arXiv subjects

Marcus W. Beims

Publications and source records attributed to Marcus W. Beims.

At least 19 recordsLinked to original sources

arXiv2020

How relevant is the decision of containment measures against COVID-19 applied ahead of time?

The cumulative number of confirmed infected individuals by the new coronavirus outbreak until April 30th, 2020, is presented for the countries: Belgium, Brazil, United Kingdom (UK), and United States of America (USA). After an initial period with a low incidence of newly infected people, a power-law growth of the number of confirmed cases is observed. For each country, a distinct growth exponent is obtained. For Belgium, UK, and USA, countries with a large number of infected people, after the power-law growth a distinct behavior is obtained when approaching saturation. Brazil is still in the power-law regime. Such updates of the data and projections corroborate recent results regarding the power-law growth of the virus and their strong Distance Correlation between some countries around the world. Furthermore, we show that act in time is one of the most relevant non-pharmacological weapons that the health organizations have in the battle against the COVID-19, infectious disease caused by the most recently discovered coronavirus. We study how changing the social distance and the number of daily tests to identify infected asymptomatic individuals can interfere in the number of confirmed cases of COVID-19 when applied in three distinct days, namely April 16th (early), April 30th (current), and May 14th (late). Results show that containment actions are necessary to flatten the curves and should be applied as soon as possible.

physics.soc-ph↗

arXiv2020

Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies

In this work we analyse the growth of the cumulative number of confirmed infected cases by the COVID-19 until March 27th, 2020, from countries of Asia, Europe, North and South America. Our results show (i) that power-law growth is observed for all countries; (ii) by using the distance correlation, that the power-law curves between countries are statistically highly correlated, suggesting the universality of such curves around the World; and (iii) that soft quarantine strategies are inefficient to flatten the growth curves. Furthermore, we present a model and strategies which allow the government to reach the flattening of the power-law curves. We found that, besides the social distance of individuals, of well known relevance, the strategy of identifying and isolating infected individuals in a large daily rate can help to flatten the power-laws. These are essentially the strategies used in the Republic of Korea. The high correlation between the power-law curves of different countries strongly indicate that the government containment measures can be applied with success around the whole World. These measures must be scathing and applied as soon as possible.

physics.soc-ph↗

arXiv2019

Optimal ratchet current for elastically interacting particles

In this work we show that optimal ratchet currents of two interacting particles are obtained when stable periodic motion is present. By increasing the coupling strength between identical ratchet maps, it is possible to find, for some parametric combinations, current reversals, hyperchaos, multistability, and duplication of the periodic motion in the parameter space. Besides that, setting a fixed value for the current of one ratchet it is possible to induce a positive/negative/null current for the whole system in certain domains of the parameter space.

nlin.CD↗

arXiv2019

Intermittent stickiness synchronization

This work uses the statistical properties of Finite-Time Lyapunov Exponents (FTLEs) to investigate the Intermittent Stickiness Synchronization (ISS) observed in the mixed phase space of high-dimensional Hamiltonian systems. Full Stickiness Synchronization (SS) occurs when all FTLEs from a chaotic trajectory tend to zero for arbitrary long time-windows. This behavior is a consequence of the sticky motion close to regular structures which live in the high-dimensional phase space and affects all unstable directions proportionally by the same amount, generating a kind of collective motion. Partial SS occurs when at least one FTLE approaches to zero. Thus, distinct degrees of partial SS may occur, depending on the values of nonlinearity and coupling parameters, on the dimension of the phase space and on the number of positive FTLEs. Through filtering procedures used to precisely characterize the sticky motion, we are able to compute the algebraic decay exponents of the ISS and to obtain remarkable evidence about the existence of a universal behavior related to the decay of time correlations encoded in such exponents. In addition, we show that even though the probability to find full SS is small compared to partial SSs, the full SS may appear for very long times due to the slow algebraic decay of time correlations in mixed phase space. In this sense, observations of very late intermittence between chaotic motion and full SSs become rare events.

nlin.CD↗

arXiv2018

Steering multiattractors to overcome parameter inaccuracy and noise effects

Steering of attractors in multistable systems is used to increase the available parameter domains which lead to stable dynamics in nonlinear physical systems, reducing substantially undesirable effects of parametric inaccuracy and noise. The procedure proposed here uses time and/or space asymmetric perturbations to move independent multistable attractors in phase space. Applying this mechanism we increase around 230% the stable domains in Hénon's map, roughly 85% in the ratchet current described by the Langevin equation and 60% in Chua's electronic circuit. The proposal is expected to have wide applications in generic nonlinear complex system presenting multistability, so that related experiments can increase robustness under parametric inaccuracy and noise.

