Behavior and Breakdown of Higher-Order Fermi-Pasta-Ulam-Tsingou Recurrences

We investigate numerically the existence and stability of higher-order recurrences (HoRs), including super-recurrences, super-super-recurrences, etc., in the alpha and beta Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions in the fundamental normal mode. Our results represent a considerable extension of the pioneering work of Tuck and Menzel on super-recurrences. For fixed lattice sizes, we observe and study apparent singularities in the periods of these HoRs, speculated to be caused by nonlinear resonances. Interestingly, these singularities depend very sensitively on the initial energy and the respective nonlinear parameters. Furthermore, we compare the mechanisms by which the super-recurrences in the two model's breakdown as the initial energy and respective nonlinear parameters are increased. The breakdown of super-recurrences in the beta-FPUT lattice is associated with the destruction of the so-called metastable state and hence is associated with relaxation towards equilibrium. For the alpha-FPUT lattice, we find this is not the case and show that the super-recurrences break down while the lattice is still metastable. We close with comments on the generality of our results for different lattice sizes

Dynamics of entanglement in a dissipative Bose-Hubbard dimer

We study the connection between the semiclassical phase space of the Bose-Hubbard dimer and inherently quantum phenomena in this model, such as entanglement and dissipation-induced coherence. Near the semiclassical self-trapping fixed points, the dynamics of Einstein-Podolski-Rosen (EPR) entanglement and condensate fraction consists of beats among just three eigenstates. Since persistent EPR entangled states arise only in the neighborhood of these fixed points, our analysis explains essentially all of the entanglement dynamics in the system. We derive accurate analytical approximations by expanding about the strong-coupling limit; surprisingly, their realm of validity is nearly the entire parameter space for which the self-trapping fixed points exist. Finally, we show significant enhancement of entanglement can be produced by applying localized dissipation.We thank Luca d'Alessio, Pjotrs Gri. sons, and especially Anatoli Polkovnikov for helpful discussions. This work was supported in part by Boston University, by the US National Science Foundation under Grant No. PHYS-1066293, and by a grant of the Max Planck Society to the MPRG Network Dynamics. H. H. acknowledges support by the German Research Foundation under Grant No. HE 6312/1-1. We are also grateful for the hospitality of the Aspen Center for Physics. (Boston University; PHYS-1066293 - US National Science Foundation; Max Planck Society; HE 6312/1-1 - German Research Foundation)First author draf

Accelerated search and design of stretchable graphene kirigami using machine learning

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks, commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of ∼4×106 candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.P. Z. H. developed the codes, performed the simulations and data analysis, and wrote the manuscript with input from all authors. P. Z. H. and E. D. C. developed the machine learning methods. P. Z. H., D. K. C. and H. S. P. acknowledge the Hariri Institute Research Incubation Grant No. 2018-02-002 and the Boston University High Performance Shared Computing Cluster. P. Z. H. is grateful for the Hariri Graduate Fellowship. P. Z. H. thank Grace Gu and Adrian Yi for helpful discussions. (2018-02-002 - Hariri Graduate Fellowship)Published versio

Graphene kirigami as a platform for stretchable and tunable quantum dot arrays

The quantum transport properties of a graphene kirigami similar to those studied in recent experiments are calculated in the regime of elastic, reversible deformations. Our results show that, at low electronic densities, the conductance profile of such structures replicates that of a system of coupled quantum dots, characterized by a sequence of minibands and stop-gaps. The conductance and I-V curves have different characteristics in the distinct stages of elastic deformation that characterize the elongation of these structures. Notably, the effective coupling between localized states is strongly reduced in the small elongation stage, whereas in the large elongation regime the development of strong, localized pseudomagnetic field barriers can reinforce the coupling and reestablish resonant tunneling across the kirigami. This provides an interesting example of interplay between geometry and pseudomagnetic field-induced confinement. The alternating miniband and stop-gaps in the transmission lead to I-V characteristics with negative differential conductance in well defined energy/doping ranges. These effects should be stable in a realistic scenario that includes edge roughness and Coulomb interactions, as these are expected to further promote localization of states at low energies in narrow segments of graphene nanostructures.Comment: 10 pages, 10 figure

Meteor light curves: the relevant parameters

We investigate a uniform sample of 113 light curves (LCs) of meteors collected at the Wise Observatory in November 2002 while observing the Leonid meteor shower. We use previously defined descriptors such as the skewness F and a recently defined pointedness parameter along with a number of other measurable or derived quantities to explore the parameter space in search of meaningful LC descriptors. We make extensive use of statistical techniques to reveal links among the variables and to understand their relative importance. In particular, we show that meteors with long-duration trails rise slowly to their maximal brightness and also decay slowly from there while showing milder flaring than other meteors. Early skewed LCs show a fast rise to the peak. We show that the duration of te luminous phase of the meteor is th emost important variable differentiating among the 2002 LCs. The skewness parameter F appears only as the 2nd or 3rd in explaining the LC variance. We suggest that the pointedness parameter P could possibly be useful to discriminate among meteors from different showers, or to compare observations and model predictions.Comment: 10 pages (2 figures) in press with MNRA

The Quintuple Helix innovation model: Global warming as a challenge and driver for innovation

The Triple Helix innovation model focuses on university-industry-government relations. The Quadruple Helix embeds the Triple Helix by adding as a fourth helix the media-based and culture-based public and civil society. The Quintuple Helix innovation model is even broader and more comprehensive by contextualizing the Quadruple Helix and by additionally adding the helix (and perspective) of the natural environments of society. The Triple Helix acknowledges explicitly the importance of higher education for innovation. However, in one line of interpretation it could be argued that the Triple Helix places the emphasis on knowledge production and innovation in the economy so it is compatible with the knowledge economy. The Quadruple Helix already encourages the perspective of the knowledge society, and of knowledge democracy for knowledge production and innovation. In a Quadruple Helix understanding, the sustainable development of a knowledge economy requires a coevolution with the knowledge society. The Quintuple Helix stresses the necessary socioecological transition of society and economy in the twenty-first century; therefore, the Quintuple Helix is ecologically sensitive. Within the framework of the Quintuple Helix innovation model, the natural environments of society and the economy also should be seen as drivers for knowledge production and innovation, therefore defining opportunities for the knowledge economy. The European Commission in 2009 identified the socioecological transition as a major challenge for the future roadmap of development. The Quintuple Helix supports here the formation of a win-win situation between ecology, knowledge and innovation, creating synergies between economy, society, and democracy. Global warming represents an area of ecological concern, to which the Quintuple Helix innovation model can be applied with greater potential