含三次耦合项的两自由度Duffing系统的共振及混沌行为

研究了一类含三次耦合项的两自由度Duffing系统的动力学行为。首先应用多尺度方法近似求解系统的一阶稳态响应。通过讨论系统的主共振和1∶1内共振,分析了三次耦合项对系统响应的影响。随后研究系统随外加周期力强度变化的分岔过程,发现除了常见的倍周期分岔通向混沌外,还存在一种直接由周期运动进入混沌的突发路径。结合对系统的最大Lyapunov指数,相轨图及Poincar啨映射的分析验证了上述结论。     

pePC-SAFT: Modeling of polyelectrolyte systems: 1. Vapor–liquid equilibria

A molecular thermodynamic model for polyelectrolyte systems—called pePC-SAFT—is proposed. The effect of charged monomers within the polyelectrolyte chain is explicitly taken into account in the reference term by replacing the hard-chain contribution of the PC-SAFT model by a charged-hard-chain contribution. Moreover, counterion condensation is accounted for to determine the effective number of charges along the polyion as well as of free counterions. The electrostatic contribution of the free counterions is described by a Debye–Hückel term.     

Hurst exponent determination for digital speckle patterns in roughness control of metallic surfaces

In this paper, we present a study of metallic surface roughness using the Hurst exponent calculated from speckle pattern. A set of samples was prepared using polishing techniques and the roughness was directly measured by means of an optical profilometer. To study the H exponent, an experiment was performed by illuminating the samples using an expanded laser beam and the surface image was captured by a CCD camera. We applied techniques of the Hurst exponent calculation, traditionally calculated from surface profile, in the digitalized speckle patterns generated by the rough surfaces. We showed a clear dependence of the H exponent on roughness of the samples. We demonstrated that this tool is very sensitive to defects in the surfaces and can be used for roughness control.     

Comparison of the Hurst and DEA exponents between the catalogue and its clusters: The California case

In this work, we analyse the long-run correlations of the seismic catalogue and of its clusters, by means of the Diffusion Entropy Analysis (DEA) and the value of the Hurst exponent. First we calculate the values for the whole catalogue, for the rate and the inter-event times and distance distribution over time, and subsequently we calculate the values for the declustered catalogue and the main clusters. We find a wide variety of behaviours, which depart from the Poisson statistics.     

Self-organized critical model for protein folding

The major factor that drives a protein toward collapse and folding is the hydrophobic effect. At the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We study the fractal behavior of 5526 protein structures present in the Brookhaven Protein Data Bank. Power laws of protein mass, volume and solvent-accessible surface area are measured independently. The present findings indicate that self-organized criticality is an alternative explanation for the protein folding. Also we note that the protein packing is an independent and constant value because the self-similar behavior of the volumes and protein masses have the same fractal dimension. This power law guarantees that a protein is a complex system. From the analyzed data, q-Gaussian distributions seem to fit well this class of systems.     

Entropy of random chaotic interval map with noise which causes coarse-graining

A random chaotic interval map with noise which causes coarse-graining induces a finite-state Markov chain. For a map topologically conjugate to a piecewise-linear map with the Lebesgue measure being ergodic, we prove that the Shannon entropy for the induced Markov chain possesses a finite limit as the noise level tends to zero. In most cases, the limit turns out to be strictly greater than the Lyapunov exponent of the original map without noise.     

Oscillatory traveling waves of polytropic filtration equation with generalized Fisher–KPP sources

The polytropic filtration equation with generalized Fisher–KPP sources is considered. We will show that the equation may have finite times oscillatory traveling waves, and try to give a complete classification by virtue of a singular exponent in the source according to the finiteness of the oscillatory times of traveling waves.     

A necessary and sufficient condition for Hardy's operator in

The equivalent conditions are proved for the Hardy inequality to be fulfilled in the norms of a Lebesgue space with variable exponent . It is assumed that the function is monotone and positive on (0, 1).