Three-dimensional non-approximate Coulomb interaction between two trapped quantum particles.

The two trapped quantum particles interacting problem is generalized to three dimensions, and the exact Coulomb potential is used. The system is solved by expanding the wavefunction in terms of the isotropic harmonic oscillator eigenfunctions and Hydrogen atom eigenfunctions independently, showing that each one results in a prime approximation for different domains of the normalized coupling constant of the relative interactions, suggesting that the combination of the basis is enough to build a well-suited base for the non-approximate problem. The results are compared to previous works that use a model of approximate finite-rage soft-core interaction model of the problem to give insights into the many-body states of strongly correlated ultracold bosons and fermions. We conclude that the proposed three-dimensional approach facilitates the distinction between bosons and fermions while the solutions given by the expansions better define the behavior of the particles for repulsive potentials. In addition, we discuss the substantial differences between our work and the previous approximate model.

Circularly polarized light-induced potentials and the demise of excited states.

In the presence of strong electric fields, the excited states of single-electron molecules and molecules with large transient dipoles become unstable because of anti-alignment, the rotation of the molecular axis perpendicular to the field vector, where bond hardening is not possible. We show how to overcome this problem by using circularly polarized electromagnetic fields. Using a full quantum description of the electronic, vibrational, and rotational degrees of freedom, we characterize the excited electronic state dressed by the field and analyze its dependence on the bond length and angle and the stability of its vibro-rotational eigenstates. Although the dynamics is metastable, most of the population remains trapped in this excited state for hundreds of femtoseconds, allowing quantum control. Contrary to what happens with linearly polarized fields, the photodissociation occurs along the initial molecular axis, not perpendicular to it.

Multifractal Characteristics of Geomagnetic Field Fluctuations for the Northern and Southern Hemispheres at Swarm Altitude.

This paper explores the spatial variations of the statistical scaling features of low to high latitude geomagnetic field fluctuations at Swarm altitude. The data for this study comes from the vector field magnetometer onboard Swarm A satellite, measured at low resolution (1 Hz) for one year (from 9 March 2016, to 9 March 2017). We estimated the structure-function scaling exponents using the p-leaders discrete wavelet multifractal technique, from which we obtained the singularity spectrum related to the magnetic fluctuations in the North-East-Center (NEC) coordinate system. From this estimation, we retain just the maximal fractal subset, associated with the Hurst exponent H. Here we present thresholding for two levels of the Auroral Electrojet index and almost the whole northern and southern hemispheres, the Hurst exponent, the structure-function scaling exponent of order 2, and the multifractal p-exponent width for the geomagnetic fluctuations. The latter quantifies the relevance of the multifractal property. Sometimes, we found negative values of H, suggesting a behavior similar to wave breaking or shocklet-like propagating front. Furthermore, we found some asymmetries in the magnetic field turbulence between the northern and southern hemispheres. These estimations suggest that different turbulent regimes of the geomagnetic field fluctuations exist along the Swarm path.

Simulations suggest that navigation software may not be as efficient as expected for city traffic.

We suggest a theoretical framework to study the dynamics of an open city, with cars entering at a certain rate and leaving as they reach their destinations. In particular, we assess through simulations some unexpected consequences of the massive use of GPS (global positioning system) navigation systems in the overall dynamics. One of our main interest is to identify what type of measurements would be the most relevant for an experimental study of this system, specifically, the ones useful for city traffic administrators. To do so, we solve the microdynamics using a cellular automaton model considering three different navigation strategies based on the minimization of the individual paths (unweighted strategy) or travel times (weighted strategies). Although the system is inherently stochastic, we found in our simulations an equivalent saddle-node bifurcation for all strategies where the input rate acts as a bifurcation parameter. There is also evidence of additional bifurcations for travel time minimization based strategies. Although we found that weighted strategies are more efficient in terms of car motion, there is a destabilization phenomenon that makes, in an unexpected way, a variation of the unweighted strategy more optimal at certain densities from the fuel efficiency of the overall city traffic point of view. These results bring new insight into the intrinsic dynamics of cities and the perturbations that individual traffic routing can produce on the city as a whole.

