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Tiago Pereira

Publications and source records attributed to Tiago Pereira.

52 records · Page 3Linked to original sources
arXiv2014

Explosive Synchronization is Discontinuous

Spontaneous explosive is an abrupt transition to collective behavior taking place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. This explosive transition was conjectured to be discontinuous. Indeed, numerical investigations reveal a hysteresis behavior associated with the transition. Here, we analyze explosive synchronization in star graphs. We show that in the thermodynamic limit the transition to (and out) collective behavior is indeed discontinuous. The discontinuous nature of the transition is related to the nonlinear behavior of the order parameter, which in the thermodynamic limit exhibits multiple fixed points. Moreover, we unravel the hysteresis behavior in terms of the graph parameters. Our numerical results show that finite size graphs are well described by our predictions.

nlin.AO↗
arXiv2014

Dynamics of Cluster Synchronisation in Modular Networks: Implications for Structural and Functional Networks

Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional network. A fundamental question in the analysis of complex systems concerns the relation between functional and structural networks. Using synchronisation as a paradigm for network functionality, we study the dynamics of cluster formation in functional networks. We show that the functional network can drastically differ from the structural network. We uncover the mechanism driving these bifurcations by obtaining necessary conditions for modular synchronisation.

nlin.AO↗
arXiv2014

Exponential energy growth in adiabatically changing Hamiltonian Systems

Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time, the energy is no longer conserved, which makes the acceleration possible. One of the main problems is how to generate a sustained and robust energy growth. We show that the non-ergodicity of any chaotic Hamiltonian system must universally lead to the exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of a Geometric Brownian Motion with a positive drift, and relate it to the entropy increase.

nlin.CD↗
arXiv2014

Bifurcations of mutually coupled equations in random graphs

We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from a situation where the isolated equations are unstable, we prove that a heterogeneous interaction structure leads to the appearance of stable subspaces of solutions. Moreover, we show that, for certain classes of heterogeneous networks, increasing the strength of interaction leads to a cascade of bifurcations in which the dimension of the stable subspace of solutions increases. We explicitly determine the bifurcation scenario in terms of the graph structure.

math.DS↗
arXiv2014

Improving the Network Structure can lead to Functional Failures

In many real-world networks the ability to synchronize is a key property for its performance. Examples include power-grid, sensor, and neuron networks as well as consensus formation. Recent work on undirected networks with diffusive interaction revealed that improvements in the network connectivity such as making the network more connected and homogeneous enhances synchronization. However, real-world networks have directed and weighted connections. In such directed networks, understanding the impact of structural changes on the network performance remains a major challenge. Here, we show that improving the structure of a directed network can lead to a failure in the network function. For instance, introducing new links to reduce the minimum distance between nodes can lead to instabilities in the synchronized motion. This counter-intuitive effect only occurs in directed networks. Our results allow to identify the dynamical importance of a link and thereby have a major impact on the design and control of directed networks.

math.DS↗
arXiv2014

Basin of Attraction Determines Hysteresis in Explosive Synchronization

Spontaneous explosive emergent behavior takes place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. A central feature of such explosive transitions is a hysteretic behavior at the transition to synchronization. We unravel the underlying mechanisms and show that the dynamical origin of the hysteresis is a change of basin of attraction of the synchronization state. Our findings hold for heterogeneous networks with star graph motifs such as scale free networks, and hence reveal how microscopic network parameters such as node degree and frequency affect the global network properties and can be used for network design and control.

nlin.CD↗
arXiv2013

Towards a general theory for coupling functions allowing persistent synchronization

We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we characterise a class of coupling functions that allows for uniformly stable synchronisation in connected complex networks --- in the sense that there is an open neighbourhood of the initial conditions that is uniformly attracted towards synchronisation. Moreover, this stable synchronisation persists under perturbations to non-identical node dynamics. We illustrate the theory with numerical examples and conclude with a discussion on embedding these results in a more general framework of spectral dichotomies.

math.DS↗
arXiv2013

Dynamics of Coupled Maps in Heterogeneous Random Networks

We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic approach which enables us to describe the effective dynamics of the massively connected nodes when taking a weak interaction limit. More precisely, we show that for almost every random network and almost all initial conditions the high dimensional network governing the dynamics of the massively connected nodes can be reduced to a few macroscopic equations. Such reduction is intimately related to the ergodic properties of the expanding maps. This reduction allows one to explore the coherent properties of the network.

