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Nowadays, explosive synchronization is a well documented phenomenon occurring in networks when the node frequency and its degree are correlated. This first-order transition, which may coexists with classical synchronization, has been recently causally linked to some pathological brain states like epilepsy and fibromyalgia. It is then intriguing how most of neuronal systems can operate in normal conditions avoiding explosive synchronization. Here, we have discovered that synchronization in networks where the oscillators are coupled via degree-biased Laplacian operators, naturally controls the transition from explosive to standard synchronization in neuronal-like systems. We prove analytically that explosive synchronization emerges when using this theoretical setting in star-like (neuronal) networks. As soon as this star-like network is topologically converted to a network containing cycles, e.g., via synaptic connections to other neurons, the explosive synchronization gives rise to classical synchronization. This allows us to hypothesize that such topological control of explosive synchronization could be a mechanism for the brain to naturally work in normal, non-pathological, conditions., Comment: 13 pages, 11 figures

The usage of neural networks (NNs) for flow reconstruction (FR) tasks from a limited number of sensors is attracting strong research interest, owing to NNs' ability to replicate high dimensional relationships. Trained on a single flow case for a given Reynolds number or over a reduced range of Reynolds numbers, these models are unfortunately not able to handle flows around different objects without re-training. We propose a new framework called Spatial Multi-Geometry FR (SMGFR) task, capable of reconstructing fluid flows around different two-dimensional objects without re-training, mapping the computational domain as an annulus. Different NNs for different sensor setups (where information about the flow is collected) are trained with high-fidelity simulation data for a Reynolds number equal to approximately $300$ for 64 objects randomly generated using Bezier curves. The performance of the models and sensor setups are then assessed for the flow around 16 unseen objects. It is shown that our mapping approach improves percentage errors by up to 15\% in SMGFR when compared to a more conventional approach where the models are trained on a Cartesian grid, and achieves errors under 3\%, 10\% and 30\% for pressure, velocity and vorticity fields predictions, respectively. Finally, SMGFR is extended to predictions of snapshots in the future, introducing the Spatio-temporal MGFR (STMGFR) task. A novel approach is developed for STMGFR involving splitting DNNs into a spatial and a temporal component. We demonstrate that this approach is able to reproduce, in time and in space, the main features of flows around arbitrary objects., 44 pages, 15 figures

The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of the applied numerical scheme. Such a dependence of the solution on the numeric scheme leads to an inadequate representation of the real chaotic system. A stochastic approach for generating training times series and characterising their predictability is suggested to address this problem. The approach is applied for analysing two chaotic systems with known properties, Lorenz system and Anishchenko-Astakhov generator. Additionally, the approach is extended to critically assess a reservoir computing model used for chaotic time series prediction. Limitations of reservoir computing for surrogate modelling of chaotic systems are highlighted., Paper published as part of the special topic on In Memory of Vadim S. Anishchenko. Dataset used for figures and some additional comments on the used numerical methods are openly available in http://wrap.warwick.ac.uk/153069/

We report on a very first experimental observation of a new curved plasmonic beam, a plasmonic hook (PH), for surface plasmon-polariton (SPP) waves. We demonstrate that the SPP PH effect could be realized within a trapezoidal dielectric microstructure with the relative ease of fabrication compared to the generation of the Airy SPP waves which require complex techniques to compensate the wave vectors mismatch. Using numerical analysis, we predicted the PH phenomenon, optimized the microstructure and then confirmed the SPP PH existence via amplitude and phase-resolved scattering scanning near-field optical microscopy at the telecom wavelengths of 1530-1570 nm. The experimental results are in reasonable agreement with our predictions. Importantly, the SPP PH demonstrates the smallest radius of curvature ever recorded for SPP waves compared to that for the Airy-family plasmonic beams providing many useful applications spreading from nanoparticles manipulation toward bio-sensing within a nanoscale., 12 pages, 3 figures

Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the Lyapunov exponent. However ordinal patterns store strictly more information than Permutation Entropy or Lyapunov exponents. We present results working with the Duffing oscillator showing that ordinal patterns reflect changes in dynamical symmetry invisible to other measures, even Permutation Entropy. We find that these changes in symmetry at given parameter values are correlated with a change in stability at neighboring parameters which suggests a novel predictive capability for this analysis technique., 8 pages, 9 figures

The introduction of accelerator devices such as graphics processing units (GPUs) has had profound impact on molecular dynamics simulations and has enabled order-of-magnitude performance advances using commodity hardware. To fully reap these benefits, it has been necessary to reformulate some of the most fundamental algorithms, including the Verlet list, pair searching and cut-offs. Here, we present the heterogeneous parallelization and acceleration design of molecular dynamics implemented in the GROMACS codebase over the last decade. The setup involves a general cluster-based approach to pair lists and non-bonded pair interactions that utilizes both GPUs and CPU SIMD acceleration efficiently, including the ability to load-balance tasks between CPUs and GPUs. The algorithm work efficiency is tuned for each type of hardware, and to use accelerators more efficiently we introduce dual pair lists with rolling pruning updates. Combined with new direct GPU-GPU communication as well as GPU integration, this enables excellent performance from single GPU simulations through strong scaling across multiple GPUs and efficient multi-node parallelization., Comment: The following article has been submitted to the Journal of Chemical Physics

