7,896 research outputs found
A Hamiltonian functional for the linearized Einstein vacuum field equations
By considering the Einstein vacuum field equations linearized about the
Minkowski metric, the evolution equations for the gauge-invariant quantities
characterizing the gravitational field are written in a Hamiltonian form by
using a conserved functional as Hamiltonian; this Hamiltonian is not the analog
of the energy of the field. A Poisson bracket between functionals of the field,
compatible with the constraints satisfied by the field variables, is obtained.
The generator of spatial translations associated with such bracket is also
obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie
Local continuity laws on the phase space of Einstein equations with sources
Local continuity equations involving background fields and variantions of the
fields, are obtained for a restricted class of solutions of the
Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the
concept of the adjoint of a differential operator. Such covariant conservation
laws are generated by means of decoupled equations and their adjoints in such a
way that the corresponding covariantly conserved currents possess some
gauge-invariant properties and are expressed in terms of Debye potentials.
These continuity laws lead to both a covariant description of bilinear forms on
the phase space and the existence of conserved quantities. Differences and
similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page
Truncation effects in superdiffusive front propagation with L\'evy flights
A numerical and analytical study of the role of exponentially truncated
L\'evy flights in the superdiffusive propagation of fronts in
reaction-diffusion systems is presented. The study is based on a variation of
the Fisher-Kolmogorov equation where the diffusion operator is replaced by a
-truncated fractional derivative of order where
is the characteristic truncation length scale. For there is no
truncation and fronts exhibit exponential acceleration and algebraic decaying
tails. It is shown that for this phenomenology prevails in the
intermediate asymptotic regime where
is the diffusion constant. Outside the intermediate asymptotic regime,
i.e. for , the tail of the front exhibits the tempered decay
, the acceleration is transient, and
the front velocity, , approaches the terminal speed as , where it is assumed that
with denoting the growth rate of the
reaction kinetics. However, the convergence of this process is algebraic, , which is very slow compared to the exponential
convergence observed in the diffusive (Gaussian) case. An over-truncated regime
in which the characteristic truncation length scale is shorter than the length
scale of the decay of the initial condition, , is also identified. In
this extreme regime, fronts exhibit exponential tails, ,
and move at the constant velocity, .Comment: Accepted for publication in Phys. Rev. E (Feb. 2009
Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
We analyze the quantum dynamics of the non-relativistic two-dimensional
isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken
as toy model to analyze some of the various quantum theories that can be built
from the application of Dirac's quantization rule to the various symplectic
structures recently reported for this classical system. It is pointed out that
that these quantum theories are inequivalent in the sense that the mean values
for the operators (observables) associated with the same physical classical
observable do not agree with each other. The inequivalence does not arise from
ambiguities in the ordering of operators but from the fact of having several
symplectic structures defined with respect to the same set of coordinates. It
is also shown that the uncertainty relations between the fundamental
observables depend on the particular quantum theory chosen. It is important to
emphasize that these (somehow paradoxical) results emerge from the combination
of two paradigms: Dirac's quantization rule and the usual Copenhagen
interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys.
Rev.
The influence of fractional diffusion in Fisher-KPP equations
We study the Fisher-KPP equation where the Laplacian is replaced by the
generator of a Feller semigroup with power decaying kernel, an important
example being the fractional Laplacian. In contrast with the case of the stan-
dard Laplacian where the stable state invades the unstable one at constant
speed, we prove that with fractional diffusion, generated for instance by a
stable L\'evy process, the front position is exponential in time. Our results
provide a mathe- matically rigorous justification of numerous heuristics about
this model
Corneal relaxation time estimation as a function of tear oxygen tension in human cornea during contact lens wear
