Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.

Study of elastic wave propagation in two phase anisotropic media by numerical modeling of pseudospectral method

When there exists anisotropy in underground media elastic parameters of the observed coordinate possibly do not coincide with that of the natural coordinate. According to the theory that the density of potential energy, dissipating energy is independent of the coordinate, the relationship of elastic parameters between two coordinates is derived for two-phase anisotropic media. Then, pseudospectral method to solve wave equations of two-phase anisotropic media is derived. At last, we use this method to simulate wave propagation in two-phase anisotropic media four types of waves are observed in the snapshots, i.e., fast P wave and slow P wave, fast S wave and slow S wave. Shear wave splitting, SV wave cusps and elastic wave reflection and transmission are also observed.

Degeneracy and discreteness in cosmological model fitting

We explore the problems of degeneracy and discreteness in the standard cosmological model（ΛCDM）. We use the Observational Hubble Data（OHD） and the type Ia supernovae（SNe Ia） data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way of model differentiation when using different models to fit the observational data.

Probing the Lambda-DGP Braneworld model

We study cosmic dynamics in the context of the normal branch of the DGP braneworld model. Using current Planck data, we find the best fitting model and associated cosmological parameters in non-fiat ADGP. With the transition redshift as a basic variable and statefinder parameters, our result shows that the Universe starts its accelerated expansion phase slightly earlier than expected in ACDM cosmology. The result also alleviates the coincidence problem of the ACDM model.

Searching for α variation and cosmic acceleration in the generalized BSBM theory with tachyonic potential

Abstract We consider the BSBM （Bekenstein, Sandvik, Barrow and Magueijo） cos- mological model in the presence of tachyon potential with the aim of studying the sta- bility of the model and test it against observations. The phase space analysis shows that from fourteen critical points that represent the state of the universe, only one is stable. With a small perturbation, the universe transits from a state of unstable deceleration to stable acceleration. The stability analysis combined with the best fitting process imposes constraints on the cosmological parameters that are in agreement with ob- servation. In the BSBM theory, the variation of fundamental constants is driven from variation of a scalar field. The tachyonic scalar field, responsible for both variation of fundamental constants and universal acceleration, is reconstructed.

Light curve inversion of asteroid(585)Bilkis with Lommel-Seeliger ellipsoid method

The basic physical parameters of asteroids, such as spin parameters, shape and scattering parameters, can provide us with information on the formation and evolution of both the asteroids themselves and the entire solar system. In a majority of asteroids, the disk-integrated photometry measurement constitutes the primary source of the above knowledge. In the present paper, newly observed photometric data and existing data on（585） Bilkis are analyzed based on a Lommel-Seeliger ellipsoid model. With a Markov chain Monte Carlo（MCMC） method, we have determined the spin parameters（period, pole orientation）and shape（b/a, c/a） of（585） Bilkis and their uncertainties. As a result, we obtained a rotational period of 8.5738209 h with an uncertainty of 9×10^-7h, and derived a pole of（136.46°, 29.0°） in the ecliptic frame of J2000.0 with uncertainties of 0.67°and 1.1°in longitude and latitude respectively. We also derived triaxial ratios b/a and c/a of（585） Bilkis as 0.736 and 0.70 with uncertainties of 0.003 and 0.03 respectively.

The effects of parametrization of the dark energy equation of state

We investigate in detail the influence of parametrizations of the dark energy equation of state on reconstructing dark energy geometrical parameters, such as the deceleration parameter q（z） and Om diagnostic. We use a type Ia supernova sample, baryon acoustic oscillation data, cosmic microwave background information along with twelve observational Hubble data points to constrain cosmological parameters. With the joint analysis of these current datasets, we find that the parametrizations of w（z） have little influence on the reconstruction result of q（z） and Ore. The same is true for the transition （cosmic deceleration to acceleration） redshift zt, for which we find that for different parametrizations of w（z）, the best fitted values of zt are very close to each other （about 0.65）. All of our results are in good agreement with the ACDM model. Furthermore, using the combination of datasets, we do not find any signal of decreasing cosmic acceleration as suggested in some recent papers. The results suggest that the influence of the prior w（z） is not as severe as one may anticipate, and thus we can, to some extent, safely use a reasonable parametrization of w（z） to reconstruct some other dark energy parameters （e.g. q（z）, Ore） with a combination of datasets.

Chaplygin gas of Tachyon Nature Imposed by Noether Symmetry and constrained via H(z)data

An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is used when varying the action so the connection is given by a more generic form. Both the self-interaction potential and the non-minimally coupling function are obtained by constraining the system to present invariability under global point transformation of the fields （Noether Symmetry）. The only possible solution is shown to be that of minimal coupling and constant potential （Chaplygin gas）. The behavior of the dynamical properties of the system is compared to recent observational data, which infers that the tachyon field must indeed be dynamical.