Nonabelian Faddeev-Niemi Decomposition of the SU(3) Yang-Mills Theory

Faddeev and Niemi (FN) have introduced an abelian gauge theory which simulates dynamical abelianization in Yang-Mills theory (YM). It contains both YM instantons and Wu-Yang monopoles and appears to be able to describe the confining phase. Motivated by the meson degeneracy problem in dynamical abelianization models, in this note we present a generalization of the FN theory. We first generalize the Cho connection to dynamical symmetry breaking pattern SU(N+1) -> U(N), and subsequently try to complete the Faddeev-Niemi decomposition by keeping the missing degrees of freedom. While it is not possible to write an on-shell complete FN decomposition, in the case of SU(3) theory of physical interest we find an off-shell complete decomposition for SU(3) -> U(2) which amounts to partial gauge fixing, generalizing naturally the result found by Faddeev and Niemi for the abelian scenario SU(N+1) -> U(1)^N. We discuss general topological aspects of these breakings, demonstrating for example that the FN knot solitons never exist when the unbroken gauge symmetry is nonabelian, and recovering the usual no-go theorems for colored dyons.Comment: Latex 30 page

Functional co-monotony of processes with applications to peacocks and barrier options

We show that several general classes of stochastic processes satisfy a functional co-monotony principle, including processes with independent increments, Brownian diffusions, Liouville processes. As a first application, we recover some recent results about peacock processes obtained by Hirsch et al. which were themselves motivated by a former work of Carr et al. about the sensitivity of Asian Call options with respect to their volatility and residual maturity (seniority). We also derive semi-universal bounds for various barrier options.Comment: 27 page

q-Deformed quaternions and su(2) instantons

We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion language we have formulated and found solutions of the (anti)selfduality equation [instantons and multi-instantons] of a would-be deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on some noncommuting parameters, indicating that the moduli space of a complete theory should be a noncommutative manifold. We summarize these results and add an explicit comparison between the two SO_q(4)-covariant differential calculi on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi- (resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially coincide.Comment: Latex file, 18 page

A Kolmogorov theorem for nearly-integrable Poisson systems with asymptotically decaying time-dependent perturbation

The aim of this paper is to prove the Kolmogorov theorem of persistence of Diophantine flows for nearly-integrable Poisson systems associated to a real analytic Hamiltonian with aperiodic time dependence, provided that the perturbation is asymptotically vanishing. The paper is an extension of an analogous result by the same authors for canonical Hamiltonian systems; the flexibility of the Lie series method developed by A. Giorgilli et al., is profitably used in the present generalisation.Comment: 10 page

Formation and Propagation of Matter Wave Soliton Trains

Attraction between atoms in a Bose-Einstein-Condensate renders the condensate unstable to collapse. Confinement in an atom trap, however, can stabilize the condensate for a limited number of atoms, as was observed with 7Li, but beyond this number, the condensate collapses. Attractive condensates constrained to one-dimensional motion are predicted to form stable solitons for which the attractive interactions exactly compensate for the wave packet dispersion. Here we report the formation or bright solitons of 7Li atoms created in a quasi-1D optical trap. The solitons are created from a stable Bose-Einstein condensate by magnetically tuning the interactions from repulsive to attractive. We observe a soliton train, containing many solitons. The solitons are set in motion by offsetting the optical potential and are observed to propagate in the potential for many oscillatory cycles without spreading. Repulsive interactions between neighboring solitons are inferred from their motion

Development and Characterization of Curcumin-Silver Nanoparticles as a Promising Formulation to Test on Human Pterygium-Derived Keratinocytes

