Korteveg-de Vries solitons in a cold quark-gluon plasma

The relativistic heavy ion program developed at RHIC and now at LHC motivated a deeper study of the properties of the quark-gluon plasma (QGP) and, in particular, the study of perturbations in this kind of plasma. We are interested on the time evolution of perturbations in the baryon and energy densities. If a localized pulse in baryon density could propagate throughout the QGP for long distances preserving its shape and without loosing localization, this could have interesting consequences for relativistic heavy ion physics and for astrophysics. A mathematical way to prove that this can happen is to derive (under certain conditions) from the hydrodynamical equations of the QGP a Korteveg-de Vries (KdV) equation. The solution of this equation describes the propagation of a KdV soliton. The derivation of the KdV equation depends crucially on the equation of state (EOS) of the QGP. The use of the simple MIT bag model EOS does not lead to KdV solitons. Recently we have developed an EOS for the QGP which includes both perturbative and nonperturbative corrections to the MIT one and is still simple enough to allow for analytical manipulations. With this EOS we were able to derive a KdV equation for the cold QGP.

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

We study trapping and propagation of a matter-wave soliton through the interface between uniform medium and a nonlinear optical lattice. Different regimes for transmission of a broad and a narrow solitons are investigated. Reflections and transmissions of solitons are predicted as a function of the lattice phase. The existence of a threshold in the amplitude of the nonlinear optical lattice, separating the transmission and reflection regimes, is verified. The localized nonlinear surface state, corresponding to the soliton trapped by the interface, is found. Variational approach predictions are confirmed by numerical simulations for the original Gross-Pitaevskii equation with nonlinear periodic potentials.

Transition to chaotic scattering: Signatures in the differential cross section

We show that bifurcations in chaotic scattering manifest themselves through the appearance of an infinitely fine-scale structure of singularities in the cross section. These ""rainbow singularities"" are created in a cascade, which is closely related to the bifurcation cascade undergone by the set of trapped orbits (the chaotic saddle). This cascade provides a signature in the differential cross section of the complex pattern of bifurcations of orbits underlying the transition to chaotic scattering. We show that there is a power law with a universal coefficient governing the sequence of births of rainbow singularities and we verify this prediction by numerical simulations.

Nonlinear waves in a quark gluon plasma

We study the propagation of perturbations in the quark gluon plasma. This subject has been addressed in other works and in most of the theoretical descriptions of this phenomenon the hydrodynamic equations have been linearized for simplicity. We propose an alternative approach, also based on hydrodynamics but taking into account the nonlinear terms of the equations. We show that these terms may lead to localized waves or even solitons. We use a simple equation of state for the QGP and expand the hydrodynamic equations around equilibrium configurations. The resulting differential equations describe the propagation of perturbations in the energy density. We solve them numerically and find that localized perturbations can propagate for long distances in the plasma. Under certain conditions our solutions mimic the propagation of Korteweg-de Vries solitons.

A vaccination game based on public health actions and personal decisions

Susceptible-infective-removed (SIR) models are commonly used for representing the spread of contagious diseases. A SIR model can be described in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. Here, this framework is employed for investigating the consequences of applying vaccine against the propagation of a contagious infection, by considering vaccination as a game, in the sense of game theory. In this game, the players are the government and the susceptible newborns. In order to maximize their own payoffs, the government attempts to reduce the costs for combating the epidemic, and the newborns may be vaccinated only when infective individuals are found in their neighborhoods and/or the government promotes an immunization program. As a consequence of these strategies supported by cost-benefit analysis and perceived risk, numerical simulations show that the disease is not fully eliminated and the government implements quasi-periodic vaccination campaigns. (C) 2011 Elsevier B.V. All rights reserved.

Relativistic dispersion effects on SS433 jets

We here investigate the dispersion properties of radiation in the SS433 relativistic jets. We assume that the jet is composed of cold electron-proton plasma immersed in a predominantly parallel magnetic field to the jet axis. We find that for the mildly relativistic source SS433 (for which similar or equal to 79 degrees), the bulk velocity is too small (v similar or equal to 0.26c) to produce significant changes in the dispersion properties of the medium. Nonetheless, in the rarefied outer regions of the jets, where radio emission dominates, even a weak magnetic field has some influence on the dispersion properties and there appear two different electromagnetic branches that are slightly sensitive to the bulk relativistic motion. In the inner, X-ray region, the magnetic field is much stronger, but in this region the high electron density preserves the isotropic character of the local plasma and no branch separation occurs. In the region of the jet where the IR and optical emission dominates, the cold plasma may be also considered isotropic, i.e., neither the magnetic field nor the bulk velocity is able to affect the propagation of the radiation. Finally, we find that the Doppler line displacement in SS433 is affected by plasma dispersion only in a narrow frequency range in the far IR. As a consequence, although the shift (z) modulation due to precession of the SS433 jets is well described by previous work, it has to be corrected by plasma dispersion effects in the far-IR range.

