Fractional Hamiltonian analysis of higher order derivatives systems

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.Comment: 13 page

Implant Site Nexplanon Reaction?

Nexplanon (Schering-Plough Limited/Merck Sharp & Dohme Limited (MSD)) is a long active reversible contraceptive method that provides effective contraception for 3 years. It consists of a single, flexible, rod-shaped implant, containing 68 mg etonogestrel. It is 4 cm long, consists of an ethylene vinyl acetate copolymer, a non-absorbable material, and also contains 15 mg of barium sulfate, which makes it visible by X-ray. We describe a case of a 39-year-old woman who experienced a local reaction to the barium sulfate in Nexplanon. She was given medical treatment, but only the removal of the implant resolved the symptoms. After removal there was gradual improvement and 72 h later the patient was asymptomatic. Allergic reaction to barium sulfate is extremely rare: until now, there have only been two cases associated with Nexplanon described in the literature

On the renormalization group flow of f(R)-gravity

We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \int d^dx \sqrt{g} f(R)$. Based on this equation we show that certain gravitational interactions monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The non-perturbative RG flow of non-local extensions of the Einstein-Hilbert truncation including $\int d^dx \sqrt{g} \ln(R)$ and $\int d^dx \sqrt{g} R^{-n}$ interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some $R^{-n}$-truncations all physical trajectories emanate from a Non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the $\ln(R)$-truncation contains an infrared attractor which drives a positive cosmological constant to zero dynamically.Comment: 55 pages, 7 figures, typos corrected, references added, version to appear in Phys. Rev.

The graphene sheet versus the 2DEG: a relativistic Fano spin-filter via STM and AFM tips

We explore theoretically the density of states (LDOS) probed by an STM tip of 2D systems hosting an adatom and a subsurface impurity,both capacitively coupled to AFM tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: the Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin-degeneracy of the LDOS is lifted exclusively in the graphene system, in particular for the asymmetric regime of Fano interference. The aftermath of this limit is a counterintuitive phenomenon, which consists of a dominant Fano factor due to the subsurface impurity even with a stronger STM-adatom coupling. Thus we find a full polarized conductance, achievable just by displacing vertically the position of the STM tip. To the best knowledge, our work is the first to propose the Fano effect as the mechanism to filter spins in graphene. This feature arises from the massless Dirac electrons within the band structure and allows us to employ the graphene host as a relativistic Fano spin-filter

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

The type N Karlhede bound is sharp

We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spacetimes are properly $CH_2$, i.e., curvature homogeneous of order 2 but non-homogeneous. This means that tetrad components of $R, \nabla R, \nabla^{(2)}R$ are constant, and that essential coordinates first appear as components of $\nabla^{(3)}R$. Covariant derivatives of orders 4,5,6 yield one additional invariant each, and $\nabla^{(7)}R$ is needed for invariant classification. Thus, our class proves that the bound of 7 on the order of the covariant derivative, first established by Karlhede, is sharp. Our finding corrects an outstanding assertion that invariant classification of four-dimensional Lorentzian manifolds requires at most $\nabla^{(6)}R$.Comment: 7 pages, typos corrected, added citation and acknowledgemen

Disinfection with neutral electrolyzed oxidizing water to reduce microbial load and to prevent biofilm regrowth in the processing of fresh-cut vegetables

Product decontamination is one of the most important processes of the hygienic practice in food industries such as Minimally Processed Vegetables (MPV) plants and sodium hypochlorite (NaOCl) solutions are commonly used as a biocide for disinfection. Although it may be corrosive and irritating when compared to alternative biocides, this biocide is frequently applied at high concentrations. This work aims at studying the use of lower concentrations of chlorine by testing neutral electrolyzed oxidizing water (NEOW) as a chlorine-source disinfectant in fresh-cut salad processing. Assays were performed at industrial and laboratory scale. Results showed that lower doses of chlorine from NEOW (30 ppm) are as effective as higher concentrations of the traditional chlorine from NaOCl (80 ppm) in the reduction of total microbial population at industrial scale. Moreover, in laboratory studies, the NEOW chlorine was also more effective in biofilm eradication, as well as a biofilm preventive agent. NEOW can thus be a successful alternative water disinfection technique, reducing the free chlorine concentration needed to sanitize salads, also decreasing water consumption whilst taking into account environmental and food quality impacts