Nonlocal self-organization of a dissipative system.

We study the self-organization process induced by a nonlocal critical field, in analogy with the electric field that is derived from the global spatial profile of electric charge density during a discharge. In this nontrivial extension of standard sandpilelike models of intermittent dissipation, the charges move in a similar manner to grains of sand when the threshold condition on the field is achieved. Here we focus our attention on the long term statistics of events, so that we consider an extremely simplified model in close similarity with sandpiles, avoiding some of the extremely interesting complexities that occur in three-dimensional electric discharges. For the observed avalanches (discharges in this case) we analyze four characteristic quantities: current, charge discharged, energy discharged, and duration of the discharge. We have run several simulations to explore the parameter space and found in general that they exhibit well defined power law event statistics spanning for one to three decades in general. For some parameter values we observe the existence of large or global events, in addition to the power law statistics, some of which may be related to finite size effects due to the size of the simulation box. This is the first step in understanding the long term statistics of systems with avalanches or discharges, when the criticality is controlled by nonlocality, as there are a number systems, such as lightning discharges or heat transport in tokamaks, where this type of dynamics is expected to occur.

Stability and robustness of asymptotic autocatalytic systems.

Here, we address the consequences of the extension in the space of a simple model of a system that is closed to efficient causation: the (M,R)-system model. To do so, we use a diffusion term to describe the collective motion of the nutrients' concentration across the compartmentalized space that defines the organism. We show that the non-trivial stable steady state remains despite such generalization, as long as the system is small enough to deal with the transport of the precursors to feed the entire protocell and dispose of a sufficient concentration of it in its surroundings. Such consideration explains the emergence of a bifurcation with two parameters that we characterize. Finally, we show that the robustness of the system under catastrophic losses of catalysts also remains, preserving the original's model character.

Speeding up maximum population transfer in periodically driven multi-level quantum systems.

A fast and robust approach to controlling the quantum state of a multi-level quantum system is investigated using a twofrequency time-varying potential. A comparison with other related approaches in the context of a two-level system is also presented, showing similar times and fidelities. As a concrete example, we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We show that the transition between the ground and first excited state is about 20 times faster than the one performed using a single frequency, both with fidelity of 99.97%. The transition time is about 3.5 times the minimum allowed by quantum mechanics. A test of the robustness of the approach is presented, concluding that, counter-intuitively, it is not only faster but also easier to tune up two frequencies than one. This robustness makes the approach suitable for real applications.

Author Correction: Nucleation of superfluid-light domains in a quenched dynamics.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.

The Stochastic Transport Dynamics of a Conserved Quantity on a Complex Network.

The stochastic dynamics of conserved quantities is an emergent phenomena observed in many complex systems, ranging from social and to biological networks. Using an extension of the Ehrenfest urn model on a complex network, over which a conserved quantity is transported in a random fashion, we study the dynamics of many elementary packets transported through the network by means of a master equation approach and compare with the mean field approximation and stochastic simulations. By use of the mean field theory, it is possible to compute an approximation to the ensemble average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the master equation. However, the master equation gives a more complete description of the stochastic system and provides a probabilistic view of the occupation number at each node. Of particular relevance is the standard deviation of the occupation number at each node, which is not uniform for a complex network. We analyze and compare different network topologies (small world, scale free, Erdos-Renyi, among others). Given the computational complexity of directly evaluating the asymptotic, or equilibrium, occupation number probability distribution, we propose a scaling relation with the number of packets in the network, that allows to construct the asymptotic probability distributions from the network with one packet. The approximation, which relies on the same matrix found in the mean field approach, becomes increasingly more accurate for a large number of packets.

Nucleation of superfluid-light domains in a quenched dynamics.

Strong correlation effects emerge from light-matter interactions in coupled resonator arrays, such as the Mott-insulator to superfluid phase transition of atom-photon excitations. We demonstrate that the quenched dynamics of a finite-sized complex array of coupled resonators induces a first-order like phase transition. The latter is accompanied by domain nucleation that can be used to manipulate the photonic transport properties of the simulated superfluid phase; this in turn leads to an empirical scaling law. This universal behavior emerges from the light-matter interaction and the topology of the array. The validity of our results over a wide range of complex architectures might lead to a promising device for use in scaled quantum simulations.

