Exact results for the Barabási model of human dynamics

Human activity patterns display a bursty dynamics with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a process that can be modeled as a priority queueing system [A.-L. Barabási, Nature (London) 435, 207 (2005)]. In this Letter we obtain exact results for the Barabási model with two tasks, calculating the priority and waiting time distribution of active tasks. We demonstrate that the model has a singular behavior in the extremal dynamics limit, when the highest priority task is selected first. We find that independently of the selection protocol, the average waiting time is smaller or equal to the number of active tasks, and discuss the asymptotic behavior of the waiting time distribution. These results have important implications for understanding complex systems with extremal dynamics.     

Damage spreading and critical exponents for “model A” Ising dynamics

Using damage spreading and heat bath dynamics, we study the Ising model in 2 and 3 dimensions with non-conservative dynamics. Our algorithm differs in some important points from previous ones, which makes it rather efficient. We give estimates for the exponent z which seem to be the most precise published so far (2.172 ± 0.006 for d = 2, 2.032 ± 0.004 for d = 3). We also give precise estimates of the exponent θ′ introduced by Janssen et al. (Z. Phys. B 73 (1989) 539) and of analogous but in principle independent exponents. We find surprisingly that some of the latter agree with θ′, and give an explanation for this.     

Damage spreading and critical exponents for ‘model A’ Ising dynamics

Recent simulations by Grassberger gave very precise estimates of the dynamical critical exponent z via damage spreading techniques. We confirm these results using a slightly altered method and we examine larger systems up to 18161² and 695² giving z = 2.18 ± 0.02 and 2.04 ± 0.01, respectively.     

A novel fluid–wall heat transfer model for molecular dynamics simulations

The ‘fluid–wall thermal equilibrium model’, to numerically simulate heating/cooling of fluid atoms by wall atoms, is used to compare molecular dynamics simulation results to the analytical solution of 1-D heat equation. Liquid argon atoms are placed between two platinum walls and simultaneous heating and cooling is simulated at the walls. Temperature gradient in liquid argon is evaluated and the results are found to match well with the analytical solution showing the physical soundness of the proposed model. Additional simulations are done where liquid argon atoms are heated by both the walls for two different channel heights and it is shown that in such cases, heat transfer occurs at a faster rate than predicted by heat equation with decreasing channel heights.     

Undulation instability under shear: A model to explain the different orientations of a lamellar phase under shear?

We study the effects of a dilation on a sheared smectic A phase. Through a linear analysis, we show that undulation may grow in the direction of the flow and of the vorticity as found in previous works. At higher shear rates, we evidence that the undulation along the flow disappears whereas it persists in the vorticity direction. We determine the stable or unstable zone as a function of the shear rate and of the lamellar spacing. This allows us to draw a theoretical shear diagram of the instability. Finally we compare our results with the orientations found experimentally in a lyotropic lamellar phase under shear. Our diagram describes qualitatively and quantitatively the transition observed at high shear rate. Received 18 October 1999     

Simulation model of speed–density characteristics for mixed bicycle flow—Comparison between cellular automata model and gas dynamics model

The mixed bicycle flow refers to the bicycle flow containing electric bicycles. The traffic characteristics data of the mixed bicycle flow was collected by the virtual coil method in Nanjing and Ningbo, China. And the speed–density characteristics of the mixed bicycle flow with different proportions of electric bicycles were obtained. The results show that the overall speed of the mixed bicycle flow containing electric bicycles is higher than that of pure bicycle flow when the density is relatively low. The speed decreases when the density is higher than 0.08 bic/m²; the speed–density characteristics of the bicycles and the electric bicycles tend to be the same when the density is higher than 0.25 bic/m². And when the density reaches 0.58 bic/m², the mixed bicycle flow becomes blocked and the speed is zero. The cellular automata model and gas dynamics model were also adopted to simulate the speed–density characteristics of the mixed bicycle flow. The simulation results of the cellular automata model are effectively consistent with the actual survey data when the density is lower than 0.225 bic/m²; the simulation results of the gas dynamics model are effectively consistent with the actual survey data when the density is higher than 0.300 bic/m²; but both of the two types of simulation models are inapplicable when the density is between 0.225 and 0.300 bic/m². These results will be used in the management of mixed bicycles and the research of vehicle–bicycle conflict and so on.     

Is there switching for replicator dynamics and bimatrix games?

We consider heteroclinic networks for replicator dynamics and bimatrix games, that is, in a simplex or product of simplices, with equilibria at the vertices and connections at the edges-edge networks. Switching dynamics near a heteroclinic network occurs whenever every (infinite) sequence of connections in the network is shadowed by at least one trajectory in its neighborhood. Aguiar and Castro [M.A.D. Aguiar, S.B.S.D. Castro Chaotic switching in a two-person game, Physica D 239 (16), 1598-1609] prove switching near an edge network for the dynamics of the rock-scissors-paper game. Here we give conditions for switching dynamics in general bimatrix games and show that switching near an edge network can never occur for replicator dynamics.     