nlin.CD↗

arXiv2018

Optimizing thermally affected ratchet currents using periodic perturbations

The purpose of the present work is to apply a recently proposed methodology to enlarge parameter domains for which optimal ratchet currents (RCs) are obtained. This task is performed by adding a suitable periodic perturbation $F_j$ on a Ratchet mapping and the procedure consists in multiplying a particular class of generic Isoperiodic Stable Structures (ISSs), since the existence of non-zero RCs is directly related to the occurrence of stable domains. By proliferating the ISSs, it is possible to: (i) postpone thermal effects that usually increase the chaotic domain and (ii) demonstrate, by using a quantitative analysis, that the area which provides optimal RCs in the two-dimensional parameter space can be enlarged about $78\%$. In addition, for some specific parameter combinations, non-zero RCs can be induced through the birth of a new attractor, which moves away as the strength of $F_j$ increases. Clearly, the methodology applied to the ratchet mapping is an efficient way to deal with unavoidable thermal effects and its consequent undesirable dynamics, specially in experimental setups. As a second general remark, we conclude that our main findings can be extended to issues related to transport problems.

cond-mat.stat-mech↗

arXiv2018

Exploring conservative islands using correlated and uncorrelated noise

In this work, noise is used to analyze the penetration of regular islands in conservative dynamical systems. For this purpose we use the standard map choosing nonlinearity parameters for which a mixed phase space is present. The random variable which simulates noise assumes three distributions, namely equally distributed, normal or Gaussian, and power-law (obtained from the same standard map but for other parameters). To investigate the penetration process and explore distinct dynamical behaviors which may occur, we use recurrence time statistics (RTS), Lyapunov exponents (LEs) and the occupation rate of the phase space. Our main findings are as follows: (i) the standard deviations of the distributions are the most relevant quantity to induce the penetration; (ii) the penetration of islands induce power-law decays in the RTS as a consequence of enhanced trapping; (iii) for the power-law correlated noise an algebraic decay of the RTS is observed, even though sticky motion is absent; and (iv) although strong noise intensities induce an ergodic-like behavior with exponential decays of RTS, the largest Lyapunov exponent is reminiscent of the regular islands.

nlin.CD↗

arXiv2017

Controlling intermediate dynamics in a family of quadratic maps

The intermediate dynamics of composed one-dimensional maps is used to multiply attractors in phase space and create multiple independent bifurcation diagrams which can split apart. Results are shown for the composition of k-paradigmatic quadratic maps with distinct values of parameters generating k-independent bifurcation diagrams with corresponding k orbital points. For specific conditions, the basic mechanism for creating the shifted diagrams is the prohibition of period doubling bifurcations transformed in saddle-node bifurcations.

nlin.CD↗

arXiv2017

Proliferation of stability in phase and parameter spaces of nonlinear systems

In this work we show how the composition of maps allows us to multiply, enlarge and move stable domains in phase and parameter spaces of discrete nonlinear systems. Using Hénon maps with distinct parameters we generate many identical copies of isoperiodic stable structures (ISSs) in the parameter space and attractors in phase space. The equivalence of the identical ISSs is checked by the largest Lyapunov exponent analysis and the multiplied basins of attraction become riddled. Our proliferation procedure should be applicable to any two-dimensional nonlinear system.

nlin.CD↗

arXiv2015

Recurrence-time statistics in non-Hamiltonian volume preserving maps and flows

We analyze the recurrence-time statistics (RTS) in three-dimensional non-Hamiltonian volume preserving systems (VPS): an extended standard map, and a fluid model. The extended map is a standard map weakly coupled to an extra-dimension which contains a deterministic regular, mixed (regular and chaotic) or chaotic motion. The extra-dimension strongly enhances the trapping times inducing plateaus and distinct algebraic and exponential decays in the RTS plots. The combined analysis of the RTS with the classification of ordered and chaotic regimes and scaling properties, allows us to describe the intricate way trajectories penetrate the before impenetrable regular islands from the uncoupled case. Essentially the plateaus found in the RTS are related to trajectories that stay long times inside trapping tubes, not allowing recurrences, and then penetrates diffusively the islands (from the uncoupled case) by a diffusive motion along such tubes in the extra-dimension. All asymptotic exponential decays for the RTS are related to an ordered regime (quasi-regular motion) and a mixing dynamics is conjectured for the model. These results are compared to the RTS of the standard map with dissipation or noise, showing the peculiarities obtained by using three-dimensional VPS. We also analyze the RTS for a fluid model and show remarkable similarities to the RTS in the extended standard map problem.

nlin.CD↗

arXiv2014

Characterizing weak chaos in nonintegrable Hamiltonian systems: the fundamental role of stickiness and initial conditions

Weak chaos in high-dimensional conservative systems can be characterized through sticky effect induced by invariant structures on chaotic trajectories. Suitable quantities for this characterization are the higher cummulants of the finite time Lyapunov exponents (FTLEs) distribution. They gather the {\it whole} phase space relevant dynamics in {\it one} quantity and give informations about ordered and random states. This is analyzed here for discrete Hamiltonian systems with local and global couplings. It is also shown that FTLEs plotted {\it versus} initial condition (IC) and the nonlinear parameter is essential to understand the fundamental role of ICs in the dynamics of weakly chaotic Hamiltonian systems.

