An algebraic SU(1,1) solution for the relativistic hydrogen atom

The bound eigenfunctions and spectrum of a Dirac hydrogen atom are found taking advantage of the $SU(1, 1)$ Lie algebra in which the radial part of the problem can be expressed. For defining the algebra we need to add to the description an additional angular variable playing essentially the role of a phase. The operators spanning the algebra are used for defining ladder operators for the radial eigenfunctions of the relativistic hydrogen atom and for evaluating its energy spectrum. The status of the Johnson-Lippman operator in this algebra is also investigated.Comment: to appear in Physics Letters A (2005). We corrected a misprint in page 7, in the paragraph baggining with "With the value of ..." the ground state should be |\lambda, \lambda>, not |\lambda, \lambda+1

Spherical void expansion in rubber-like materials: The stabilizing effects of viscosity and inertia

Dynamic cavitation is known to be a typical failure mechanism in rubber-like solids. While the mechanical behaviour of these materials is generally rate-dependent, the number of theoretical and numerical works addressing the problem of cavitation using nonlinear viscoelastic constitutive models is scarce. It has been only in recent years when some authors have suggested that cavitation in rubber-like materials is a dynamic fracture process strongly affected by the rate-dependent behaviour of the material because of the large strains and strain rates that develop near the cavity. In the present work we further investigate previous idea and perform finite element simulations to model the dynamic expansion of a spherical cavity embedded into a rubber-like ball and subjected to internal pressure. To describe the mechanical behaviour of the rubber-like material we have used an experimentally calibrated constitutive model which includes rate-dependent effects and material failure. The numerical results demonstrate that inertia and viscosity play a fundamental role in the cavitation process since they stabilize the material behaviour and thus delay failure

Some Topics on the Physics of Bubble Dynamics in Beer

Besides being the favorite beverage of a large percentage of the population, a glass or bottle of beer is a test bench for a myriad of phenomena involving mass transfer, bubble-laden flows, natural convection, and many more topics of interest in Physical Chemistry. This paper summarizes some representative physical problems related to bubbles that occur in beer containers, pointing out their practical importance for the industry of beverage processing, as well as their potential connection to other processes occurring in natural sciences. More specifically, this paper describes the physics behind the sudden foam explosion occurring after a beer bottled is tapped on its mouth, gushing, buoyancy-induced motions in beer glasses, and bubble growth in stout beers.We acknowledge the support of the Spanish Ministry of Economy and Competitiveness through grants DPI2014-59292-C3-1-P and DPI2015-71901-REDT, partly funded through European Funds. We are also grateful to Jaume Lluis Tartera, from the beer company Mahou-San Miguel, for pointing out to the authors some very interesting aspects of the role of foam in beer

Kinetic study of the gas-phase reaction of atomic chlorine with a series of aldehydes

The reactions of Cl atoms with a series of unsaturated aldehydes have been investigated for the first time using a relative method. In order to obtain additional information for a qualitative structure versus reactivity discussion, we have also determined the rate coefficients for the reactions of atomic chlorine with their respective saturated aldehydes. These relative measurements were performed at room temperature and atmospheric pressure of air and N₂, by using ethane, propene and 1-butene as reference compounds. The weighted average relative rate constants obtained, k_Cl&plusmn;2&sigma; (in units of cm³ molecule^&minus;1 s^&minus;1) were: trans-2-pentenal (1.31&plusmn;0.19)&times;10^&minus;10; trans-2-hexenal (1.92&plusmn;0.22)&times;10^&minus;10; trans-2-heptenal (2.40&plusmn;0.29)&times;10^&minus;10; n-pentanal (2.56&plusmn;0.27)&times;10^&minus;10; n-hexanal (2.88&plusmn;0.37)&times;10^&minus;10; n-heptanal (3.00&plusmn;0.34)&times;10^&minus;10. <P style='line-height: 20px;'> Finally, results and atmospheric implications are discussed and compared with the reactivity with OH and NO₃ radicals

On the relation between shape imperfections of a specimen and necking growth rate under dynamic conditions

