Central Schemes for Porous Media Flows

We are concerned with central differencing schemes for solving scalar hyperbolic conservation laws arising in the simulation of multiphase flows in heterogeneous porous media. We compare the Kurganov-Tadmor, 2000 semi-discrete central scheme with the Nessyahu-Tadmor, 1990 central scheme. The KT scheme uses more precise information about the local speeds of propagation together with integration over nonuniform control volumes, which contain the Riemann fans. These methods can accurately resolve sharp fronts in the fluid saturations without introducing spurious oscillations or excessive numerical diffusion. We first discuss the coupling of these methods with velocity fields approximated by mixed finite elements. Then, numerical simulations are presented for two-phase, two-dimensional flow problems in multi-scale heterogeneous petroleum reservoirs. We find the KT scheme to be considerably less diffusive, particularly in the presence of high permeability flow channels, which lead to strong restrictions on the time step selection; however, the KT scheme may produce incorrect boundary behavior

Parity doublers in chiral potential quark models

The effect of spontaneous breaking of chiral symmetry over the spectrum of highly excited hadrons is addressed in the framework of a microscopic chiral potential quark model (Generalised Nambu-Jona-Lasinio model) with a vectorial instantaneous quark kernel of a generic form. A heavy-light quark-antiquark bound system is considered, as an example, and the Lorentz nature of the effective light-quark potential is identified to be a pure Lorentz-scalar, for low-lying states in the spectrum, and to become a pure spatial Lorentz vector, for highly excited states. Consequently, the splitting between the partners in chiral doublets is demonstrated to decrease fast in the upper part of the spectrum so that neighboring states of an opposite parity become almost degenerate. A detailed microscopic picture of such a "chiral symmetry restoration" in the spectrum of highly excited hadrons is drawn and the corresponding scale of restoration is estimated.Comment: LaTeX2e, 4 pages, uses aipproc class, Talk given by A.Nefediev at the conference "Quark Confinement and the Hadron Spectrum VII", 2-7 September 2006, Acores, Portugal, to appear in Proceeding

Confinement and parity doubling in heavy-light mesons

In this paper, we study the chiral symmetry restoration in the hadronic spectrum in the framework of generalised Nambu-Jona-Lasinio quark models with instantaneous confining quark kernels. We investigate a heavy-light quarkonium and derive its bound-state equation in the form of a Schroedingerlike equation and, after the exact inverse Foldy-Wouthuysen transformation, in the form of a Diraclike quation. We discuss the Lorentz nature of confinement for such a system and demonstrate explicitly the effective chiral symmetry restoration for highly excited states in the mesonic spectrum. We give an estimate for the scale of this restoration.Comment: RevTeX4, 21 pages, 6 Postscript figures, uses epsfig.sty, to appear in Phys.Rev.

Mutual information in random Boolean models of regulatory networks

The amount of mutual information contained in time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell, the average of the mutual information over all pairs is a global measure of how well the system can coordinate its internal dynamics. We study this average pairwise mutual information in random Boolean networks (RBNs) as a function of the distribution of Boolean rules implemented at each element, assuming that the links in the network are randomly placed. Efficient numerical methods for calculating show that as the number of network nodes N approaches infinity, the quantity N exhibits a discontinuity at parameter values corresponding to critical RBNs. For finite systems it peaks near the critical value, but slightly in the disordered regime for typical parameter variations. The source of high values of N is the indirect correlations between pairs of elements from different long chains with a common starting point. The contribution from pairs that are directly linked approaches zero for critical networks and peaks deep in the disordered regime.Comment: 11 pages, 6 figures; Minor revisions for clarity and figure format, one reference adde