The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets

The analytic continuation of the Lippmann-Schwinger bras and kets is obtained and characterized. It is shown that the natural mathematical setting for the analytic continuation of the solutions of the Lippmann-Schwinger equation is the rigged Hilbert space rather than just the Hilbert space. It is also argued that this analytic continuation entails the imposition of a time asymmetric boundary condition upon the group time evolution, resulting into a semigroup time evolution. Physically, the semigroup time evolution is simply a (retarded or advanced) propagator.Comment: 32 pages, 3 figure

On the inconsistency of the Bohm-Gadella theory with quantum mechanics

The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann-Schwinger equation are functionals over spaces of Hardy functions. The preparation-registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that the Hardy axiom is incorrect, because the solutions of the Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also shown that the derivation of the preparation-registration arrow of time is flawed. Thus, Hardy functions neither appear when we solve the Lippmann-Schwinger equation nor they should appear. It is also shown that the Bohm-Gadella theory does not rest on the same physical principles as quantum mechanics, and that it does not solve any problem that quantum mechanics cannot solve. The Bohm-Gadella theory must therefore be abandoned.Comment: 16 page

Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''

In this reply, we show that when we apply standard distribution theory to the Lippmann-Schwinger equation, the resulting spaces of test functions would comply with the Hardy axiom only if classic results of Paley and Wiener, of Gelfand and Shilov, and of the theory of ultradistributions were wrong. As well, we point out several differences between the ``standard method'' of constructing rigged Hilbert spaces in quantum mechanics and the method used in Time Asymmetric Quantum Theory.Comment: 13 page

The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I

We exemplify the way the rigged Hilbert space deals with the Lippmann-Schwinger equation by way of the spherical shell potential. We explicitly construct the Lippmann-Schwinger bras and kets along with their energy representation, their time evolution and the rigged Hilbert spaces to which they belong. It will be concluded that the natural setting for the solutions of the Lippmann-Schwinger equation--and therefore for scattering theory--is the rigged Hilbert space rather than just the Hilbert space.Comment: 34 pages, 1 figur

Impact of Exhaust Gas Recirculation on Gaseous Emissions of Turbocharged Spark-Ignition Engines