The Earth's Magnetosphere: A Systems Science Overview and Assessment.

A systems science examination of the Earth's fully interconnected dynamic magnetosphere is presented. Here the magnetospheric system (a.k.a. the magnetosphere-ionosphere-thermosphere system) is considered to be comprised of 14 interconnected subsystems, where each subsystem is a characteristic particle population: 12 of those particle populations are plasmas and two (the atmosphere and the hydrogen geocorona) are neutrals. For the magnetospheric system, an assessment is made of the applicability of several system descriptors, such as adaptive, nonlinear, dissipative, interdependent, open, irreversible, and complex. The 14 subsystems of the magnetospheric system are cataloged and described, and the various types of magnetospheric waves that couple the behaviors of the subsystems to each other are explained. This yields a roadmap of the connectivity of the magnetospheric system. Various forms of magnetospheric activity beyond geomagnetic activity are reviewed, and four examples of emergent phenomena in the Earth's magnetosphere are presented. Prior systems science investigations of the solar-wind-driven magnetospheric system are discussed: up to the present these investigations have not accounted for the full interconnectedness of the system. This overview and assessment of the Earth's magnetosphere hopes to facilitate (1) future global systems science studies that involve the entire interconnected magnetospheric system with its diverse time and spatial scales and (2) connections of magnetospheric systems science with the broader Earth systems science.

Bending energy of 2D materials: graphene, MoS2 and imogolite.

The bending process of 2D materials, subject to an external force, is investigated, and applied to graphene, molybdenum disulphide (MoS2), and imogolite. For graphene we obtained 3.43 eV Å2 per atom for the bending modulus, which is in good agreement with the literature. We found that MoS2 is ∼11 times harder to bend than graphene, and has a bandgap variation of ∼1 eV as a function of curvature. Finally, we also used this strategy to study aluminosilicate nanotubes (imogolite) which, in contrast to graphene and MoS2, present an energy minimum for a finite curvature radius. Roof tile shaped imogolite precursors turn out to be stable, and thus are expected to be created during imogolite synthesis, as predicted to occur by self-assembly theory.

Controlling the Quantum State with a time varying potential.

The problem of controlling the quantum state of a system is investigated using a time varying potential. As a concrete example we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We derive an analytic expression for the frequencies of resonance between states, and against standard intuition, we show how to use this behavior to control the quantum state of the system at will. In particular, we offer as an example the transition from the ground state to the first excited state of the square well potential. At first sight, it may be counter intuitive that we can control the state of such a quantum Hamiltonian, as the Schrödinger equation conserves the norm of the wave function. In this manuscript, we show how that can be achieved.

Using agent based modeling to assess the effect of increased Bus Rapid Transit system infrastructure on walking for transportation.

The effect of transport infrastructure on walking is of interest to researchers because it provides an opportunity, from the public policy point of view, to increase physical activity (PA). We use an agent based model (ABM) to examine the effect of transport infrastructure on walking. Particular relevance is given to assess the effect of the growth of the Bus Rapid Transit (BRT) system in Bogotá on walking. In the ABM agents are assigned a home, work location, and socioeconomic status (SES) based on which they are assigned income for transportation. Individuals must decide between the available modes of transport (i.e., car, taxi, bus, BRT, and walking) as the means of reaching their destination, based on resources and needed travel time. We calibrated the model based on Bogota's 2011 mobility survey. The ABM results are consistent with previous empirical findings, increasing BRT access does indeed increase the number of minutes that individuals walk for transportation, although this effect also depends on the availability of other transport modes. The model indicates a saturation process: as more BRT lanes are added, the increment in minutes walking becomes smaller, and eventually the walking time decreases. Our findings on the potential contribution of the expansion of the BRT system to walking for transportation suggest that ABMs may prove helpful in designing policies to continue promoting walking.

Au13-nAgn clusters: a remarkably simple trend.

