Communication Complexity and Intrinsic Universality in Cellular Automata

The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce necessary conditions for a cellular automaton to be "universal", according to a precise notion of simulation, related both to the dynamics of cellular automata and to their computational power. This notion of simulation relies on simple operations of space-time rescaling and it is intrinsic to the model of cellular automata. Intrinsinc universality, the derived notion, is stronger than Turing universality, but more uniform, and easier to define and study. Our approach builds upon the notion of communication complexity, which was primarily designed to study parallel programs, and thus is, as we show in this article, particulary well suited to the study of cellular automata: it allowed to show, by studying natural problems on the dynamics of cellular automata, that several classes of cellular automata, as well as many natural (elementary) examples, could not be intrinsically universal

Long Range Bond-Bond Correlations in Dense Polymer Solutions

The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $\rho$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) \sim s^{-\omega}$ with $\omega=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) \approx g^{-\omega_0} (s/g)^{-\omega}$ with $\omega_0=2-2\nu=0.824$ ($\nu=0.588$ being Flory's exponent) is set by the number of monomers $g(\rho)$ contained in an excluded volume blob of size $\xi$. % Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains on distances $s \gg g$ caused by the connectivity of chains and the incompressibility of the melt. %Comment: 4 pages, 4 figure

Portable implementation of a quantum thermal bath for molecular dynamics simulations

Recently, Dammak and coworkers (H. Dammak, Y. Chalopin, M. Laroche, M. Hayoun, and J.J. Greffet. Quantumthermal bath for molecular dynamics simulation. Phys. Rev. Lett., 103:190601, 2009.) proposed that the quantum statistics of vibrations in condensed systems at low temperature could be simulated by running molecular dynamics simulations in the presence of a colored noise with an appropriate power spectral density. In the present contribution, we show how this method can be implemented in a flexible manner and at a low computational cost by synthesizing the corresponding noise 'on the fly'. The proposed algorithm is tested for a simple harmonic chain as well as for a more realistic model of aluminium crystal. The energy and Debye-Waller factor are shown to be in good agreement with those obtained from harmonic approximations based on the phonon spectrum of the systems. The limitations of the method associated with anharmonic effects are also briefly discussed. Some perspectives for disordered materials and heat transfer are considered.Comment: Accepted for publication in Journal of Statistical Physic

Predicting epidemic evolution on contact networks from partial observations

The massive employment of computational models in network epidemiology calls for the development of improved inference methods for epidemic forecast. For simple compartment models, such as the Susceptible-Infected-Recovered model, Belief Propagation was proved to be a reliable and efficient method to identify the origin of an observed epidemics. Here we show that the same method can be applied to predict the future evolution of an epidemic outbreak from partial observations at the early stage of the dynamics. The results obtained using Belief Propagation are compared with Monte Carlo direct sampling in the case of SIR model on random (regular and power-law) graphs for different observation methods and on an example of real-world contact network. Belief Propagation gives in general a better prediction that direct sampling, although the quality of the prediction depends on the quantity under study (e.g. marginals of individual states, epidemic size, extinction-time distribution) and on the actual number of observed nodes that are infected before the observation time

Experimental and simulation study on the aerodynamic performance of a counter rotating vertical axis wind turbine

The Darrieus H-rotor has gained much interest in the last few decades as among the reliable devices for wind energy conversion techniques, for their relatively simple structure and aerodynamic performance. In the present work, development and aerodynamic performance predictions of a unique contra-rotating VAWT have been studied through experimental and computational approaches as it has yet to be applied to a VAWT. The main purpose of this study is to develop and investigate the practicality of employing the contra-rotating concept to a VAWT system while enhancing its conversion efficiency. The simulation study was performed using three-dimensional computational fluid dynamics (CFD) models based on K-omega shear stress transport (SST) model. The computational work covers a wider range of simulation processes compared to the experiment which includes a parametric study based on the axial distance between the two rotors and blade height. The performance evaluations of the current models were established in terms of key aerodynamic parameters such as torque and power. The systematic analysis of these quantities showed the usefulness of the contra-rotating technique on a VAWT system and the ability to extract additional more than threefold power over the entire operating wind speeds covered. The system has also improved the inherent difficulties of the Darrieus rotor to self-start. The results also demonstrated a significant increase in terms of conversion efficiency for both power and torque compared to a single-rotor system of a similar type. A maximum of 43% and 46% of power and torque coefficients were respectively possible with the current dual-rotor system. The simulation results indicate that smaller axial distance tends to enhance the performance output of the system relatively better compared to a larger distance. However, in terms of the blade height, longer blades generated the highest amount of power. It is anticipated that this current technique could revolutionize wind energy harvesting strategies and would find applications in a wide range of sites that are characterized by low and moderate wind regimes and particularly be useful in the urban environment where turbulence is high