math.DS↗
arXiv2013

Connectivity-Driven Coherence in Complex Networks

We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the coupling function. These findings predict that in random graphs, the enhancement of coherence is proportional to the mean degree. In locally connected networks, coherence is no longer controlled by the mean degree, but rather on how the mean degree scales with the network size. In these networks, even when the coherence is absent, adding a fraction s of random connections leads to an enhancement of coherence proportional to s. Our results provide a way to control the emergent properties by the manipulation of the dynamics of the elements and the network connectivity.

nlin.AO↗
arXiv2012

Fast approximation of angle-dependent partial redistribution in moving atmospheres

Radiative transfer modeling of spectral lines including partial redistribution (PRD) effects requires the evaluation of the ratio of the emission to the absorption profile. This quantity requires a large amount of computational work if one employs the angle-dependent redistribution function, which prohibits its use in 3D radiative transfer computations with model atmospheres containing velocity fields. We aim to provide a method to compute the emission to absorption profile ratio that requires less computational work but retains the effect of angle-dependent scattering in the resulting line profiles. We present a method to compute the profile ratio that employs the angle-averaged redistribution function and wavelength transforms to and from the rest frame of the scattering particles. We compare the emergent line profiles of the \MgII\,k and \Lyalpha\ lines computed with angle-dependent PRD, angle-averaged PRD and our new method in two representative test atmospheres. The new method yields a good approximation of true angle-dependent profile ratio and the resulting emergent line profiles while keeping the computational speed and simplicity of angle-averaged PRD theory.

astro-ph.SR↗
arXiv2011

Is the solar spectrum latitude dependent? An investigation with SST/TRIPPEL

Context: In studies of the solar spectrum relative to spectra of solar twin stars, it has been found that the chemical composition of the Sun seems to depart systematically from those of the twins. One possible explanation is that the effect is due to the special aspect angle of the Sun when observed from Earth, as compared with the aspect angles of the twins. Thus, a latitude dependence of the solar spectrum, even with the heliocentric angle constant, could lead to effects of the type observed. Aim: We explore a possible variation in the strength of certain spectral lines, used in the comparisons between the composition of the Sun and the twins, at loci on the solar disk with different latitudes but at constant heliocentric angle. Methods: We use the TRIPPEL spectrograph at the Swedish 1-m Solar Telescope on La Palma to record spectra in five spectral regions in order to compare different locations on the solar disk at a heliocentric angle of 45 deg. Equivalent widths and other parameters are measured for fifteen different lines representing nine atomic species. Results: The relative variations in equivalent widths at the equator and at solar latitude 45 deg are found to be less than 1.5 % for all spectral lines studied. Translated to elemental abundances as they would be measured from a terrestrial and a hypothetical pole-on observer, the difference is estimated to be within 0.005 dex in all cases. Conclusion: It is very unlikely that latitude effects could cause the reported abundance difference between the Sun and the solar twins. The accuracy obtainable in measurements of small differences in spectral line strengths between different solar disk positions is very high.

astro-ph.SR↗
arXiv2011

Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials

We use the steepest descents method to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P_{N}(z_{1},...,z_{N}) = Z_{N}^{-1} e^{-NΣ_{i=1}^{N}V_α(z_{i})} Π_{1\leqi<j\leqN}|z_{i}-z_{j}|^{2} where V_α(z)=|z|^α, z \in C and α\in ]0,\infty[. Asymptotic analysis with error estimates are obtained. A corollary of this expansion is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal--Bargmann space.

math-ph↗
arXiv2010

Hub Synchronization in Scale-Free Networks

Heterogeneity in the degree distribution is known to suppress global synchronization in complex networks of symmetrically coupled oscillators. Scale-free networks display a great deal of heterogeneity, containing a few nodes, termed hubs, that are highly connected, while most nodes receive only a few connections. Here, we show that a group of synchronized nodes may appear in scale-free networks: hubs undergo a transition to synchronization while the other nodes remain unsynchronized. This general phenomenon can occur even in the absence of global synchronization. Our results suggest that scale-free networks may have evolved to complement various levels of synchronization.

nlin.CD↗
arXiv2009

Conformal Universality in Normal Matrix Ensembles

A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted increasing attention, however, questions on universality for these ensembles still remain under debate. We analyze the universality properties of random normal ensembles. We show that the concept of universality used for Hermitian ensembles cannot be directly extrapolated to normal ensembles. Moreover, we show that the eigenvalue statistics of random normal matrices with radially symmetric potential can be made universal under a conformal transformation.

math-ph↗
arXiv2009

Conformal Deformation from Normal to Hermitian Random Matrix Ensembles

We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We study the conformal deformations of normal random ensembles to Hermitian random ensembles and give sufficient conditions for the latter to be a Wigner ensemble.

math.PR↗