Incompatibility networks as models of scale-free small-world graphs

We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory.     

How mobile NMR can help with the conservation of paintings

The conservation of paintings is fundamental to ensure that future generations will have access to the ideas of the grand masters who created these art pieces. Many factors, such as humidity, temperature, light, and pollutants, pose a risk to the conservation of paintings. To help with painting conservation, it is essential to be able to noninvasively study how these factors affect paintings and to develop methods to investigate their effects on painting degradation. Hence, the use of mobile nuclear magnetic resonance (NMR) as a method of investigation of paintings is gaining increased attention in the world of Heritage Science. In this mini-review, we discuss how this method was used to better understand the stratigraphy of paintings and the effect different factors have on the painting integrity, to analyze the different cleaning techniques suitable for painting conservation, and to show how mobile NMR can be used to identify forgeries. It is also important to keep in mind its limitations and build upon this information to optimize it to extend its applicability to the study of paintings and other precious objects of cultural heritage.     

A filter‐based,mass‐conserving lattice Boltzmann method for immiscible multiphase flows

Some issues of He–Chen–Zhang lattice Boltzmann equation (LBE) method (referred as HCZ model) (J. Comput. Physics 1999; 152 :642–663) for immiscible multiphase flows with large density ratio are assessed in this paper. An extended HCZ model with a filter technique and mass correction procedure is proposed based on HCZ's LBE multiphase model. The original HCZ model is capable of maintaining a thin interface but is prone to generating unphysical oscillations in surface tension and index function at moderate values of density ratio. With a filtering technique, the monotonic variation of the index function across the interface is maintained with larger density ratio. Kim's surface tension formulation for diffuse–interface method (J. Comput. Physics 2005; 204 :784–804) is then used to remove unphysical oscillation in the surface tension. Furthermore, as the density ratio increases, the effect of velocity divergence term neglected in the original HCZ model causes significant unphysical mass sources near the interface. By keeping the velocity divergence term, the unphysical mass sources near the interface can be removed with large density ratio. The long‐time accumulation of the modeling and/or numerical errors in the HCZ model also results in the error of mass conservation of each dispersed phase. A mass correction procedure is devised to improve the performance of the method in this regard. For flows over a stationary and a rising bubble, and capillary waves with density ratio up to 100, the present approach yields solutions with interface thickness of about five to six lattices and no long‐time diffusion, significantly advancing the performance of the LBE method for multiphase flow simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

On the discontinuous Galerkin computation of N‐waves focusing

Sonic boom focusing phenomenon can be predicted using the solution to the nonlinear Tricomi equation which is a hybrid (hyperbolic‐elliptic) second‐order partial differential equation. In this paper, the hyperbolic conservation law form is derived, which is valid in the entire domain. In this manner, the presence of two regions where the equation behaves differently (hyperbolic in the upper and elliptic in the lower half‐plane) is avoided. On the upper boundary, a new mixed boundary condition for the acoustic pressure is employed. The discretization is carried out using a discontinuous Galerkin (DG) method combined with a Runge–Kutta total‐variation diminishing scheme. The results show the accuracy of DG methods to solve problems involving sharp gradients and discontinuities. Comparisons with analytical results for the linear case, and other numerical results using classical explicit and compact finite difference schemes and weighted essentially non‐oscillatory schemes are included. Copyright © 2010 John Wiley & Sons, Ltd.     

SHORT COMMUNICATION SECTION Some Geometric Flows on Kahler Manifolds

We define a kind of KdV （Korteweg-de Vries） geometric flow for maps from a real line or a circle into a Kahler manifold （N,J,h） with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By using the geometric analysis, the existence of the Cauchy problems of the KdV geometric flows will be investigated in this note.     

Does the Electrical Conductivity of W/O Microemulsions Follow a Percolative Behaviour?

Abstract

The conductivities of different microemulsions prepared with triethanolamine were measured as a function of concentration for several temperatures. The goal of this work has been to test the degree of accuracy of the application of the scaling laws used in the literature. Our conclusion is that there is no general validity even though the abrupt variation of conductivity with concentration may be seen as a percolative phenomenon.     

Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method

This paper is devoted to the study of the oscillatory behavior of solutions of nonlinear hyperbolic equations with functional arguments by using integral averaging method and a generalized Riccati technique. First, we establish oscillation results for nonlinear hyperbolic equations by applying oscillation criteria for Riccati inequality. Secondly, we present interval oscillation results for nonlinear hyperbolic equations. These results improve and extend oscillation results of Cui and Xu [1].     

Volatility return intervals analysis of the Japanese market

We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval τ and its mean 〈τ〉. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.     

Diffusive-Dispersive Traveling Waves and Kinetic Relations: Part I: Nonconvex Hyperbolic Conservation Laws

Motivated by the theory of phase transition dynamics, we consider one-dimensional, nonlinear hyperbolic conservation laws with nonconvex flux-function containing vanishing nonlinear diffusive-dispersive terms. Searching for traveling wave solutions, we establish general results of existence, uniqueness, monotonicity, and asymptotic behavior. In particular, we investigate the properties of the traveling waves in the limits of dominant diffusion, dominant dispersion, and asymptotically small or large shock strength. As the diffusion and dispersion parameters tend to 0, the traveling waves converge to shock wave solutions of the conservation law, which either satisfy the classical Oleinik entropy criterion or are nonclassical undercompressive shocks violating it.