[EN] The purpose is to estimate the oxygen diffusion coefficient and the relaxation time of the cornea with respect to the oxygen tension at the cornea-tears interface. Both findings are discussed. From the experimental data provided by Bonanno et al., the oxygen tension measurements in vivo for human cornea-tears-contact lens (CL), the relaxation time of the cornea, and their oxygen diffusion coefficient were obtained by numerical calculation using the Monod-kinetic model. Our results, considering the relaxation time of the cornea, observe a different behavior. At the time less than 8 s, the oxygen diffusivity process is upper-diffusive, and for the relaxation time greater than 8 s, the oxygen diffusivity process is lower-diffusive. Both cases depend on the partial pressure of oxygen at the entrance of the cornea. The oxygen tension distribution in the cornea-tears interface is separated into two different zones: one for conventional hydrogels, which is located between 6 and 75 mmHg, with a relaxation time included between 8 and 19 s, and the other zone for silicone hydrogel CLs, which is located at high oxygen tension, between 95 and 140 mmHg, with a relaxation time in the interval of 1.5-8 s. It is found that in each zone, the diffusion coefficient varies linearly with the oxygen concentration, presenting a discontinuity in the transition of 8 s. This could be interpreted as an aerobic-to-anaerobic transition. We attribute this behavior to the coupling formalism between oxygen diffusion and biochemical reactions to produce adenosine triphosphate.Contract grant sponsor: Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México; contract grant number: UNAM-DGAPA-PAPIIT projects IG 100618 and IN-114818 Contract grant sponsor: Secretaría de Estado de Investigación, Desarrollo e Innovación; contract grant number: ENE/2015-69203-RDel Castillo, LF.; Ramírez-Calderón, JG.; Del Castillo, RM.; Aguilella-Arzo, M.; Compañ Moreno, V. (2020). Corneal relaxation time estimation as a function of tear oxygen tension in human cornea during contact lens wear. Journal of Biomedical Materials Research Part B Applied Biomaterials. 108(1):14-21. https://doi.org/10.1002/jbm.b.34360S14211081Freeman, R. D. (1972). Oxygen consumption by the component layers of the cornea. The Journal of Physiology, 225(1), 15-32. doi:10.1113/jphysiol.1972.sp009927CHALMERS, R. L., McNALLY, J. J., SCHEIN, O. D., KATZ, J., TIELSCH, J. M., ALFONSO, E., … SHOVLIN, J. (2007). Risk Factors for Corneal Infiltrates with Continuous Wear of Contact Lenses. Optometry and Vision Science, 84(7), 573-579. doi:10.1097/opx.0b013e3180dc9a12Schein, O. D., McNally, J. J., Katz, J., Chalmers, R. L., Tielsch, J. M., Alfonso, E., … Shovlin, J. (2005). The Incidence of Microbial Keratitis among Wearers of a 30-Day Silicone Hydrogel Extended-Wear Contact Lens. Ophthalmology, 112(12), 2172-2179. doi:10.1016/j.ophtha.2005.09.014Sweeney, D. F. (2003). Clinical Signs of Hypoxia with High-Dk Soft Lens Extended Wear: Is the Cornea Convinced? Eye & Contact Lens: Science & Clinical Practice, S22-S25. doi:10.1097/00140068-200301001-00007HARVITT, D. M., & BONANNO, J. A. (1999). Re-Evaluation of the Oxygen Diffusion Model for Predicting Minimum Contact Lens Dk/t Values Needed to Avoid Corneal Anoxia. Optometry and Vision Science, 76(10), 712-719. doi:10.1097/00006324-199910000-00023Polse, K. A., & Mandell, R. B. (1970). Critical Oxygen Tension at the Corneal Surface. Archives of Ophthalmology, 84(4), 505-508. doi:10.1001/archopht.1970.00990040507021Giasson, C., & Bonanno, J. A. (1995). Acidification of rabbit corneal endothelium during contact lens wearin vitro. Current Eye Research, 14(4), 311-318. doi:10.3109/02713689509033531Riley, M. V. (1969). Glucose and oxygen utilization by the rabbit cornea. Experimental Eye Research, 8(2), 193-200. doi:10.1016/s0014-4835(69)80031-xFrahm, B., Lane, P., M�rkl, H., & P�rtner, R. (2003). Improvement of a mammalian cell culture process by adaptive, model-based dialysis fed-batch cultivation and suppression of apoptosis. Bioprocess and Biosystems Engineering, 26(1), 1-10. doi:10.1007/s00449-003-0335-zCompañ, V., Aguilella-Arzo, M., Del Castillo, L. F., Hernández, S. I., & Gonzalez-Meijome, J. M. (2016). Analysis of the application of the generalized monod kinetics model to describe the human corneal oxygen-consumption rate during soft contact lens wear. Journal of Biomedical Materials Research Part B: Applied Biomaterials, 105(8), 2269-2281. doi:10.1002/jbm.b.33764Bonanno, J. A., Clark, C., Pruitt, J., & Alvord, L. (2009). Tear Oxygen Under Hydrogel and Silicone Hydrogel Contact Lenses in Humans. Optometry and Vision Science, 86(8), E936-E942. doi:10.1097/opx.0b013e3181b2f582Chhabra, M., Prausnitz, J. M., & Radke, C. J. (2008). Diffusion and Monod kinetics to determine in vivo human