Regular Series


Vol. 41 (2010), No. 9, pp. 1999 – 2182


New Classes of Stable Exact Solutions for a Nonlinear Rotational DNA Model

abstract

We consider a system of two coupled nonlinear partial differential equations for describing the rotational motions of bases in both polynucleotide chains of the DNA molecule. The model was proposed by L.V. Yakushevich and it is well known that the model supports, for some operating regimes, traveling wave solutions as kink–(antikink) soliton solutions. We have tried to make some progress by performing an analysis of the classical symmetries of this model. Our study shows that the model does not have enough symmetries as to reduce the equations to ordinary differential equations. Nevertheless, the known symmetries have been useful for finding several classes of exact solutions, by imposing adequate Ansätze. Some of them are kink–(antikink) like solutions, but other ones are not traveling wave solutions. For some of the new solutions, we have carried out a qualitative study and analyzed some stability properties. We think that they could be significant for the description of the DNA molecule as well as for some other applications.


The Stability of Thin-shell Wormholes With a Phantom-like Equation of State

abstract

This paper discusses the stability to linearized radial perturbations of spherically symmetric thin-shell wormholes with a “phantom-like” equation of state for the exotic matter at the throat: \(\mathcal {P}= \omega \sigma \), \(\omega \lt 0\), where \(\sigma \) is the energy-density of the shell and \(\mathcal {P}\) the lateral pressure. This equation is analogous to the generalized Chaplygin-gas equation of state used by E.F. Eiroa. The analysis, which differs from Eiroa’s in its basic approach, is carried out for wormholes constructed from the following spacetimes: Schwarzschild, de Sitter and anti de Sitter, Reissner–Nordström, and regular charged black-hole spacetimes, followed by black holes in dilaton and generalized dilaton-axion gravity.


New Horizons in Gravity: The Trace Anomaly, Dark Energy and Condensate Stars

abstract

General Relativity receives quantum corrections relevant at macroscopic distance scales and near event horizons. These arise from the conformal scalar degrees of freedom in the extended effective field theory of gravity generated by the trace anomaly of massless quantum fields in curved space. The origin of these conformal scalar degrees of freedom as massless poles in two-particle intermediate states of anomalous amplitudes in flat space is exposed. These are non-local quantum pair correlated states, not present in the classical theory. At event horizons the conformal anomaly scalar degrees of freedom can have macroscopically large effects on the geometry, potentially removing the classical event horizon of black hole and cosmological spacetimes, replacing them with a quantum boundary layer where the effective value of the gravitational vacuum energy density can change. In the effective theory, the cosmological term becomes a dynamical condensate, whose value depends upon boundary conditions near the horizon. In the conformal phase where the anomaly induced fluctuations dominate, and the condensate dissolves, the effective cosmological “constant” is a running coupling which has an infrared stable fixed point at zero. By taking a positive value in the interior of a fully collapsed star, the effective cosmological term removes any singularity, replacing it with a smooth dark energy interior. The resulting gravitational condensate star configuration resolves all black hole paradoxes, and provides a testable alternative to black holes as the final state of complete gravitational collapse. The observed dark energy of our universe likewise may be a macroscopic finite size effect whose value depends not on microphysics but on the cosmological horizon scale. The physical arguments and detailed calculations involving the trace anomaly effective action, auxiliary scalar fields and stress tensor in various situations and backgrounds supporting this hypothesis are reviewed. Originally delivered as a series of lectures at the Kraków School, the paper is pedagogical in style, and wide ranging in scope, collecting and presenting a broad spectrum of results on black holes, the trace anomaly, and quantum effects in cosmology.


Uncovering the Density of Matter from Multiplicity Distribution

abstract

Multiplicity distributions in the form of superposition of Poisson distributions which are observed in multiparticle production are interpreted as reflection of a two-step nature of this process: the creation and evolution of the strongly interacting fluid, followed by its uncorrelated decay into observed hadrons. A method to uncover the density of the fluid from the observed multiplicity distribution is described.


Nuclear Symmetry Energy in Relativistic Hadronic Models

abstract

The density dependence of the symmetry energy and the correlation between parameters of the symmetry energy and the neutron skin thickness in the nucleus \(^{208}\)Pb are investigated in relativistic hadronic models. The dependency of the symmetry energy on density is linear around saturation density. The existence of correlation between the neutron skin thickness in the nucleus \(^{208}\)Pb and the value and the slope of the nuclear symmetry energy at saturation density is found to be dependent on the model used.


top

ver. 2024.03.17 • we use cookies and MathJax