[EN] Exhaust gas recirculation is one of the technologies that can be used to improve the efficiency of spark-ignition engines. However, apart from fuel consumption reduction, this technology has a significant impact on exhaust gaseous emissions, inducing a significant reduction in nitrogen oxides and an increase in unburned hydrocarbons and carbon monoxide, which can affect operation of the aftertreatment system. In order to evaluate these effects, data extracted from design of experiments done on a multi-cylinder 1.3 L turbocharged spark-ignition engine with variable valve timing and low-pressure exhaust gas recirculation (EGR) are used. The test campaign covers the area of interest for the engine to be used in new-generation hybrid electric platforms. In general, external EGR provides an approximately linear decrease of nitrogen oxides and deterioration of unburned hydrocarbon emissions due to thermal and flame quenching effects. At low load, the impact on emissions is directly linked to actuation of the variable valve timing system due to the interaction of EGR with internal residuals. For the same external EGR rate, running with high valve overlap increases the amount of internal residuals trapped inside the cylinder, slowing down combustion and increasing Unburnt hydrocarbon (HC) emissions. However, low valve overlap (i.e., low internal residuals) operation implies a decrease in oxygen concentration in the exhaust line for the same air-fuel ratio inside the cylinders. At high load, interaction with the variable valve timing system is reduced, and general trends of HC increase and of oxygen and carbon monoxide decrease appear as EGR is introduced. Finally, a simple stoichiometric model evaluates the potential performance of a catalyst targeted for EGR operation. The results highlight that the decrease of nitrogen oxides and oxygen availability together with the increase of unburned hydrocarbons results in a huge reduction of the margin in oxygen availability to achieve a complete oxidation from a theoretical perspective. This implies the need to rely on the oxygen storage capability of the catalyst or the possibility to control at slightly lean conditions, taking advantage of the nitrogen oxide reduction at engine-out with EGR.Piqueras, P.; De La Morena, J.; Sanchis-Pacheco, EJ.; Pitarch-Berná, R. (2020). Impact of Exhaust Gas Recirculation on Gaseous Emissions of Turbocharged Spark-Ignition Engines. Applied Sciences. 10(21):1-17. https://doi.org/10.3390/app10217634S1171021Kolodziej, C. P., Pamminger, M., Sevik, J., Wallner, T., Wagnon, S. W., & Pitz, W. J. (2017). Effects of Fuel Laminar Flame Speed Compared to Engine Tumble Ratio, Ignition Energy, and Injection Strategy on Lean and EGR Dilute Spark Ignition Combustion. SAE International Journal of Fuels and Lubricants, 10(1), 82-94. doi:10.4271/2017-01-0671Sjerić, M., Taritaš, I., Tomić, R., Blažić, M., Kozarac, D., & Lulić, Z. (2016). Efficiency improvement of a spark-ignition engine at full load conditions using exhaust gas recirculation and variable geometry turbocharger – Numerical study. Energy Conversion and Management, 125, 26-39. doi:10.1016/j.enconman.2016.02.047Grover, Jr., R. O., & Cleary, D. (2013). Correlating Measured Combustion Performance with CFD Predicted In-Cylinder Flows for a Spark-Ignition Direct-Injection (SIDI) Engine with Enhanced Charge Motion. SAE Technical Paper Series. doi:10.4271/2013-01-1090Costa, M., Catapano, F., Sementa, P., Sorge, U., & Vaglieco, B. M. (2016). Mixture preparation and combustion in a GDI engine under stoichiometric or lean charge: an experimental and numerical study on an optically accessible engine. Applied Energy, 180, 86-103. doi:10.1016/j.apenergy.2016.07.089Alagumalai, A. (2014). Internal combustion engines: Progress and prospects. Renewable and Sustainable Energy Reviews, 38, 561-571. doi:10.1016/j.rser.2014.06.014Dong, X., Wang, B., Yip, H. L., & Chan, Q. N. (2019). CO2 Emission of Electric and Gasoline Vehicles under Various Road Conditions for China, Japan, Europe and World Average—Prediction through Year 2040. Applied Sciences, 9(11), 2295. doi:10.3390/app9112295Vafamehr, H., Cairns, A., Sampson, O., & Koupaie, M. M. (2016). The competing chemical and physical effects of transient fuel enrichment on heavy knock in an optical spark ignition engine. Applied Energy, 179, 687-697. doi:10.1016/j.apenergy.2016.07.038Gröger, O., Gasteiger, H. A., & Suchsland, J.