Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics

We explore the existence of time reparametrization symmetry in p-spin models. Using the Martin-Siggia-Rose generating functional, we analytically probe the long-time dynamics. We perform a renormalization group analysis where we systematically integrate over short timescale fluctuations. We find three families of stable fixed points and study the symmetry of those fixed points with respect to time reparametrizations. One of those families is composed entirely of symmetric fixed points, which are associated with the low temperature dynamics. The other two families are composed entirely of non-symmetric fixed points. One of these two non-symmetric families corresponds to the high temperature dynamics. Time reparametrization symmetry is a continuous symmetry that is spontaneously broken in the glass state and we argue that this gives rise to the presence of Goldstone modes. We expect the Goldstone modes to determine the properties of fluctuations in the glass state, in particular predicting the presence of dynamical heterogeneity.Comment: v2: Extensively modified to discuss both high temperature (non-symmetric) and low temperature (symmetric) renormalization group fixed points. Now 16 pages with 1 figure. v1: 13 page

Dimensionalities of Weak Solutions in Hydrogenic Systems

A close inspection on the 3D hydrogen atom Hamiltonian revealed formal eigenvectors often discarded in the literature. Although not in its domain, such eigenvectors belong to the Hilbert space, and so their time evolution is well defined. They are then related to the 1D and 2D hydrogen atoms and it is numerically found that they have continuous components, so that ionization can take place

Experimental procedures for precision measurements of the Casimir force with an Atomic Force Microscope

Experimental methods and procedures required for precision measurements of the Casimir force are presented. In particular, the best practices for obtaining stable cantilevers, calibration of the cantilever, correction of thermal and mechanical drift, measuring the contact separation, sphere radius and the roughness are discussed.Comment: 14 pages, 7 figure

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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Journal of The Royal Society Interface, 3(7), 303-310. doi:10.1098/rsif.2005.008

Discovery of a 0.42-s pulsar in the ultraluminous X-ray source NGC 7793 P13

NGC 7793 P13 is a variable (luminosity range ~100) ultraluminous X-ray source (ULX) proposed to host a stellar-mass black hole of less than 15 M$_{\odot}$ in a binary system with orbital period of 64 d and a 18-23 M$_{\odot}$ B9Ia companion. Within the EXTraS project we discovered pulsations at a period of ~0.42 s in two XMM-Newton observations of NGC 7793 P13, during which the source was detected at $L_{\mathrm{X}}\sim2.1\times10^{39}$ and $5\times10^{39}$ erg s$^{-1}$ (0.3-10 keV band). These findings unambiguously demonstrate that the compact object in NGC 7793 P13 is a neutron star accreting at super-Eddington rates. While standard accretion models face difficulties accounting for the pulsar X-ray luminosity, the presence of a multipolar magnetic field with $B$ ~ few $\times$ 10$^{13}$ G close to the base of the accretion column appears to be in agreement with the properties of the system.Comment: 5 pages, 5 figures, 2 tables; Version accepted for publication in MNRAS Letter

Geometrothermodynamics

We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the thermodynamic phase space and, on the other hand, on the metric structure of the space of thermodynamic equilibrium states. In order to make these two structures compatible we introduce a Legendre invariant set of metrics in the phase space, and demand that their pullback generates metrics on the space of equilibrium states. We show that Weinhold's metric, which was introduced {\it ad hoc}, is not contained within this invariant set. We propose alternative metrics which allow us to redefine the concept of thermodynamic length in an invariant manner and to study phase transitions in terms of curvature singularities.Comment: Revised version, to be published in Jour. Math. Phy

The Little-Hopfield model on a Random Graph

We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model).We solve this model within replica symmetry and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetictransition lines of our phase diagram are identical to those of sequential dynamics.The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement.Comment: 14 pages, 4 figure

Fluctuations in glassy systems

We summarize a theoretical framework based on global time-reparametrization invariance that explains the origin of dynamic fluctuations in glassy systems. We introduce the main ideas without getting into much technical details. We describe a number of consequences arising from this scenario that can be tested numerically and experimentally distinguishing those that can also be explained by other mechanisms from the ones that we believe, are special to our proposal. We support our claims by presenting some numerical checks performed on the 3d Edwards-Anderson spin-glass. Finally, we discuss up to which extent these ideas apply to super-cooled liquids that have been studied in much more detail up to present.Comment: 33 pages, 7 figs, contribution to JSTAT special issue `Principles of Dynamical Systems' work-shop at Newton Institute, Univ. of Cambridge, U