Linear analysis of degree correlations in complex networks

Many real-world networks such as the protein–protein interaction networks and metabolic networks often display nontrivial correlations between degrees of vertices connected by edges. Here, we analyse the statistical methods used usually to describe the degree correlation in the networks, and analytically give linear relation in the degree correlation. It provides a simple and interesting perspective on the analysis of the degree correlation in networks, which is usefully complementary to the existing methods for degree correlation in networks. Especially, the slope in the linear relation corresponds exactly to the degree correlation coefficient in networks, meaning that it can not only characterize the level of degree correlation in networks, but also reflects the speed that the average nearest neighbours’ degree varies with the vertex degree. Finally, we applied our results to several real-world networks, validating the conclusions of the linear analysis of degree correlation. We hope that the work in this paper can be helpful for further understanding the degree correlation in complex networks.     

Generation of Bianchi type V cosmological models with varying Λ-term

Bianchi type V perfect fluid cosmological models are investigated with cosmological term varying with time. Using a generation technique (Camci et al., 2001), it is shown that Einsteins field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. The cosmological constant is found to be a decreasing function of time, which is supported by results from recent type Ia supernovae observations. Some physical aspects of the models are also discussed.     

Periodic Solutions for Completely Resonant Nonlinear Wave Equations with Dirichlet Boundary Conditions

We consider the nonlinear string equation with Dirichlet boundary conditions u_tt–u_xx=(u), with (u)=u³+O(u⁵) odd and analytic, 0, and we construct small amplitude periodic solutions with frequency for a large Lebesgue measure set of close to 1. This extends previous results where only a zero-measure set of frequencies could be treated (the ones for which no small divisors appear). The proof is based on combining the Lyapunov-Schmidt decomposition, which leads to two separate sets of equations dealing with the resonant and non-resonant Fourier components, respectively the Q and the P equations, with resummation techniques of divergent powers series, allowing us to control the small divisors problem. The main difficulty with respect to the nonlinear wave equations u_tt–u_xx+Mu=(u), M0, is that not only the P equation but also the Q equation is infinite-dimensional.     

Characterization of electrical charge separation at the interface of two aqueous solutions in the presence of concentration gradients and cation/anion mobility ratio asymmetry

Physical consequences of ionic diffusion processes play a major role on the outcome of electrophysiology experiments due to both their contribution to the ionic transmembrane transport and phenomena taking place at the measuring instruments interface. As most of the time heterogenities in biological media with respect to ionic diffusion constants are disregarded, we intended to look upon the general case of ionic diffusion at the interface of two liquids on which gradients of these diffusion constants no longer can be neglected. We developed a theoretical model for the diffusion potential which emerges at an aqueous interface under gradients of concentration and diffusion constants. The experimental validation of our model was achieved through potential difference measurements of the diffusion potential between two solutions containing sodium chloride (NaCl) and glycerine solutions of various concentrations. Within the studied domain of the electrical charge mobility ratio, we noticed that experimental results are in agreement with the theoretically inferred diffusion potential values. This demonstrates that the resulting relationship for the diffusion potential inferred from our model could be applied for other cases, as well. When the ionic solutions contains an indefinite quantity of glycerine or an unknown substance able to modify diffusion constants of sodium and chloride, it was shown that through measurements of the diffusion potential one can infer the unknown concentration of glycerine and the modified ionic mobility ratio. This, in turn, builds up the foundation for a novel yet simple and efficient analitycal sensing device for quantitative determination in the field.     

Resonantly enhanced off-specular X-ray scattering from polymer/polymer interfaces<Superscript>⋆</Superscript>

We have used measurements of the absolute intensity of diffuse X-ray scattering to extract the interfacial tension of a buried polymer/polymer interface. Diffuse scattering was excited by an X-ray standing wave whose phase was adjusted to have a high intensity at the polymer/polymer interface and simultaneously a node at the polymer/air interface. This method permits the capillary-wave-induced roughness of the interface, and hence the interfacial tension, to be measured independently of the polymer/polymer interdiffusion.     

Influence of the Grain Boundaries on the Heat Transfer in Laser Ceramics

Grain boundaries play a key role in determining several key properties of polycrystalline laser ceramics. Heat transfer measurements at low temperature constitute a good tool to probe grain boundaries. We review the results of heat transfer measurements in polycrystalline Y₃Al₅O₁₂ garnets as well as Y₂O₃ and Lu₂O₃ sesquioxide materials obtained by self-energy-driven sintering of nano-particles. The average phonon mean free path in Y₃Al₅O₁₂ was found to be significantly larger than the average grain size and to scale with temperature as T ⁻² at low temperature. Existing models describing the interaction between phonons and grain boundaries are reviewed. Correct temperature dependence of the mean free path and order of magnitude of scattering rates were found by assuming the existence of a grain boundary layer having acoustic properties different from those of the bulk. A different temperature dependence of phonon mean free path was found for the sesquioxides and was ascribed to the stronger elastic anisotropy of these materials. The thermal resistance associated to the grain boundaries of laser ceramics was found to be lower than in other dense polycrystalline ceramic materials reported in the literature.