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

Diffusive transport and self-consistent dynamics in coupled maps

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e. the back-influence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e. through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure

Clustering transition in a system of particles self-consistently driven by a shear flow

We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists in that the effective velocity of every particle is given by the average of the external flow velocities felt by the particles located at a distance less than a typical radius, $R$. Numerical analysis reveals the existence of a transition to clustering depending on the parameters of the external flow and on $R$. A continuum description in terms of the number density of particles is derived, and a linear stability analysis of the density equation is performed in order to characterize the transitions observed in the model of interacting particles.Comment: 11 pages, 2 figures. To appear in PR

Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow

Finite Larmor radius (FLR) effects on non-diffusive transport in a prototypical zonal flow with drift waves are studied in the context of a simplified chaotic transport model. The model consists of a superposition of drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. High frequency FLR effects are incorporated by gyroaveraging the ExB velocity. Transport in the direction of the density gradient is negligible and we therefore focus on transport parallel to the zonal flows. A prescribed asymmetry produces strongly asymmetric non- Gaussian PDFs of particle displacements, with L\'evy flights in one direction but not the other. For zero Larmor radius, a transition is observed in the scaling of the second moment of particle displacements. However, FLR effects seem to eliminate this transition. The PDFs of trapping and flight events show clear evidence of algebraic scaling with decay exponents depending on the value of the Larmor radii. The shape and spatio-temporal self-similar anomalous scaling of the PDFs of particle displacements are reproduced accurately with a neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma

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.

Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation

By using conformal Killing-Yano tensors, and their generalisations, we obtain scalar potentials for both the source-free Maxwell and massless Dirac equations. For each of these equations we construct, from conformal Killing-Yano tensors, symmetry operators that map any solution to another.Comment: 35 pages, plain Te

Experimental and computational study of conductivity of multilayer graphene in polypropylene nanocomposites