Connexin-mediated communication controls cell proliferation and is essential in retinal histogenesis

Connexin (Cx) channels and hemichannels are involved in essential processes during nervous system development such as apoptosis, propagation of spontaneous activity and interkinetic nuclear movement. In the first part of this study, we extensively characterized Cx gene and protein expression during retinal histogenesis. We observed distinct spatio-temporal patterns among Studied Cx and an overriding, ubiquitous presence of Cx45 in progenitor cells. The role of Cx-mediated communication was assessed by using broad-spectrum (carbenoxotone, CBX) and Cx36/Cx50 channel-specific (quinine) blockers. In vivo application of CBX, but not quinine, caused remarkable reduction in retinal thickness, suggesting changes in cell proliferation/apoptosis ratio. Indeed, we observed a decreased number of mitotic cells in CBX-injected retinas, with no significant changes in the expression of PCNA, a marker for cells in proliferative state. Taken together, Our results pointed a pivotal role of Cx45 in the developing retina. Moreover, this study revealed that Cx-mediated Communication is essential in retinal histogenesis, particularly in the control of cell proliferation. (C) 2009 ISDN. Published by Elsevier Ltd. All rights reserved.

3-manifolds in Euclidean space from a contact viewpoint

We study the geometry of 3-manifolds generically embedded in R(n) by means of the analysis of the singularities of the distance-squared and height functions on them. We describe the local structure of the discriminant (associated to the distribution of asymptotic directions), the ridges and the flat ridges.

BREAKING WAVES IN AN IDEAL QUARK GLUON PLASMA

We study the propagation of perturbations in the energy density in a quark gluon plasma. Expanding the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations we obtain a nonlinear differential equation called the breaking wave equation. We solve it numerically and follow the time-evolution of initially localized pulses. We find that, quite unexpectedly, these pulses live for a very long time (compared to the reaction time-scales) before breaking. In practice, they mimick the Korteweg-de Vries solitons. Their existence may have some observable consequences.

Sound waves and solitons in hot and dense nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ""radiation"". Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. (C) 2009 Elseiver. B.V. All rights reserved.

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.

1,4-Diamino-2-butanone, a wide-spectrum microbicide, yields reactive species by metal-catalyzed oxidation

The alpha-aminoketone 1,4-diamino-2-butanone (DAB), a putrescine analogue, is highly toxic to various microorganisms, including Trypanosoma cruzi. However, little is known about the molecular mechanisms underlying DAB`s cytotoxic properties. We report here that DAB (pK(a) 7.5 and 9.5) undergoes aerobic oxidation in phosphate buffer, pH 7.4, at 37 degrees C, catalyzed by Fe(II) and Cu(II) ions yielding NH(4)(+) ion, H(2)O(2), and 4-amino-2-oxobutanal (oxoDAB). OxoDAB, like methylglyoxal and other alpha-oxoaldehydes, is expected to cause protein aggregation and nucleobase lesions. Propagation of DAB oxidation by superoxide radical was confirmed by the inhibitory effect of added SOD (50 U ml(-1)) and stimulatory effect of xanthine/xanthine oxidase, a source of superoxide radical. EPR spin trapping studies with 5,5-dimethyl-1-pyrroline-1-oxide (DMPO) revealed an adduct attributable to DMPO-HO(center dot), and those with alpha-(4-pyridyl-1-oxide)-N-tert-butylnitrone or 3,5-dibromo-4-nitrosobenzenesulfonic acid, a six-line adduct assignable to a DAB(center dot) resonant enoyl radical adduct. Added horse spleen ferritin (HoSF) and bovine apo-transferrin underwent oxidative changes in tryptophan residues in the presence of 1.0-10 mM DAB. Iron release from HoSF was observed as well. Assays performed with fluorescein-encapsulated liposomes of cardiolipin and phosphatidylcholine (20:80) incubated with DAB resulted in extensive lipid peroxidation and consequent vesicle permeabilization. DAB (0-10 mM) administration to cultured LLC-MK2 epithelial cells caused a decline in cell viability, which was inhibited by preaddition of either catalase (4.5 mu M) or aminoguanidine (25 mM). Our findings support the hypothesis that DAB toxicity to several pathogenic microorganisms previously described may involve not only reported inhibition of polyamine metabolism but also DAB pro-oxidant activity. (C) 2011 Elsevier Inc. All rights reserved.