In this paper, the recently proposed technique to produce photonic jets (terajets at THz frequencies) using 3D dielectric cuboids is applied in the design of mesoscale cuboid-chain waveguide. The chains are basically designed with several dielectric cubes with dimensions {\lambda}0 along the x, y and z axes placed periodically along the axial z-axis and separated by an air-gap. Based on this, a systematic study of the focusing properties and wave guiding of this chain is performed when the air-gap between the dielectric cubes is changed from 0.25{\lambda}0 to 2.5{\lambda}0 with the best performance achieved with the latter design. The numerical results of focusing and transport properties are carried out using Finite Integration Technique. The results here presented may be scaled to any frequency ranges such as millimeter, sub-millimeter or optical frequencies., Comment: 8 pages, 5 figures

Adsorption and dissociation of hydrocarbons on metallic surfaces represent crucial steps to carburization of metal. Here, we use density functional theory total energy calculations with the climbing-image nudged elastic band method to estimate the adsorption energies and dissociation barriers for different CO coverages with surface supercells of different sizes. For the absorption of CO, the contribution from van der Waals interaction in the computation of adsorption parameters is found important in small systems with high CO-coverages. The dissociation process involves carbon insertion into the Fe surface causing a lattice deformation that requires a larger surface system for unrestricted relaxation. We show that, in larger surface systems associated with dilute CO-coverages, the dissociation barrier is significantly decreased. The elastic deformation of the surface is generic and can potentially applicable for all similar metal-hydrocarbon reactions and therefore a dilute coverage is necessary for the simulation of these reactions as isolated processes., 12 pages, 6 figures. Submitted to Journal of Applied Physics

We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure of the continuum equation. Specifically, it conserves the total number of particles and fulfills an H-theorem as the original partial differential equation. Guided by the Theory of Coarse-Graining, we discuss the inclusion of thermal fluctuations in the non-linear diffusion equation. This sheds light on the meaning of such a fluctuating hydrodynamics equation and to the limitations of the approximations involved. The methodology proposed for the introduction of thermal fluctuations in finite element methods is general and valid for both regular and irregular grids in arbitrary dimensions. We focus here on simulations of the Ginzburg-Landau free energy functional using both regular and irregular 1D grids. Convergence of the numerical results is obtained for the static and dynamic structure factors as the resolution of the grid is increased., Comment: Updated version after review. Accepted for publication in the Journal of Chemical Physics

In twistor theory, the canonical quantization procedure, called twistor quantization, is performed with the twistor operators represented as \hat{Z}^{A}=Z^{A}(\in C) and \hat{\bar{Z}}_{A}=-\frac{\partial}{\partial Z^{A}}. However, it has not been clarified what kind of function spaces this representation is valid in. In the present paper, we try to find appropriate (pre-)Hilbert spaces in which the above representation is realized as an adjoint pair of operators. To this end, we define an inner product for the helicity eigenfunctions by an integral over the product space of the circular space S^{1} and the upper half of projective twistor space. Using this inner product, we define a Hilbert space in some particular case and indefinite-metric pre-Hilbert spaces in other particular cases, showing that the above- mentioned representation is valid in these spaces. It is also shown that only the Penrose transform in the first particular case yields positive-frequency massless fields without singularities, while the Penrose transforms in the other particular cases yield positive-frequency massless fields with singularities., Comment: Typos corrected

A two-step unified framework for the evaluation of continuum field expressions from molecular simulations for arbitrary interatomic potentials is presented. First, pointwise continuum fields are obtained using a generalization of the Irving-Kirkwood procedure to arbitrary multi-body potentials. Two ambiguities associated with the original Irving-Kirkwood procedure (which was limited to pair potential interactions) are addressed in its generalization. The first ambiguity is due to the non-uniqueness of the decomposition of the force on an atom as a sum of central forces, which is a result of the non-uniqueness of the potential energy representation in terms of distances between the particles. This is in turn related to the shape space of the system. The second ambiguity is due to the non-uniqueness of the energy decomposition between particles. The latter can be completely avoided through an alternate derivation for the energy balance. It is found that the expressions for the specific internal energy and the heat flux obtained through the alternate derivation are quite different from the original Irving-Kirkwood procedure and appear to be more physically reasonable. Next, in the second step of the unified framework, spatial averaging is applied to the pointwise field to obtain the corresponding macroscopic quantities. These lead to expressions suitable for computation in molecular dynamics simulations. It is shown that the important commonly-used microscopic definitions for the stress tensor and heat flux vector are recovered in this process as special cases (generalized to arbitrary multi-body potentials). Several numerical experiments are conducted to compare the new expression for the specific internal energy with the original one., arXiv admin note: text overlap with arXiv:1008.4819