[EN] We study the electric conductivity of compounds formed by multilayer graphene in polypropylene. Our study makes a comparative analysis between the experimental and computational results. To obtain an experimental measurement of the electronic properties, we deposited multilayer graphene (MLG) nanoparticles over a polypropylene matrix. The deposition was made over several stages, in which we added to the polymer matrix different percentages of MLG nanoparticles using the melt compounding technique, and we studied the conductivities of the nanocomposites by means of electrochemical impedance spectroscopy (EIS). The second part consists of computational calculations, in which we studied the electronic properties of a graphene sheet under a polypropylene molecule with different slabs in the monomer. In both analyses, there is a strong percolation phenomenon with a percolation threshold of around 18% of the MLG nanoparticles. Before the percolation threshold, the charge carriers are constrained in the polypropylene molecule, making the system an insulating material and creating p-type doping. After the percolation threshold, the charge carriers are constrained in the graphene, making the system a conductor material and creating n-type doping with conductivity values of around 20 S m(-1). This phenomenon is a consequence of a change in the mechanism of charge transfer in the interface between the polypropylene molecule and graphene sheet. To describe the charge transfer mechanism, it is necessary to consider the quantum effect. The incorporation of the quantum effects and the percolation phenomenon make it possible for the theoretical conductivity to be close to the conductivity measured experimentally.This research has been supported by the ENE/2015-69203-R project, granted by the Ministerio de Economia y Competitividad (MINECO), Spain. Also, the authors are grateful to UNAM-DGAPA-PAPIIT projects IG 100618 y IG 114818, DGTIC-UNAM for access to the Miztli-UNAM supercomputer LANCAD-UNAM-DGTIC-055, and UNAM-DGAPA for the Postdoctoral grant for Roxana M. del Castillo.Del Castillo, RM.; Del Castillo, LF.; Calles, AG.; Compañ Moreno, V. (2018). Experimental and computational study of conductivity of multilayer graphene in polypropylene nanocomposites. Journal of Materials Chemistry C. 6:7232-7241. https://doi.org/10.1039/c8tc01135dS723272416H. G. Karian , Handbook of polypropylene and polypropylene composites , RheTec, Inc. , Whitmore Lake, Michigan , 2nd edn, 2003 , https://books.google.es/books?hl=es&lr=&id=C0nzeNPUpoIC&oi=fnd&pg=PP1&dq=Handbook+of+polypropylene+and+polypropylene+composites&ots=LYqYBYg45n&sig=3gtYXigr8_O8CUJeefBCtGI7QXA#v=onepage&q=Handbook%20of%20polypropylene%20and%20polypropylene%20composites&f=falseRath, T., & Li, Y. (2011). Nanocomposites based on polystyrene-b-poly(ethylene-r-butylene)-b-polystyrene and exfoliated graphite nanoplates: Effect of nanoplatelet loading on morphology and mechanical properties. Composites Part A: Applied Science and Manufacturing, 42(12), 1995-2002. doi:10.1016/j.compositesa.2011.09.002Kim, M.-S., Yan, J., Kang, K.-M., Joo, K.-H., Kang, Y.-J., & Ahn, S.-H. (2013). Soundproofing ability and mechanical properties of polypropylene/exfoliated graphite nanoplatelet/carbon nanotube (PP/xGnP/CNT) composite. International Journal of Precision Engineering and Manufacturing, 14(6), 1087-1092. doi:10.1007/s12541-013-0146-3Zhang, K., Yu, H.-O., Shi, Y.-D., Chen, Y.-F., Zeng, J.-B., Guo, J., … Wang, M. (2017). Morphological regulation improved electrical conductivity and electromagnetic interference shielding in poly(l-lactide)/poly(ε-caprolactone)/carbon nanotube nanocomposites via constructing stereocomplex crystallites. Journal of Materials Chemistry C, 5(11), 2807-2817. doi:10.1039/c7tc00389gMohd Radzuan, N. A., Yusuf Zakaria, M., Sulong, A. B., & Sahari, J. (2017). The effect of milled carbon fibre filler on electrical conductivity in highly conductive polymer composites. Composites Part B: Engineering, 110, 153-160. doi:10.1016/j.compositesb.2016.11.021Li, Q., Yao, F.