Does the standard model of low-temperature glass dynamics describe a real glass?

We present the first experimental single-molecule (SM) spectroscopy study of the local dynamics in molecular glasses (frozen toluene and deuterated toluene weakly doped with a substituted terrylene) at T=2-30 K. Surprisingly, the dynamics does not follow the standard model of low-temperature glasses. An extra contribution to the dynamics was detected causing drifts and irreproducible jumps of the SM spectra. The isotope effects in the SM linewidth distribution and the density of states (boson peak) show that the fast dynamics at T=2 K is due to excitations of tunneling nature, whereas at T>7 K it is related to vibrations; H/D atoms are directly involved in both types of excitations.     

Ab?initio molecular dynamics model for density, elastic properties and short range order of Co-Fe-Ta-B metallic glass thin films

Density, elastic modulus and the pair distribution function of Co-Fe-Ta-B metallic glasses were obtained by ab initio molecular dynamics simulations and measured for sputtered thin films using x-ray reflectivity, nanoindentation and x-ray diffraction using high energy photons. The computationally obtained density of 8.19 g cm(-3) for Co(43)Fe(20)Ta(5.5)B(31.5) and 8.42 g cm(-3) for Co(45.5)Fe(24)Ta(6)B(24.5), as well as the Young's moduli of 273 and 251 GPa, respectively, are consistent with our experiments and literature data. These data, together with the good agreement between the theoretical and the experimental pair distribution functions, indicate that the model established here is useful to describe the density, elasticity and short range order of Co-Fe-Ta-B metallic glass thin films. Irrespective of the investigated variation in chemical composition, (Co, Fe)-B cluster formation and Co-Fe interactions are identified by density-of-states analysis. Strong bonds within the structural units and between the metallic species may give rise to the comparatively large stiffness.     

What dynamics can be expected for mixed states in two-slit experiments?

Weak-measurement-based experiments (Kocsis et al., 2011) have shown that, at least for pure states, the average evolution of independent photons in Young’s two-slit experiment is in compliance with the trajectories prescribed by the Bohmian formulation of quantum mechanics. But, what happens if the same experiment is repeated assuming that the wave function associated with each particle is different, i.e., in the case of mixed (incoherent) states? This question is investigated here by means of two alternative numerical simulations of Young’s experiment, purposely devised to be easily implemented and tested in the laboratory. Contrary to what could be expected a priori, it is found that even for conditions of maximal mixedness or incoherence (total lack of interference fringes), experimental data will render a puzzling and challenging outcome: the average particle trajectories will still display features analogous to those for pure states, i.e., independently of how mixedness arises, the associated dynamics is influenced by both slits at the same time. Physically this simply means that weak measurements are not able to discriminate how mixedness arises in the experiment, since they only provide information about the averaged system dynamics.     

Undulation instability of lamellar phases under shear: A mechanism for onion formation?

We consider a lamellar phase of bilayer membranes held between two parallel plates and subject to a steady shear. Accounting for the coupling with the shear flow of the short wavelength undulation modes that are responsible for the membrane excess area, we argue that the flow generates an effective force which acts to reduce the excess area. From the viewpoint of the macroscopic lamellar whose geometric dimensions are fixed, this force translates into an effective lateral pressure. At low shear rates this pressure is balanced by the elastic restoring forces of the lamellar. Above a critical shear rate , where d is the interlayer distance and D is the gap spacing, the lamellar buckles into a harmonic shape modulation, and we predict its wavelength and amplitude . We show that our model is isomorphic to a dilative strain, which is known to induce a similar buckling (undulation) instability. Indeed, at threshold the wavelength is and is identical in both cases. Using a non-linear analysis, we discuss how the wavelength and amplitude vary with shear rate away from the threshold. For we find and . We then focus on the coupling of the buckling modulation itself with the flow, and obtain a criterion for the limit of its stability. Motivated by experiments of D. Roux and coworkers, we assume that at this limit of stability the lamellar breakups into “onion"-like, multilamellar, vesicles. The critical shear rate for the formation of onions is predicted to scale as . The scaling with d is consistent with available experimental data. Received 15 April 1998 and Received in final form 4 March 1999     

Why does shear banding behave like first-order phase transitions? Derivation of a potential from a mechanical constitutive model

Numerous numerical and experimental evidence suggest that shear banding behavior looks like first-order phase transitions. In this paper, we demonstrate that this correspondence is actually established in the so-called non-local diffusive Johnson-Segalman model (the DJS model), a typical mechanical constitutive model that has been widely used for describing shear banding phenomena. In the neighborhood of the critical point, we apply the reduction procedure based on the center manifold theory to the governing equations of the DJS model. As a result, we obtain a time evolution equation of the flow field that is equivalent to the time-dependent Ginzburg-Landau (TDGL) equations for modeling thermodynamic first-order phase transitions. This result, for the first time, provides a mathematical proof that there is an analogy between the mechanical instability and thermodynamic phase transition at least in the vicinity of the critical point of the shear banding of DJS model. Within this framework, we can clearly distinguish the metastable branch in the stress-strain rate curve around the shear banding region from the globally stable branch. A simple extension of this analysis to a class of more general constitutive models is also discussed. Numerical simulations for the original DJS model and the reduced TDGL equation is performed to confirm the range of validity of our reduction theory.     