-P. (2015). Review—Electromobility: Batteries or Fuel Cells? Journal of The Electrochemical Society, 162(14), A2605-A2622. doi:10.1149/2.0211514jesPham, A., & Jeftic, M. (2018). Characterization of Gaseous Emissions from Blended Plug-In Hybrid Electric Vehicles during High-Power Cold-Starts. SAE Technical Paper Series. doi:10.4271/2018-01-0428Yamada, H., Inomata, S., & Tanimoto, H. (2017). Particle and VOC Emissions from Stoichiometric Gasoline Direct Injection Vehicles and Correlation Between Particle Number and Mass Emissions. Emission Control Science and Technology, 3(2), 135-141. doi:10.1007/s40825-016-0060-0Zinola, S., Raux, S., & Leblanc, M. (2016). Persistent Particle Number Emissions Sources at the Tailpipe of Combustion Engines. SAE Technical Paper Series. doi:10.4271/2016-01-2283Xie, F., Li, X., Su, Y., Hong, W., Jiang, B., & Han, L. (2016). Influence of air and EGR dilutions on improving performance of a high compression ratio spark-ignition engine fueled with methanol at light load. Applied Thermal Engineering, 94, 559-567. doi:10.1016/j.applthermaleng.2015.10.046Wei, H., Zhu, T., Shu, G., Tan, L., & Wang, Y. (2012). Gasoline engine exhaust gas recirculation – A review. Applied Energy, 99, 534-544. doi:10.1016/j.apenergy.2012.05.011Ghazikhani, M., Feyz, M. E., & Joharchi, A. (2010). Experimental investigation of the Exhaust Gas Recirculation effects on irreversibility and Brake Specific Fuel Consumption of indirect injection diesel engines. Applied Thermal Engineering, 30(13), 1711-1718. doi:10.1016/j.applthermaleng.2010.03.030Al-Qurashi, K., Lueking, A. D., & Boehman, A. L. (2011). The deconvolution of the thermal, dilution, and chemical effects of exhaust gas recirculation (EGR) on the reactivity of engine and flame soot. Combustion and Flame, 158(9), 1696-1704. doi:10.1016/j.combustflame.2011.02.006Ladommatos, N., Abdelhalim, S. M., Zhao, H., & Hu., Z. (1998). Effects of EGR on Heat Release in Diesel Combustion. SAE Technical Paper Series. doi:10.4271/980184Li, T., Wu, D., & Xu, M. (2013). Thermodynamic analysis of EGR effects on the first and second law efficiencies of a boosted spark-ignited direct-injection gasoline engine. Energy Conversion and Management, 70, 130-138. doi:10.1016/j.enconman.2013.03.001Roy, M. M., Tomita, E., Kawahara, N., Harada, Y., & Sakane, A. (2011). Comparison of performance and emissions of a supercharged dual-fuel engine fueled by hydrogen and hydrogen-containing gaseous fuels. International Journal of Hydrogen Energy, 36(12), 7339-7352. doi:10.1016/j.ijhydene.2011.03.070Wang, Zhang, Wang, Han, & Chen. (2019). Numerical Simulation of Knock Combustion in a Downsizing Turbocharged Gasoline Direct Injection Engine. Applied Sciences, 9(19), 4133. doi:10.3390/app9194133Caton, J. A. (2012). The thermodynamic characteristics of high efficiency, internal-combustion engines. Energy Conversion and Management, 58, 84-93. doi:10.1016/j.enconman.2012.01.005Su, J., Xu, M., Li, T., Gao, Y., & Wang, J. (2014). Combined effects of cooled EGR and a higher geometric compression ratio on thermal efficiency improvement of a downsized boosted spark-ignition direct-injection engine. Energy Conversion and Management, 78, 65-73. doi:10.1016/j.enconman.2013.10.041Gu, X., Huang, Z., Cai, J., Gong, J., Wu, X., & Lee, C. (2012). Emission characteristics of a spark-ignition engine fuelled with gasoline-n-butanol blends in combination with EGR. Fuel, 93, 611-617. doi:10.1016/j.fuel.2011.11.040Galloni, E. (2009). Analyses about parameters that affect cyclic variation in a spark ignition engine. Applied Thermal Engineering, 29(5-6), 1131-1137. doi:10.1016/j.applthermaleng.2008.06.001Bermúdez, V., Luján, J. M., Climent, H., & Campos, D. (2015). Assessment of pollutants emission and aftertreatment efficiency in a GTDi engine including cooled LP-EGR system under different steady-state operating conditions. Applied Energy, 158, 459-473. doi:10.1016/j.apenergy.2015.08.071Park, C., Kim, S., Kim, H., & Moriyoshi, Y. (2012). Stratified lean combustion characteristics of a spray-guided combustion system in a gasoline direct injection engine. Energy, 41(1), 401-407. doi:10.1016/j.energy.2012.02.060Galindo, J., Navarro, R., Tarí, D., & Moya, F. (2020). Development of an experimental test bench and a psychrometric model for assessing condensation on a low-pressure exhaust gas recirculation cooler. International Journal of Engine Research, 22(5), 1540-1550. doi:10.1177/1468087420909735Luján, J. M., Dolz, V., Monsalve-Serrano, J., & Bernal Maldonado, M. A. (2019). High-pressure exhaust gas recirculation line condensation model of an internal combustion diesel engine operating at cold conditions. International Journal of Engine Research, 22(2), 407-416. doi:10.1177/1468087419868026Boccardi, S., Catapano, F., Costa, M., Sementa, P., Sorge, U., & Vaglieco, B. M. (2016). Optimization of a GDI engine operation in the absence of knocking through numerical 1D and 3D modeling. Advances in Engineering Software, 95, 38-50. doi:10.1016/j.advengsoft.2016.01.023Pla, B., De La Morena, J., Bares, P., & Jiménez, I. (2020). Knock Analysis in the Crank Angle Domain for Low-Knocking Cycles Detection. SAE Technical Paper Series. doi:10.4271/2020-01-0549Serrano, J., Climent, H., Navarro, R., & González-Domínguez, D. (2020). Methodology to Standardize and Improve the Calibration Process of a 1D Model of a GTDI Engine. SAE Technical Paper Series. doi:10.4271/2020-01-1008Nishiyama, A., Le, M. K., Furui, T., & Ikeda, Y. (2019). The Relationship between In-Cylinder Flow-Field near Spark Plug Areas, the Spark Behavior, and the Combustion Performance inside an Optical S.I. Engine. Applied Sciences, 9(8), 1545. doi:10.3390/app908154