The planar to three dimensional transition of Au13-nAgn clusters is investigated. To do so the low lying energy configurations for all possible concentrations (n values) are evaluated. Many thousands of possible conformations are examined. They are generated using the procedure developed by Rogan et al. in combination with the semi-empirical Gupta potential. A large fraction of these (the low lying energy ones) are minimized by means of Density Functional Theory (DFT) calculations. We employ the Tao, Perdew, Staroverov, and Scuseria (TPSS) meta-GGA functional and the Perdew, Burke and Ernzerhof (PBE) GGA functional, and compare their results. The effect of spin-orbit coupling is studied as well as the s-d hybridization. As usual in this context the results are functional-dependent. However, both functionals lead to agreement as far as trends are concerned, yielding just two relevant motifs, but their results differ quantitatively.

Generalization of the Ehrenfest urn model to a complex network.

The Ehrenfest urn model is extended to a complex directed network, over which a conserved quantity is transported in a random fashion. The evolution of the conserved number of packets in each urn, or node of the network, is illustrated by means of a stochastic simulation. Using mean-field theory we were able to compute an approximation to the ensemble-average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the stochastic simulation. Using this analytic approximation we are able to find the asymptotic dynamical state of the system and the time scale to approach the equilibrium state, for different networks. The study is extended to large scale-free and small-world networks, in which the relevance of the connectivity distribution and the topology of the network for the distribution of time scales of the system is apparent. This analysis may contribute to the understanding of the transport properties in real networks subject to a perturbation, e.g., the asymptotic state and the time scale required to approach it.

Modeling a bus through a sequence of traffic lights.

We propose a model of a bus traveling through a sequence of traffic lights, which is required to stop between the traffic signals to pick up passengers. A two dimensional model, of velocity and traveled time at each traffic light, is constructed, which shows non-trivial and chaotic behaviors for realistic city traffic parameters. We restrict the parameter values where these non-trivial and chaotic behaviors occur, by following analytically and numerically the fixed points and period 2 orbits. We define conditions where chaos may arise by determining regions in parameter space where the maximum Lyapunov exponent is positive. Chaos seems to occur as long as the ratio of the braking and accelerating capacities are greater than about ∼3.

Regular transport dynamics produce chaotic travel times.

In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

A strategy to find minimal energy nanocluster structures.

An unbiased strategy to search for the global and local minimal energy structures of free standing nanoclusters is presented. Our objectives are twofold: to find a diverse set of low lying local minima, as well as the global minimum. To do so, we use massively the fast inertial relaxation engine algorithm as an efficient local minimizer. This procedure turns out to be quite efficient to reach the global minimum, and also most of the local minima. We test the method with the Lennard-Jones (LJ) potential, for which an abundant literature does exist, and obtain novel results, which include a new local minimum for LJ13 , 10 new local minima for LJ14 , and thousands of new local minima for 15≤N≤65. Insights on how to choose the initial configurations, analyzing the effectiveness of the method in reaching low-energy structures, including the global minimum, are developed as a function of the number of atoms of the cluster. Also, a novel characterization of the potential energy surface, analyzing properties of the local minima basins, is provided. The procedure constitutes a promising tool to generate a diverse set of cluster conformations, both two- and three-dimensional, that can be used as an input for refinement by means of ab initio methods.

Thermal effects on the propagation of large-amplitude electromagnetic waves in magnetized relativistic electron-positron plasma.

The propagation of circularly polarized electromagnetic waves along a constant background magnetic field in an electron-positron plasma is calculated by means of both a fluid and a kinetic theory treatment. In the fluid theory, relativistic effects are included in the particle motion, the wave field, and in the thermal motion by means of a function f, which depends only on the plasma temperature. In this work we analyze the consistency of the fluid results with those obtained from a kinetic treatment, based on the relativistic Vlasov equation. The corresponding kinetic dispersion relation is numerically studied for various temperatures, and results are compared with the fluid treatment. Analytic expressions for the Alfvén velocity are obtained for the fluid and kinetic models, and it is shown that, in the kinetic treatment, the Alfvén branch is suppressed for large temperatures.