approaches, namely approximate forms of the strong-potential Born (SPB) and impulse approximations (IA) as well as the continuum distorted-wave (CDW) approximation. In the latter case, however, the authors limit the calculation to an initial 1s state. The transition amplitudes are reduced in all cases to closed-form analytical formulae leaving a single numerical integration to obtain the capture cross sections. The author discusses some symmetry and scaling properties of the post (+) and prior (-) forms of the different methods and, as a first application of the newly gained analytical amplitudes, the author extracts some new asymptotic results. The necessary mathematical tools for the evaluation of a common matrix element appearing in the SPB, IA and CDW are provided in an appendix, where it is shown how the relevant transition amplitudes can all be obtained from one generating integral.
Various nonlinear rotation regimes are observed in an optically excited nematic liquid crystal film under boundary conditions (for the light and the material) that are invariant by rotation. Th excitation light is circularly polarized,... more
Various nonlinear rotation regimes are observed in an optically excited nematic liquid crystal film under boundary conditions (for the light and the material) that are invariant by rotation. Th excitation light is circularly polarized, the intensity profile is circularly symmetric and the beam diameter at the sample location is a few times smaller than the cell thickness. A transition to chaos via quasiperiodicity is identified when the light intensity is taken as the control parameter. Transverse nonlocal effects are suggested to be the cause of the observed dynamics and a simple model consisting of a collection of coupled rotators is developed to provide a qualitative explanation. *Also at Laboratoire de Chimie-Physique-Matière et Rayonnement, Université Pierre et Marie Curie, Paris, France.
The authors present a comparison of theoretical cross sections for electron capture to Rydberg states (ECR) with the corresponding experimental quantities for electron capture to the continuum (ECC).
We investigate the problem of hydrogenic ion transport through solids. To this end, we consider a system made of a single electron in a given potential and driven by a stochastic force uniformly distributed in time [D.G. Arbò et al.,... more
We investigate the problem of hydrogenic ion transport through solids. To this end, we consider a system made of a single electron in a given potential and driven by a stochastic force uniformly distributed in time [D.G. Arbò et al., Phys. Rev. A 60 (1999) 1091], and we derive the time evolution equation of the ensemble average density matrix. We
ABSTRACT
The authors develop the structural properties of the eikonal approximation (EA) to the electron capture process by comparison with the corresponding terms of the Born series. This allows one to extract the physical content of the EA and... more
The authors develop the structural properties of the eikonal approximation (EA) to the electron capture process by comparison with the corresponding terms of the Born series. This allows one to extract the physical content of the EA and to point out the similarities and differences with Born-type expansions. In so doing they also pay attention to the interpretation of the two inequivalent (post and prior) forms of the EA. In the asymptotic regime, as nu to infinity , inspection of the eikonal amplitudes reveal that only the single and double scattering terms of the eikonal expansion contribute (to leading order) to the asymptotic cross section. This result appears to be shared by all multiple scattering descriptions of the charge exchange mechanism and underlines anew the special role played by the double-scattering term in the rearrangement problem.
ABSTRACT
Using high-resolution x-ray spectroscopy, we have measured, as a function of target thickness, the relative intensities of the fine-structure components of the Balmer 0953-4075/31/1/013/img9 line emitted by fast hydrogen-like krypton ions... more
Using high-resolution x-ray spectroscopy, we have measured, as a function of target thickness, the relative intensities of the fine-structure components of the Balmer 0953-4075/31/1/013/img9 line emitted by fast hydrogen-like krypton ions 0953-4075/31/1/013/img10 propagating through thin carbon and copper targets. Our results are in clear disagreement with the predictions of a rate-equation model accounting for collisional l mixing. On the other
This volume contains the proceedings of the 19th International Conference held in Whistler, Canada in July 1995, which covered the physics of electronic and atomic collisions.
We introduce an intuitive mechanism to describe both the emergence of community structure and the evolution of the internal structure of communities in social networks. Our idea is based on the simple assumption that each individual can,... more
We introduce an intuitive mechanism to describe both the emergence of community structure and the evolution of the internal structure of communities in social networks. Our idea is based on the simple assumption that each individual can, for every social group to which it belongs, develop connections and introduce new members. Complex behaviors emerge from opposing time scales for the activities of individuals and for the sum of individuals gathered in groups. We show how the resulting model reproduces behaviors observed in real social networks and in the anthropological theory known as Dunbar's number, i.e. the empirical observation of a maximal number of ties which an average individual can sustain within its social groups. Using this growth process, we organically reproduce the micro and mesoscopic structure of social networks. In so doing, we highlight two interesting properties of the community structure of social networks. First, strong correlations between the number of communities to which a node belong and the number of connections therein; correlating the role of a node in the community structure and its role in the structure of the communities. Second, Dunbar's number in the structure of communities implies a vanishing group density regardless of the nature of the network or of the detection algorithm.
The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model... more
The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model that generates maximally random networks with arbitrary degree distribution and arbitrary k-core structure. We then solve exactly the bond percolation problem on the HRN model and produce fast and precise analytical estimates for the corresponding real networks. Extensive comparison with selected databases reveals that our approach performs better than existing models, while requiring less input information.
<p>(<i>Left</i>) The number of unassigned links after one iteration of the CPA (corresponding to a typical use) is shown in yellow, and the final state is shown in dark brown. Whenever more than 2 iterations were... more
<p>(<i>Left</i>) The number of unassigned links after one iteration of the CPA (corresponding to a typical use) is shown in yellow, and the final state is shown in dark brown. Whenever more than 2 iterations were performed, the intermediate results are shown in orange. For the <i>Gnutella</i> network, the optimal value was <i>k</i> = 3 at the first iteration, leading to an immediate complete detection of the community structure. For the purpose of selecting <i>k</i>, we consider that a cover contains an extensive community if the largest community is twice as large as the second largest community. In the case of the <i>Internet</i> and <i>Protein</i> networks, which contains large unbreakable clique, we used a looser criterion (<i>c</i> ⋅ <i>n</i><sub>largest</sub> < <i>n</i><sub>2nd largest</sub>, with <i>c</i> = 0.25 and <i>c</i> = 0.30, respectively). (<i>Center</i>) Results of a canonical use of GCE are shown in beige and shades of red correspond to subsequent iterations. The final state is shown in dark red. (<i>Right</i>) Results of a canonical use of the LCA are shown in white and shades of blue correspond to subsequent iterations. The final state is shown in dark blue. Note that all results are normalized to the number of assignable links in the original network. For the CPA, this corresponds to the number of links that belong to at least one 3-clique. For GCE, this corresponds to the number of links that belong to a component that contains at least one <i>k</i>-clique (<i>k</i> ≥ 3). For the LCA, a link is considered assignable if at least one of the two nodes it joins have a degree greater than one. Numerical results are summarized in the Supporting Information (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0140133#pone.0140133.s002" target="_blank">S2 Table</a>).</p

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