A Comparative Study of Disordered and Ordered Protein Folding Dynamics Using Computational Simulation

Folding protein dynamics has been an area of high interest for quite some time, especially given the increased focus on the field of Biophysics. Because folding dynamics occur on such short time scales, empirical techniques developed for more "static" protein events, such as X-ray crystallography, nuclear magnetic resonance, and green fluorescent protein (GFP) labelling, aren't as applicable. Instead, computational methods must often be used to simulate these short lived yet highly dynamic events. One such computational method that is proven to provide much valuable insight into protein folding dynamics is Molecular Dynamics Simulation (MD Simulation). This simulation method is both highly computationally demanding, yet highly accurate in its modelling of a proteins physical behaviour. Besides MD Simulation, simulations in general are quite applicable in the context of these protein events. For example, the simple Gillespie algorithm, a computational technique which can be executed on almost any personal computer, provides quite the robust view into protein dynamics given its computational simplicity. This paper will compare the results of two simulations, an MD simulation of a disordered, six-residue, carcinogenic protein fragment, and a Gillespie algorithm based simulation of an ordered folding protein: the mathematically identical nature of the Gillespie algorithm time series of the asymptotically stochastic hyperbolic tangent dynamics for the wild type predicting the exact behaviour of the carcinogenic protein system time series will show the computational power simulations provide for analyzing both disordered and ordered protein systems.Comment: 13 pages, draft 1, 8 figure

Cellular-Automata model for dense-snow avalanches

This paper introduces a three-dimensional model for simulating dense-snow avalanches, based on the numerical method of cellular automata. This method allows one to study the complex behavior of the avalanche by dividing it into small elements, whose interaction is described by simple laws, obtaining a reduction of the computational power needed to perform a three-dimensional simulation. Similar models by several authors have been used to model rock avalanches, mud and lava flows, and debris avalanches. A peculiar aspect of avalanche dynamics, i.e., the mechanisms of erosion of the snowpack and deposition of material from the avalanche is taken into account in the model. The capability of the proposed approach has been illustrated by modeling three documented avalanches that occurred in Susa Valley (Western Italian Alps). Despite the qualitative observations used for calibration, the proposed method is able to reproduce the correct three-dimensional avalanche path, using a digital terrain model, and the order of magnitude of the avalanche deposit volume

Data-driven Models to Anticipate Critical Voltage Events in Power Systems

This paper explores the effectiveness of data-driven models to predict voltage excursion events in power systems using simple categorical labels. By treating the prediction as a categorical classification task, the workflow is characterized by a low computational and data burden. A proof-of-concept case study on a real portion of the Italian 150 kV sub-transmission network, which hosts a significant amount of wind power generation, demonstrates the general validity of the proposal and offers insight into the strengths and weaknesses of several widely utilized prediction models for this application.Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canad

Identification of criticality in neuronal avalanches: II. A theoretical and empirical investigation of the Driven case

The observation of apparent power laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a separation of timescales is thought to be crucial for the observation of power-law dynamics and computational models are often constructed with this property. However, this is not necessarily a characteristic of physiological neural networks—external input does not only occur when the network is at rest/a steady state. In this paper we study a simple neuronal network model driven by a continuous external input (i.e. the model does not have an explicit separation of timescales from seeding the system only when in the quiescent state) and analytically tuned to operate in the region of a critical state (it reaches the critical regime exactly in the absence of input—the case studied in the companion paper to this article). The system displays avalanche dynamics in the form of cascades of neuronal firing separated by periods of silence. We observe partial scale-free behaviour in the distribution of avalanche size for low levels of external input. We analytically derive the distributions of waiting times and investigate their temporal behaviour in relation to different levels of external input, showing that the system’s dynamics can exhibit partial long-range temporal correlations. We further show that as the system approaches the critical state by two alternative ‘routes’, different markers of criticality (partial scale-free behaviour and long-range temporal correlations) are displayed. This suggests that signatures of criticality exhibited by a particular system in close proximity to a critical state are dependent on the region in parameter space at which the system (currently) resides