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

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

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

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). Gas and Vapor Sorption, Permeation, and Diffusion in Glassy Amorphous Teflon AF1600. Macromolecules, 35(25), 9513-9522. doi:10.1021/ma020494fLin, H., & Freeman, B. D. (2005). Gas and Vapor Solubility in Cross-Linked Poly(ethylene Glycol Diacrylate). Macromolecules, 38(20), 8394-8407. doi:10.1021/ma051218eKoros, W. J., Paul, D. R., & Rocha, A. A. (1976). Carbon dioxide sorption and transport in polycarbonate. Journal of Polymer Science: Polymer Physics Edition, 14(4), 687-702. doi:10.1002/pol.1976.180140410Nicolson, P. C., & Vogt, J. (2001). Soft contact lens polymers: an evolution. Biomaterials, 22(24), 3273-3283. doi:10.1016/s0142-9612(01)00165-xCheng, X., & Pinsky, P. M. (2017). A numerical model for metabolism, metabolite transport and edema in the human cornea. Computer Methods in Applied Mechanics and Engineering, 314, 323-344. doi:10.1016/j.cma.2016.09.014Li, L., & Tighe, B. (2005). Numerical simulation of corneal transport processes. Journal of The Royal Society Interface, 3(7), 303-310. doi:10.1098/rsif.2005.008

Genetic algorithms for the scheduling in additive manufacturing

[EN] Genetic Algorithms (GAs) are introduced to tackle the packing problem. The scheduling in Additive Manufacturing (AM) is also dealt with to set up a managed market, called “Lonja3D”. This will enable to determine an alternative tool through the combinatorial auctions, wherein the customers will be able to purchase the products at the best prices from the manufacturers. Moreover, the manufacturers will be able to optimize the production capacity and to decrease the operating costs in each case.This research has been partially financed by the project: “Lonja de Impresión 3D para la Industria 4.0 y la Empresa Digital (LONJA3D)” funded by the Regional Government of Castile and Leon and the European Regional Development Fund (ERDF, FEDER) with grant VA049P17Castillo-Rivera, S.; De Antón, J.; Del Olmo, R.; Pajares, J.; López-Paredes, A. (2020). Genetic algorithms for the scheduling in additive manufacturing. International Journal of Production Management and Engineering. 8(2):59-63. https://doi.org/10.4995/ijpme.2020.12173OJS596382Ahsan, A., Habib, A., Khoda, B. (2015). Resource based process planning for additive manufacturing. Computer-Aided Design, 69, 112-125. https://doi.org/10.1016/j.cad.2015.03.006Araújo, L., Özcan, E., Atkin, J., Baumers, M., Tuck, C., Hague, R. (2015). Toward better build volume packing in additive manufacturing: classification of existing problems and benchmarks. 26th Annual International Solid Freeform Fabrication Symposium - an Additive Manufacturing Conference, 401-410.Berman, B. (2012). 3-D printing: The new industrial revolution. Business Horizons, 55: 155-162. https://doi.org/10.1016/j.bushor.2011.11.003Canellidis, V., Dedoussis, V., Mantzouratos, N., Sofianopoulou, S. (2006). Preprocessing methodology for optimizing stereolithography apparatus build performance. Computers in Industry, 57, 424-436. https://doi.org/10.1016/j.compind.2006.02.004Chergui, A., Hadj-Hamoub, K., Vignata, F. (2018). Production scheduling and nesting in additive manufacturing. Computers & Industrial Engineering, 126, 292-301. https://doi.org/10.1016/j.cie.2018.09.048Demirel, E., Özelkan, E.C., Lim, C. (2018). Aggregate planning with flexibility requirements profile. International Journal of Production Economics, 202, 45-58. https://doi.org/10.1016/j.ijpe.2018.05.001Fera, M., Fruggiero, F., Lambiase, A., Macchiaroli, R., Todisco, V. (2018). A modified genetic algorithm for time and cost optimization of an additive manufacturing single-machine scheduling. International Journal of Industrial Engineering Computations, 9, 423-438. https://doi.org/10.5267/j.ijiec.2018.1.001Hopper, E., Turton, B. (1997). Application of genetic algorithms to packing problems - A Review. Proceedings of the 2nd Online World Conference on Soft Computing in Engineering Design and Manufacturing, Springer Verlag, London, 279-288. https://doi.org/10.1007/978-1-4471-0427-8_30Ikonen, I., Biles, W.E., Kumar, A., Wissel, J.C., Ragade, R.K. (1997). A genetic algorithm for packing three-dimensional non-convex objects having cavities and holes. ICGA, 591-598.Kim, K.H., Egbelu, P.J. (1999). Scheduling in a production environment with multiple process plans per job. International Journal of Production Research, 37, 2725-2753. https://doi.org/10.1080/002075499190491Lawrynowicz, A. (2011). Genetic algorithms for solving scheduling problems in manufacturing systems. Foundations of Management, 3(2), 7-26. https://doi.org/10.2478/v10238-012-0039-2Li, Q., Kucukkoc, I., Zhang, D. (2017). Production planning in additive manufacturing and 3D printing. Computers and Operations Research, 83, 157-172. https://doi.org/10.1016/j.cor.2017.01.013Milošević, M., Lukić, D., Đurđev, M., Vukman, J., Antić, A. (2016). Genetic Algorithms in Integrated Process Planning and Scheduling-A State of The Art Review. Proceedings in Manufacturing Systems, 11(2), 83-88.Pour, M.A., Zanardini, M., Bacchetti, A., Zanoni, S. (2016). Additive manufacturing impacts on productions and logistics systems. IFAC, 49(12), 1679-1684. https://doi.org/10.1016/j.ifacol.2016.07.822Wilhelm, W.E., Shin, H.M. (1985). Effectiveness of Alternate Operations in a Flexible Manufacturing System. International Journal of Production Research, 23(1), 65-79. https://doi.org/10.1080/00207548508904691Xirouchakis, P., Kiritsis, D., Persson, J.G. (1998). A Petri net Technique for Process Planning Cost Estimation. Annals of the CIRP, 47(1), 427-430. https://doi.org/10.1016/S0007-8506(07)62867-4Zhang, Y., Bernard, A., Gupta, R.K., Harik, R. (2014). Evaluating the design for additive manufacturing: a process planning perspective. Procedia CIRP, 21, 144-150. https://doi.org/10.1016/j.procir.2014.03.17

Anomalous transport in Charney-Hasegawa-Mima flows

Transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a non linear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around $\mu=1.75$, which is also the one found for simple point vortex flows in the literature, indicating some kind of universality. Moreover the law $\gamma=\mu+1$ linking the trapping time exponent within jets to the transport exponent is confirmed and an accumulation towards zero of the spectrum of finite time Lyapunov exponent is observed. The localization of a jet is performed, and its structure is analyzed. It is clearly shown that despite a regular coarse grained picture of the jet, motion within the jet appears as chaotic but chaos is bounded on successive small scales.Comment: revised versio