Pterygium is a progressive disease of the human eye arising from sub-conjunctival tissue and extending onto the cornea. Due to its invasive growth, pterygium can reach the pupil compromising visual function. Currently available medical treatments have limited success in suppressing efficiently the disease. Previous studies have demonstrated that curcumin, polyphenol isolated from the rhizome of Curcuma longa, induces apoptosis of human pterygium fibroblasts in a dose- and time-dependent manner showing promising activity in the treatment of this ophthalmic disease. However, this molecule is not very soluble in water in either neutral or acidic pH and is only slightly more soluble in alkaline conditions, while its dissolving in organic solvents drastically reduces its potential use for biomedical applications. A nanoformulation of curcumin stabilized silver nanoparticles (Cur-AgNPs) seems an effective strategy to increase the bioavailability of curcumin without inducing toxic effects. In fact, silver nitrates have been used safely for the treatment of many ophthalmic conditions and diseases for a long time and the concentration of AgNPs in this formulation is quite low. The synthesis of this new compound was achieved through a modified Bettini's method adapted to improve the quality of the product intended for human use. Indeed, the pH of the reaction was changed to 9, the temperature of the reaction was increased from 90 °C to 100 °C and after the synthesis the Cur-AgNPs were dispersed in Borax buffer using a dialysis step to improve the biocompatibility of the formulation. This new compound will be able to deliver both components (curcumin and silver) at the same time to the affected tissue, representing an alternative and a more sophisticated strategy for the treatment of human pterygium. Further in vitro and in vivo assays will be required to validate this formulation

Fluctuations of particle ratios as a freeze-out probe

We explain how event-by-event fluctuations of particle ratios can constrain and falsify the statistical model of particle production in heavy ion collisions, using $K/\pi$ fluctuations as an example. We define an observable capable of determining which statistical model, if any, governs freeze-out in ultrarelativistic heavy ion collisions. We calculate this observable for $K/\pi$ fluctuations, and show that it should be the same for RHIC and LHC energies, as well as independent of centrality, if the Grand-Canonical statistical model is an appropriate description and chemical equilibrium applies. We describe what happens in case of deviations from this scenario, such as light quark chemical non-equilibrium, strange quark over-saturation and local conservation (canonical ensemble) for strange quarks. We also introduce a similar observable capable, together with the published $K^*/K$ measurement, of ascertaining if an interacting hadron gas phase governs the system between thermal and chemical freeze-out, and of ascertaining its duration and impact on hadronic chemistryComment: Proceedings for talk given at Strangeness 2007, Levoca, Slovaki

Non-linear evolution in CCFM: The interplay between coherence and saturation

We solve the CCFM equation numerically in the presence of a boundary condition which effectively incorporates the non-linear dynamics. We retain the full dependence of the unintegrated gluon distribution on the coherence scale, and extract the saturation momentum. The resulting saturation scale is a function of both rapidity and the coherence momentum. In Deep Inelastic Scattering this will lead to a dependence of the saturation scale on the photon virtuality in addition to the usual x-Bjorken dependence. At asymptotic energies the interplay between the perturbative non-linear physics, and that of the QCD coherence, leads to an interesting and novel dynamics where the saturation momentum itself eventually saturates. We also investigate various implementations of the "non-Sudakov" form factor. It is shown that the non-linear dynamics leads to almost identical results for different form factors. Finally, different choices of the scale of the running coupling are analyzed and implications for the phenomenology are discussed.Comment: 37 pages, 21 figure

Sociobiological Control of Plasmid copy number

Background:
All known mechanisms and genes responsible for the regulation of plasmid replication lie with the plasmid rather than the chromosome. It is possible therefore that there can be copy-up mutants. Copy-up mutants will have within host selective advantage. This would eventually result into instability of bacteria-plasmid association. In spite of this possibility low copy number plasmids appear to exist stably in host populations. We examined this paradox using a computer simulation model.

Model:
Our multilevel selection model assumes a wild type with tightly regulated replication to ensure low copy number. A mutant with slightly relaxed replication regulation can act as a “cheater” or “selfish” plasmid and can enjoy a greater within-host-fitness. However the host of a cheater plasmid has to pay a greater cost. As a result, in host level competition, host cell with low copy number plasmid has a greater fitness. Furthermore, another mutant that has lost the genes required for conjugation was introduced in the model. The non-conjugal mutant was assumed to undergo conjugal transfer in the presence of another conjugal plasmid in the host cell.

Results:
The simulatons showed that if the cost of carrying a plasmid was low, the copy-up mutant could drive the wild type to extinction or very low frequencies. Consequently, another mutant with a higher copy number could invade the first invader. This process could result into an increasing copy number. However above a certain copy number within-host selection was overcompensated by host level selection leading to a rock-paper-scissor (RPS) like situation. The RPS situation allowed the coexistence of high and low copy number plasmids. The non-conjugal “hypercheaters” could further arrest the copy numbers to a substantially lower level.

Conclusions:
These sociobiological interactions might explain the stability of copy numbers better than molecular mechanisms of replication regulation alone