corneal oxygen-consumption rate during soft contact-lens wear. Journal of Biomedical Materials Research Part B: Applied Biomaterials, 90B(1), 202-209. doi:10.1002/jbm.b.31274Chhabra, M., Prausnitz, J. M., & Radke, C. J. (2009). Modeling Corneal Metabolism and Oxygen Transport During Contact Lens Wear. Optometry and Vision Science, 86(5), 454-466. doi:10.1097/opx.0b013e31819f9e70Larrea, X., & Bu¨chler, P. (2009). A Transient Diffusion Model of the Cornea for the Assessment of Oxygen Diffusivity and Consumption. Investigative Opthalmology & Visual Science, 50(3), 1076. doi:10.1167/iovs.08-2479Alvord, L. A., Hall, W. J., Keyes, L. D., Morgan, C. F., & Winterton, L. C. (2007). Corneal Oxygen Distribution With Contact Lens Wear. Cornea, 26(6), 654-664. doi:10.1097/ico.0b013e31804f5a22Del Castillo, L. F., da Silva, A. R. F., Hernández, S. I., Aguilella, M., Andrio, A., Mollá, S., & Compañ, V. (2015). Diffusion and Monod kinetics model to determine in vivo human corneal oxygen-consumption rate during soft contact lens wear. Journal of Optometry, 8(1), 12-18. doi:10.1016/j.optom.2014.06.002Chandel, N. S., Budinger, G. R. S., Choe, S. H., & Schumacker, P. T. (1997). Cellular Respiration during Hypoxia. Journal of Biological Chemistry, 272(30), 18808-18816. doi:10.1074/jbc.272.30.18808Leung, B. K., Bonanno, J. A., & Radke, C. J. (2011). Oxygen-deficient metabolism and corneal edema. Progress in Retinal and Eye Research, 30(6), 471-492. doi:10.1016/j.preteyeres.2011.07.001Chhabra, M., Prausnitz, J. M., & Radke, C. J. (2008). Polarographic Method for Measuring Oxygen Diffusivity and Solubility in Water-Saturated Polymer Films: Application to Hypertransmissible Soft Contact Lenses. Industrial & Engineering Chemistry Research, 47(10), 3540-3550. doi:10.1021/ie071071aCompañ, V., Andrio, A., López-Alemany, A., Riande, E., & Refojo, M. F. (2002). Oxygen permeability of hydrogel contact lenses with organosilicon moieties. Biomaterials, 23(13), 2767-2772. doi:10.1016/s0142-9612(02)00012-1Gonzalez-Meijome, J. M., Compañ-Moreno, V., & Riande, E. (2008). Determination of Oxygen Permeability in Soft Contact Lenses Using a Polarographic Method: Estimation of Relevant Physiological Parameters. Industrial & Engineering Chemistry Research, 47(10), 3619-3629. doi:10.1021/ie071403bCompa�, V., L�pez, M. L., Andrio, A., L�pez-Alemany, A., & Refojo, M. F. (1999). Determination of the oxygen transmissibility and permeability of hydrogel contact lenses. Journal of Applied Polymer Science, 72(3), 321-327. doi:10.1002/(sici)1097-4628(19990418)72:33.0.co;2-lGavara, R., & Compañ, V. (2016). Oxygen, water, and sodium chloride transport in soft contact lenses materials. Journal of Biomedical Materials Research Part B: Applied Biomaterials, 105(8), 2218-2231. doi:10.1002/jbm.b.33762Compañ, V., Tiemblo, P., García, F., García, J. M., Guzmán, J., & Riande, E. (2005). A potentiostatic study of oxygen transport through poly(2-ethoxyethyl methacrylate-co-2,3-dihydroxypropylmethacrylate) hydrogel membranes. Biomaterials, 26(18), 3783-3791. doi:10.1016/j.biomaterials.2004.09.061Wang, J., Fonn, D., Simpson, T. L., & Jones, L. (2003). Precorneal and Pre- and Postlens Tear Film Thickness Measured Indirectly with Optical Coherence Tomography. Investigative Opthalmology & Visual Science, 44(6), 2524. doi:10.1167/iovs.02-0731Nichols, J. J., & King-Smith, P. E. (2003). Thickness of the Pre- and Post–Contact Lens Tear Film Measured In Vivo by Interferometry. Investigative Opthalmology & Visual Science, 44(1), 68. doi:10.1167/iovs.02-0377Compañ, V., Aguilella-Arzo, M., Edrington, T. B., & Weissman, B. A. (2016). Modeling Corneal Oxygen with Scleral Gas Permeable Lens Wear. Optometry and Vision Science, 93(11), 1339-1348. doi:10.1097/opx.0000000000000988Compañ, V., Aguilella-Arzo, M., & Weissman, B. A. (2017). Corneal Equilibrium Flux as a Function of Corneal Surface Oxygen Tension. Optometry and Vision Science, 94(6), 672-679. doi:10.1097/opx.0000000000001083Papas, E. B., & Sweeney, D. F. (2016). Interpreting the corneal response to oxygen: Is there a basis for re-evaluating data from gas-goggle studies? Experimental Eye Research, 151, 222-226. doi:10.1016/j.exer.2016.08.019Alentiev, A. Y., Shantarovich, V. P., Merkel, T. C., Bondar, V. I., Freeman, B. D., & Yampolskii, Y. P. (2002). 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Separatrix Reconnections in Chaotic Regimes
In this paper we extend the concept of separatrix reconnection into chaotic
regimes. We show that even under chaotic conditions one can still understand
abrupt jumps of diffusive-like processes in the relevant phase-space in terms
of relatively smooth realignments of stable and unstable manifolds of unstable
fixed points.Comment: 4 pages, 5 figures, submitted do Phys. Rev. E (1998
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