Salimicrobium salexigens sp. nov., a moderately halophilic bacterium from salted hides

Two Gram-positive, moderately halophilic bacteria, designated strains 29CMIT and 53CMI, were isolated from salted hides. Both strains were non-motile, strictly aerobic cocci, growing in the presence of 3-25 % (w/v) NaCl (optimal growth at 7.5-12.5 % [w/v] NaCl), between pH 5.0 and 10.0 (optimal growth at pH 7.5) and at temperatures between 15 and 40 ºC (optimal growth at 37 ºC). Phylogenetic analysis based on 16S rRNA gene sequence comparison showed that both strains showed a similarity of 98.7 % and were closely related to species of the genus Salimicrobium, within the phylum Firmicutes. Strains 29CMIT and 53CMI exhibited 16S rRNA gene sequence similarity values of 97.9 % to 97.6 % with Salimicrobium album DSM 20748T, Salimicrobium halophilum DSM 4771T, Salimicrobium flavidum ISL-25T and Salimicrobium luteum BY-5T. The DNA G+C content was 50.7 mol% and 51.5 mol% for strains 29CMIT and 53CMI, respectively. The DNA-DNA hybridization between both strains was 98 %, whereas the values between strain 29CMIT and the species Salimicrobium album CCM 3517T, Salimicrobium luteum BY-5T, Salimicrobium flavidum ISL-25T and Salimicrobium halophilum CCM 4074T were 45 %, 28 %,

The role of the rigged Hilbert space in Quantum Mechanics

There is compelling evidence that, when continuous spectrum is present, the natural mathematical setting for Quantum Mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.Comment: 29 pages, 2 figures; a pedestrian introduction to the rigged Hilbert spac

Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity

Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physical and mathematical literature. In the cases we study, the boundary of the Siegel disk is a Jordan curve containing a critical point of the map (we consider critical maps of different orders), and there exists a natural parametrization which transforms the dynamics on the boundary into a rotation. We compute numerically this parameterization and use methods of harmonic analysis to compute the global Holder regularity of the parametrization for different maps and rotation numbers. We obtain that the regularity of the boundaries and the scaling exponents are universal numbers in the sense of renormalization theory (i.e., they do not depend on the map when the map ranges in an open set), and only depend on the order of the critical point of the map in the boundary of the Siegel disk and the tail of the continued function expansion of the rotation number. We also discuss some possible relations between the regularity of the parametrization of the boundaries and the corresponding scaling exponents. (C) 2008 American Institute of Physics.NSFMathematic