-Z., Liu, Y., Zhang, G., Wang, H., & Wang, Q. (2018). High-Temperature Dielectric Materials for Electrical Energy Storage. Annual Review of Materials Research, 48(1), 219-243. doi:10.1146/annurev-matsci-070317-124435Qiao, Y., Yin, X., Zhu, T., Li, H., & Tang, C. (2018). Dielectric polymers with novel chemistry, compositions and architectures. Progress in Polymer Science, 80, 153-162. doi:10.1016/j.progpolymsci.2018.01.003Rosehr, A., & Luinstra, G. A. (2017). Polypropylene composites with finely dispersed multi-walled carbon nanotubes covered with an aluminum oxide shell. Polymer, 120, 164-175. doi:10.1016/j.polymer.2017.05.045Bolotin, K. I., Sikes, K. J., Jiang, Z., Klima, M., Fudenberg, G., Hone, J., … Stormer, H. L. (2008). Ultrahigh electron mobility in suspended graphene. Solid State Communications, 146(9-10), 351-355. doi:10.1016/j.ssc.2008.02.024Banszerus, L., Schmitz, M., Engels, S., Goldsche, M., Watanabe, K., Taniguchi, T., … Stampfer, C. (2016). Ballistic Transport Exceeding 28 μm in CVD Grown Graphene. Nano Letters, 16(2), 1387-1391. doi:10.1021/acs.nanolett.5b04840Terrés, B., Chizhova, L. A., Libisch, F., Peiro, J., Jörger, D., Engels, S., … Stampfer, C. (2016). Size quantization of Dirac fermions in graphene constrictions. Nature Communications, 7(1). doi:10.1038/ncomms11528Zhang, H.-B., Zheng, W.-G., Yan, Q., Yang, Y., Wang, J.-W., Lu, Z.-H., … Yu, Z.-Z. (2010). Electrically conductive polyethylene terephthalate/graphene nanocomposites prepared by melt compounding. Polymer, 51(5), 1191-1196. doi:10.1016/j.polymer.2010.01.027Chung, D. D. L. (2015). A review of exfoliated graphite. Journal of Materials Science, 51(1), 554-568. doi:10.1007/s10853-015-9284-6T. Bayerl , A.Benedito , A.Gallegos , G. B.Mitschang and B.Galindo , Melting of Polymer-Polymer Composites by Particulate Heating Promoters and Electromagnetic Radiation , in Synthetic Polymer-Polymer Composites , ed. D. Bhattacharyya and S. Fakirov , Carl HanserVerlag GmbH & Co. KG , 2012 , ch. 24, pp. 39–64 10.3139/9781569905258.002Harper, J., Price, D., & Zhang, J. (2005). Use of Fillers to Enable the Microwave Processing of Polyethylene. Journal of Microwave Power and Electromagnetic Energy, 40(4), 219-227. doi:10.1080/08327823.2005.11688543Galindo, B., Benedito, A., Gimenez, E., & Compañ, V. (2016). Comparative study between the microwave heating efficiency of carbon nanotubes versus multilayer graphene in polypropylene nanocomposites. Composites Part B: Engineering, 98, 330-338. doi:10.1016/j.compositesb.2016.04.082Asadi, K., Kronemeijer, A. J., Cramer, T., Jan Anton Koster, L., Blom, P. W. M., & de Leeuw, D. M. (2013). Polaron hopping mediated by nuclear tunnelling in semiconducting polymers at high carrier density. Nature Communications, 4(1). doi:10.1038/ncomms2708Fan, Z., Gong, F., Nguyen, S. T., & Duong, H. M. (2015). Advanced multifunctional graphene aerogel – Poly (methyl methacrylate) composites: Experiments and modeling. Carbon, 81, 396-404. doi:10.1016/j.carbon.2014.09.072Zabihi, Z., & Araghi, H. (2016). Monte Carlo simulations of effective electrical conductivity of graphene/poly(methyl methacrylate) nanocomposite: Landauer-Buttiker approach. Synthetic Metals, 217, 87-93. doi:10.1016/j.synthmet.2016.03.024Xia, X., Zhong, Z., & Weng, G. J. (2017). Maxwell–Wagner–Sillars mechanism in the frequency dependence of electrical conductivity and dielectric permittivity of graphene-polymer nanocomposites. Mechanics of Materials, 109, 42-50. doi:10.1016/j.mechmat.2017.03.014F. M. Bickelhaupt and E. J.Baerends , Kohn–Sham Density Functional Theory: Predicting and Understanding Chemistry . in Reviews in Computational Chemistry , 2007 , ed. K. B. Lipkowitz and B. Boyd Donald , John Wiley & Sons, Inc. , vol. 15, pp. 1–89 10.1002/9780470125922.ch1/summaryPerdew, J. P., Burke, K., & Ernzerhof, M. (1996). Generalized Gradient Approximation Made Simple. Physical Review Letters, 77(18), 3865-3868. doi:10.1103/physrevlett.77.3865Methfessel, M., & Paxton, A. T. (1989). High-precision sampling for Brillouin-zone integration in metals. Physical Review B, 40(6), 3616-3621. doi:10.1103/physrevb.40.3616Monkhorst, H. J., & Pack, J. D. (1976). Special points for Brillouin-zone integrations. Physical Review B, 13(12), 5188-5192. doi:10.1103/physrevb.13.5188Files: C.pbe-van_ak.UPF, H.pbe-van_ak.UPF, N.pbe-van_ak.UPF, and O.pbe-van_ak.UPF, http://www.quantum-espresso.orgVanderbilt, D. (1990). Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Physical Review B, 41(11), 7892-7895. doi:10.1103/physrevb.41.7892Sørensen, T. S., & Compañ, V. (1995). Complex permittivity of a conducting, dielectric layer containing arbitrary binary Nernst–Planck electrolytes with applications to polymer films and cellulose acetate membranes. J. Chem. Soc., Faraday Trans., 91(23), 4235-4250. doi:10.1039/ft9959104235Drüschler, M., Huber, B., & Roling, B. (2011). On Capacitive Processes at the Interface between 1-Ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate and Au(111). The Journal of Physical Chemistry C, 115(14), 6802-6808. doi:10.1021/jp200395jSerghei, A., Tress, M., Sangoro, J. R., & Kremer, F. (2009). Electrode polarization and charge transport at solid interfaces. Physical Review B, 80(18). doi:10.1103/physrevb.80.184301F. Kremer and A.Schoenhals , Broadban Dielectric Spectroscopy , Springer , Berlin , 2003Coelho, R. (1983). Sur la relaxation d’une charge d’espace. Revue de Physique Appliquée, 18(3), 137-146. doi:10.1051/rphysap:01983001803013700Macdonald, J. R. (1953). Theory of ac Space-Charge Polarization Effects in Photoconductors, Semiconductors, and Electrolytes. Physical Review, 92(1), 4-17. doi:10.1103/physrev.92.4Klein, R. J., Zhang, S., Dou, S., Jones, B. H., Colby, R. H., & Runt, J. (2006). Modeling electrode polarization in dielectric spectroscopy: Ion mobility and mobile ion concentration of single-ion polymer electrolytes. The Journal of Chemical Physics, 124(14), 144903. doi:10.1063/1.2186638Greenhoe, B. M., Hassan, M. K., Wiggins, J. S., & Mauritz, K. A. (2016). Universal power law behavior of the AC conductivity versus frequency of agglomerate morphologies in conductive carbon nanotube-reinforced epoxy networks. Journal of Polymer Science Part B: Polymer Physics, 54(19), 1918-1923. doi:10.1002/polb.24121Novoselov, K. S. (2004). Electric Field Effect in Atomically Thin Carbon Films. Science, 306(5696), 666-669. doi:10.1126/science.1102896Del Castillo, R. M., & Sansores, L. E. (2015). Study of the electronic structure of Ag, Au, Pt and Pd clusters adsorption on graphene and their effect on conductivity. The European Physical Journal B, 88(10). doi:10.1140/epjb/e2015-60001-2Galpaya, D., Wang, M., Liu, M., Motta, N., Waclawik, E., & Yan, C. (2012). Recent Advances in Fabrication and Characterization of Graphene-Polymer Nanocomposites. Graphene, 01(02), 30-49. doi:10.4236/graphene.2012.12005I. Zvyagin . Charge Transport via Delocalized States in Disordered Materials . in Charge Transport in Disordered Solids with Applications in Electronics , ed. S. Baranovsky , John Wiley & Sons, Inc. , 2006 , pp. 1–48 10.1002/0470095067.ch1/summaryLeenaerts, O., Partoens, B., & Peeters, F. M. (2009). Adsorption of small molecules on graphene. Microelectronics Journal, 40(4-5), 860-862. doi:10.1016/j.mejo.2008.11.022Hashemi, R., & Weng, G. J. (2016). A theoretical treatment of graphene nanocomposites with percolation threshold, tunneling-assisted conductivity and microcapacitor effect in AC and DC electrical settings. Carbon, 96, 474-490. doi:10.1016/j.carbon.2015.09.103Xia, X., Wang, Y., Zhong, Z., & Weng, G. J. (2017). A frequency-dependent theory of electrical conductivity and dielectric permittivity for graphene-polymer nanocomposites. Carbon, 111, 221-230. doi:10.1016/j.carbon.2016.09.078The determination of the elastic field of an ellipsoidal inclusion, and related problems. (1957). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 241(1226), 376-396. doi:10.1098/rspa.1957.0133Trotta, S., Marmo, F., & Rosati, L. (2017). Evaluation of the Eshelby tensor for polygonal inclusions. Composites Part B: Engineering, 115, 170-181. doi:10.1016/j.compositesb.2016.10.018L. D. Landau , E. M.Lifshitz and L. P.Pitaevskii , Electrodynamics of Continuous Media , Pergamon Press , New York , 3rd edn, 1984Wang, Y., Weng, G. J., Meguid, S. A., & Hamouda, A. M. (2014). A continuum model with a percolation threshold and tunneling-assisted interfacial conductivity for carbon nanotube-based nanocomposites. Journal of Applied Physics, 115(19), 193706. doi:10.1063/1.4878195Wang, Y., Shan, J. W., & Weng, G. J. (2015). Percolation threshold and electrical conductivity of graphene-based nanocomposites with filler agglomeration and interfacial tunneling. Journal of Applied Physics, 118(6), 065101. doi:10.1063/1.4928293Wehling, T. O., Yuan, S., Lichtenstein, A. I., Geim, A. K., & Katsnelson, M. I. (2010). Resonant Scattering by Realistic Impurities in Graphene. Physical Review Letters, 105(5). doi:10.1103/physrevlett.105.056802Stauber, T., Peres, N. M. R., & Guinea, F. (2007). Electronic transport in graphene: A semiclassical approach including midgap states. Physical Review B, 76(20). doi:10.1103/physrevb.76.205423R. M. Del Castillo and L. E.Sansores . Adsorption of Metal Clusters on Graphene and Their Effect on the Electrical Conductivity , in Graphene Materials – Advanced Applications , ed. G. Z. Kyzas and A. C. Mitropoulos , INTECH , 2017 , https://www.intechopen.com/books/graphene-materials-advanced-applications/adsorption-of-metal-clusters-on-graphene-and-their-effect-on-the-electrical-conductivit