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

Three-dimensional aspects of fluid flows in channels. II. Effects of Meniscus and Thin Film regimes on Viscous Fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional Lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Secondly, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.Comment: 9 pages, 10 figure

Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors

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

Palinología, Estratigrafía y Geometría de la cuenca continental pensIlvaniense de Santa Susana (Suroeste de Portugal)

The continental Pennsylvanian Santa Susana Basin (SSB) is located along an important N-S strike shear zone (Santa Susana Shear Zone - SSSZ) that separates the Ossa-Morena and South Portuguese Zones (SW Portugal). This shear zone controlled the sedimentation of the basin and probably its post-sedimentary evolution. The lower (basal) unit is mostly conglomeratic and is known essentially from drill-hole data while the upper unit, that covers most of the current surface area, is composed by sandstones, shales and some coal beds. Fluvial sedimentary rocks seem to prevail, but evidences of lacustrine sedimentation can be found in restricted areas within the upper unit. Palynological data indicate that at least part of the sedimentation took place during the Early Kasimovian (Cantabrian) but the sporomorph content of different localities suggest that significantly older sediments (Late Moscovian -Early Bashkirian) may be present. Geometrical, structural, and cartographical evidences indicate that the SSB formed as a pull-apart basin along the SSSZ and was later partially uplifted during latest Varsican and Alpine orogenies.>La cuenca continental Pensilvaniense de Santa Susana (SSB) está localizada a lo largo de una importante zona de cizalla con dirección aproximada N-S (Zona de Cizalla de Santa Susana - SSSZ) que separa las Zonas de Ossa-Morena y Sur-Portuguesa (Suroeste de Portugal). La zona de cizalla ha controlado la sedimentación en la cuenca y posiblemente su evolución post-sedimentaria. La unidad inferior (basal), estudiada fundamentalmente mediante datos de sondeos, es mayormente conglomerática, mientras que su unidad superior, que cubre actualmente una gran parte de la superficie expuesta, está compuesta por areniscas, pizarras y niveles de carbón. Las rocas de origen fluvial son las más abundantes, sin embargo existen evidencias de sedimentación lacustre en áreas muy limitadas de la unidad superior. Los datos palinológicos indican que al menos parte de la sedimentación tuvo lugar durante el Kasimoviense temprano (Cantabriense) aunque el contenido en esporomorfos de diferentes localidades sugieren la existencia de sedimentos significativamente más antiguos (Moscoviense tardio/Bashkiriense temprano). Evidencias geométricas, estructurales y cartográficas sugieren la creación de una cuenca en pull-apart a lo largo de la ZCSS

Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

Identification of Leishmania Mexicana Mexicana in the State of São Paulo, Brazil

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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.