Bright solitary waves on a torus: Existence,stability and dynamics for the nonlinear Schrödinger model

Motivated by recent developments in the realm of matter waves, we explore the potential of creating solitary waves on the surface of a torus. This is an intriguing perspective due to the role of curvature in the shape and dynamics of the coherent structures. We find different families of bright solitary waves for attractive nonlinearities including ones localized in both angular directions, as well as waves localized in one direction and homogeneous in the other. The waves localized in both angular directions have also been partitioned into two types: those whose magnitude decays to zero and those who do not. The stability properties of the waves are examined and one family is found to be spectrally stable in a suitable parametric regime while most are spectrally unstable, a feature that we comment on. Finally, the nature of the ensuing nonlinear dynamics is touched upon.     

The Massachusetts Toxics Use Reduction Act: a model for nanomaterials regulation?

Polyvinylimidazole (PVIm)-grafted superparamagnetic iron oxide nanoparticles (SPION) (Si-PVIm-grafted Fe₃O₄ NPs) were prepared by grafting of telomere of PVIm on the SPION. The product identified as magnetite, which has an average crystallite size of 9?±?2?nm as estimated from X-ray line profile fitting. Particle size was estimated as 10.0?±?0.5?nm from TEM micrographs. Mean particle size is found as 8.4?±?1.0?nm which agrees well with the values calculated from XRD patterns (9?±?2?nm). Vibrating Sample Magnetometer (VSM) analysis explained the superparamagnetic nature of the nanocomposite. Thermogravimetric analysis showed that the Si-Imi is 25?% of the Si-PVIm-grafted SPION, which means an inorganic content is about 75?%. Detailed electrical and dielectric properties of the properties of the product are also presented. The conductivity of the sample increases significantly with temperature and has the value in the range of 1.14?×?10^?7?C1.78?×?10^?4?S?cm^?1. Analysis of the real and imaginary parts of the permittivities indicated temperature and frequency dependency representing interfacial polarization and temperature-assisted reorganization effects.     

How to improve the accuracy of equilibrium molecular dynamics for computation of thermal conductivity?

Equilibrium molecular dynamics (EMD) simulations through Green-Kubo formula (GKF) have been widely used in the study of thermal conductivity of various materials. However, there exist controversial simulation results which have huge discrepancies with experimental ones in literatures. In this Letter, we demonstrate that the fluctuation in calculated thermal conductivity is due to the uncertainty in determination of the truncation time, which is related to the ensemble and size dependent phonon relaxation time. We thus propose a new scheme in the direct integration of heat current autocorrelation function (HCACF) and a nonzero correction in the double-exponential-fitting of HCACF to describe correctly the contribution to thermal conductivity from low frequency phonons. By using crystalline Silicon (Si) and Germanium (Ge) as examples, we demonstrate that our method can give rise to the values of thermal conductivity in an excellent agreement with experimental ones.     

Formation of Gyrs old black holes in the centers of galaxies within the Lema?tre–Tolman model

In this article we present a model of formation of a galaxy with a black hole in the center. It is based on the Lema?tre–Tolman solution and is a refinement of an earlier model. The most important improvement is the choice of the interior geometry of the black hole allowing for the formation of Gyrs old black holes. Other refinements are the use of an arbitrary Friedmann model as the background (unperturbed) initial state and the adaptation of the model to an arbitrary density profile of the galaxy. Our main interest was the M87 galaxy (NGC 4486), which hosts a supermassive black hole of mass 3.2 × 10⁹ M⊙. It is shown that for this particular galaxy, within the framework of our model and for the initial state being a perturbation of the ΛCDM model, the age of the black hole can be up to 12.7 Gyrs. The dependence of the model on the chosen parameters at the time of last scattering was also studied. The maximal age of the black hole as a function of the Ω _m and Ω_Λ parameters for the M87 galaxy can be 3.717 or 12.708 Gyr.     

Description of small-angle neutron scattering data for nickel–chromium–aluminum alloy within quantum mechanics and classic polydisperse sphere model

The modified Yukawa potential is used to fit the nucleus model parameters to the data on small-angle neutron scattering on nickel—chromium—aluminum alloy for the product of the transferred momentum Q and the effective nucleus radius R, satisfying the condition QR ≤ ?. The analytical polydisperse sphere model is used to calculate the neutron scattering intensity and to determine the most probable macroscopic sphere radius R ₀ at QR ₀ ≥ 3?.