U Geminorum: a test case for orbital parameters determination

High-resolution spectroscopy of U Gem was obtained during quiescence. We did not find a hot spot or gas stream around the outer boundaries of the accretion disk. Instead, we detected a strong narrow emission near the location of the secondary star. We measured the radial velocity curve from the wings of the double-peaked H$\alpha$ emission line, and obtained a semi-amplitude value that is in excellent agreement with the obtained from observations in the ultraviolet spectral region by Sion et al. (1998). We present also a new method to obtain K_2, which enhances the detection of absorption or emission features arising in the late-type companion. Our results are compared with published values derived from the near-infrared NaI line doublet. From a comparison of the TiO band with those of late type M stars, we find that a best fit is obtained for a M6V star, contributing 5 percent of the total light at that spectral region. Assuming that the radial velocity semi-amplitudes reflect accurately the motion of the binary components, then from our results: K_em = 107+/-2 km/s; K_abs = 310+/-5 km/s, and using the inclination angle given by Zhang & Robinson(1987); i = 69.7+/-0.7, the system parameters become: M_WD = 1.20+/-0.05 M_sun,; M_RD = 0.42+/-0.04 M_sun; and a = 1.55+/- 0.02 R_sun. Based on the separation of the double emission peaks, we calculate an outer disk radius of R_out/a ~0.61, close to the distance of the inner Lagrangian point L_1/a~0.63. Therefore we suggest that, at the time of observations, the accretion disk was filling the Roche-Lobe of the primary, and that the matter leaving the L_1 point was colliding with the disc directly, producing the hot spot at this location.Comment: 36 pages, 14 figures, ccepted for publication in A

Evaluación de la sustentabilidad en agroecosistemas

Sustainability needs to be assessed by means of ordinal scales, allowing their categorization. Indicators and indexes have emerged as the basis for sustainability assessment methodologies; they have had to meet certain requirements to be useful. Among these requirements, the integration of the three dimensions of sustainability (economic, social and environmental) is essential. The evaluation is based on the use of indicators that describe a feature of the state of a system, generally through observed or estimated data, and indexes that consist of a quantitative aggregation of indicators. The indicators are generated from analysis of processes that uses environmental resources to produce results and they can be environmental or sustainability (when the factors of time, limits and objectives are considered). Indexes such as the Ecological Footprint, Human Development Index, Gross Domestic Product, among others give an idea on the extent of global inequality and the overuse of resources by the economies of some countries, but also with application to productive sectors, such as stockbreeding. A large number of indicators in agroecosystems have been defined depending on the system under study, most focusing on economic returns or productivity of the farm. Both regression equations and simulation models have been used to estimate indicators, due to the difficulty of obtaining direct measures or for the purpose of discovering the futures effects of action taken today.La sustentabilidad requiere ser valorada con el propósito final de implementar técnicas o tecnologías que mejoren o minimicen el impacto ambiental, para ello deben emplearse escalas de medición ordinales, que permitan su categorización. Indicadores e índices surgen como la base de las metodologías de evaluación de sustentabilidad, debiendo cumplir una serie de requisitos para ser de utilidad. Entre estos requisitos, la integración de las tres dimensiones de la sustentabilidad (económica, social y ambiental) es básica. La evaluación se sustenta en el empleo de indicadores que describen una característica del estado de un sistema, generalmente a través de datos observados o estimados, e índices que consisten en una agregación cuantitativa de indicadores. Los indicadores se generan del análisis de los procesos que utilizan recursos ambientales para producir resultados y pueden ser medioambientales o de sustentabilidad (cuando se tienen en cuenta los factores de tiempo, límites y objetivos) Índices como la Huella Ecológica, el Índice de Desarrollo Humano, el Producto Interno Bruto, entre otros informan tanto del grado de inequidad global como de la sobreutilización de recursos por parte de las economías de algunos países, Pero también con aplicación a sectores productivos, como por ejemplo a la ganadería.En agroecosistemas se ha definido un gran número de indicadores dependientes del sistema en estudio, la mayor parte centrados en la productividad o los retornos económicos de la explotación. Tanto ecuaciones de regresión como modelos de simulación han sido utilizados para la estimación de indicadores, debido a la dificultad de obtención de medidas directas o con el propósito de descubrir qué efectos tendrá en el futuro una medida adoptada hoy