nlin.CD↗

arXiv2012

Conservative Generalized Bifurcation Diagrams

Bifurcation cascades in conservative systems are shown to exhibit a generalized diagram, which contains all relevant informations regarding the location of periodic orbits (resonances), their width (island size), irrational tori and the infinite higher-order resonances, showing the intricate way they are born. Contraction rates for islands sizes, along period-doubling bifurcations, are estimated to be $α_I\sim 3.9$. Results are demonstrated for the standard map and for the continuous Hénon-Heiles potential. The methods used here are very suitable to find periodic orbits in conservative systems, and to characterize the regular, mixed or chaotic dynamics as the nonlinear parameter is varied.

nlin.CD↗

arXiv2012

Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems

The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and four particles globally coupled on a discrete lattice, we show that in these models the transition from integrable motion to weak chaos emerges via chaotic stripes as the nonlinear parameter is increased. The stripes represent intervals of initial conditions which generate chaotic trajectories and increase with the nonlinear parameter of the system. In the billiard case the initial conditions are the injection angles. For higher-dimensional systems and small nonlinearities the chaotic stripes are the initial condition inside which Arnold diffusion occurs.

nlin.CD↗

arXiv2011

Generic Structures in Parameter Space and Ratchet Transport

This work reports the existence of Isoperiodic Stable Ratchet Transport Structures in the parameter spaces dissipation versus spatial asymmetry and versus phase of a ratchet model. Such structures were found [Phys. Rev. Lett. 106, 234101 (2011)] in the parameter space dissipation versus amplitude of the ratchet potential and they appear to have generic shapes and to align themselves along preferred directions in the parameter space. Since the ratchet current is usually larger inside these structures, this allows us to make general statements about the relevant parameters combination to obtain an efficient ratchet current. Results of the present work give further evidences of the suggested generic properties of the isoperiodic stable structures in the context of ratchet transport.

nlin.CD↗

arXiv2011

Ratchet transport and periodic structures in parameter space

Ratchet models are prominent candidates to describe the transport phenomenum in nature in the absence of external bias. This work analyzes the parameter space of a discrete ratchet model and gives direct connections between chaotic domains and a family of isoperiodic stable structures with the ratchet current. The isoperiodic structures appear along preferred direction in the parameter space giving a guide to follow the current, which usually increases inside the structures but is independent of the corresponding period. One of such structures has the shrimp-shaped form which is known to be an universal structure in the parameter space of dissipative systems. Currents in parameter space provide a direct measure of the momentum asymmetry of the multistable and chaotic attractors times the size of the corresponding basin of attraction. Transport structures are shown to exist in the parameter space of the Langevin equation with an external oscillating force.

nlin.CD↗

arXiv2009

Chaotic motion at the emergence of the time averaged energy decay

A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the $N$ environment oscillators and becomes chaotic in the interval $13\le N\le15$, where the system time averaged energy starts to decay. To characterize the nonlinear motion we estimate the Lyapunov exponent (LE), determine the power spectrum and the Kaplan-Yorke dimension. For much larger values of $N$ the energy of the system particle is completely transferred to the environment and the corresponding LEs decrease. Numerical evidences show the connection between the variations of the {\it amplitude} of the particles energy time oscillation with the time averaged energy decay and trapped trajectories.

nlin.CD↗

arXiv2009

Origin of chaos in soft interactions and signatures of nonergodicity

The emergence of chaotic motion is discussed for hard-point like and soft collisions between two particles in a one-dimensional box. It is known that ergodicity may be obtained in hard-point like collisions for specific mass ratios $γ=m2/m1$ of the two particles and that Lyapunov exponents are zero. However, if a Yukawa interaction between the particles is introduced, we show analytically that positive Lyapunov exponents are generated due to double collisions close to the walls. While the largest finite-time Lyapunov exponent changes smoothly with $γ$, the number of occurrences of the most probable one, extracted from the distribution of finite-time Lyapunov exponents over initial conditions, reveals details about the phase-space dynamics. In particular, the influence of the integrable and pseudointegrable dynamics without Yukawa interaction for specific mass ratios can be clearly identified and demonstrates the sensitivity of the finite-time Lyapunov exponents as a phase-space probe. Being not restricted to two-dimensional problems such as Poincaré sections, the number of occurrences of the most probable Lyapunov exponents suggests itself as a suitable tool to characterize phase-space dynamics in higher dimensions. This is shown for the problem of two interacting particles in a circular billiard.

nlin.CD↗

arXiv2009

Gauss map and Lyapunov exponents of interacting particles in a billiard

We show that the Lyapunov exponent (LE) of periodic orbits with Lebesgue measure zero from the Gauss map can be used to determine the main qualitative behavior of the LE of a Hamiltonian system. The Hamiltonian system is a one-dimensional box with two particles interacting via a Yukawa potential and does not possess Kolmogorov-Arnold-Moser (KAM) curves. In our case the Gauss map is applied to the mass ratio $γ= m_2/m_1$ between particles. Besides the main qualitative behavior, some unexpected peaks in the $γ$ dependence of the mean LE and the appearance of 'stickness' in phase space can also be understand via LE from the Gauss map. This shows a nice example of the relation between the "instability" of the continued fraction representation of a number with the stability of non-periodic curves (no KAM curves) from the physical model. Our results also confirm the intuition that pseudo-integrable systems with more complicated invariant surfaces of the flow (higher genus) should be more unstable under perturbation.

nlin.CD↗