In this work, the growth rate of necks formed in dynamically loaded tensile steel samples is investigated. For that purpose, a combined experimental-numerical approach, in which the experimental results are systematically compared with finite element calculations, has been developed. The specimens have a machined sinusoidal geometrical imperfection that covers the whole gauge, introducing a characteristic wavelength in the samples. For a given cross-section diameter, specimens with 6 different gauge lengths (i.e. 6 different specimen wavelengths) were tested. Using a high-speed camera, we measured the time evolution of the radial contraction of the central section of the samples (central section of the neck), thus obtaining the growth rate of the necks. The experiments show that the speed of growth of the necks increases non-linearly with the specimen wavelength (concave-downward shape) until saturation is reached for the longest tested specimens. Numerical simulations performed for the strain rates attained in the experiments (from 900 s−1 to 2100 s−1) confirm this trend and demonstrate that the damping of short specimen wavelengths is caused by stress multiaxiality effects. Numerical simulations performed for strain rates greater than those attained in the experiments (above 7500 s−1) show that long specimen wavelengths become damped by inertia effects at sufficiently high strain rates. For strain rates greater than 7500 s−1, the maximum growth rate of the neck corresponds to an intermediate specimen wavelength defined by the joint action of stress multiaxiality and inertia on damping short and long wavelengths, respectively. Altogether, our experimental and numerical results suggest the existence of a specimen wavelength that, when inertia effects become important, determines the maximum growth rate of dynamic necks, in agreement with the predictions of the dynamic stability analyses developed by Molinari and co-workers (Fressengeas and Molinari, 1985, 1994; Mercier and Molinari, 2003, 2004).AVR and JARM are indebted to the Ministerio de Economía y Competitividad de España (Projects EUIN2015-62556 and DPI2014-57989-P) for the financial support which permitted to conduct part of this work. The research leading to these results has received funding from the European Union’s Horizon2020 Programme (Excellent Science, Marie-Sklodowska-Curie Actions) under REA grant agreement 675602 (Project OUTCOME)

Acotaciones a la visión orsiana de los fundamentos jurídicos del sistema económico capitalista

D’Ors no escribió muchas páginas sobre economía, pero tenía ideas muy claras al respecto. Entendía que el derecho era autónomo con respecto a la economía, o más bien que ésta debería estar condicionada por él. Los autores consideran que su oposición al sistema capitalista es una de las consecuencias de abordar la economía desde una perspectiva jurídica, aunque no cabe negar la razonabilidad de sus argumentos. Hay dos puntos básicamente, que le suscitan problemas: la percepción de un interés por el préstamo de dinero y la confusión entre préstamo y propiedad en el caso de las sociedades anónimas.D'Ors did not write many pages about economics but had very clear ideas about it. He understood that law was autonomous with respect to economy, or rather that economy should be conditioned by law. The authors consider that his opposition to the capitalist system is one of the consequences of approaching the economy from a legal perspective although it should not be ignored the reasonableness of d’Ors arguments. There are basically two issues that are problematics for him: the perception of an interest in the loan of money and the confusion between loan and property in the case of corporations

Dynamic Necking of Notched Tensile Bars: An Experimental Study

The mechanics of necking inception in dynamically-stretched notched specimens have been investigated. For that task, a systematic experimental campaign of quasi-static and dynamic tensile tests on martensitic steel specimens has been conducted. Samples with and without notches have been considered. Unlike the quasi-static tests, the dynamically-tested notched samples revealed that, under certain loading conditions, flow localization may develop away from the groove. The experimental results presented in this investigation show that the presence of sharp geometrical imperfections in ductile materials subjected to dynamic loading does not necessarily dictate the necking and fracture locus.D. Rittel acknowledges the support of Carlos III University with a Cátedra de Excelencia funded by Banco Santander during academic year 2011–2012. The researchers of the University Carlos III of Madrid are indebted to the Ministerio de Ciencia e Innovación de España (Projects DPI/2011-24068 and DPI/2011-23191) for the financial support.Publicad

Periocular Myxoma in a Child

Myxomas are locally invasive, benign mesenchymal neoplasms with odontogenic, osteogenic, or soft tissue origin. Facial myxomas probably account for less than 0.5% of all paranasal sinus and nasal tumors. We report a case of a left painless periocular mass in a 11-month-old girl. The lesion was resected with a clinical diagnosis of lacrimal sac tumor. Histopathology and immunohistochemistry proved the tumor to be a myxoma. There has been no recurrence after 4 years of followup. Midfacial myxomas should be differentiated from other benign and malignant tumors such as dermoid, hamartoma, neurofibroma, nasolacrimal duct cyst, and sarcomas in particular embryonal rhabdomyosarcoma. Because of the infiltrative nature of these tumors, a wide surgery is required to achieve clear resection margins and avoid recurrence

Orchestrating learning analytics (OrLA): Supporting inter-stakeholder communication about adoption of learning analytics at the classroom level

© 2019 Australasian Journal of Educational Technology. Despite the recent surge of interest in learning analytics (LA), their adoption in everyday classroom practice is still slow. Knowledge gaps and lack of inter-stakeholder communication (particularly with educational practitioners) have been posited as critical factors for previous LA adoption failures. Yet, what issues should researchers, practitioners and other actors communicate about, when considering the adoption of an LA innovation in a particular context? We reviewed and synthesised existing literature on four focus areas related to LA, their adoption, implications for practice, and more general factors that have emerged as crucial when studying everyday classroom adoption of technologies (i.e., classroom orchestration). This synthesis resulted in two conversational frameworks and an inter-stakeholder communication tool. These can be used to guide and support conversations and decision-making about the adoption of LA innovations. We illustrate their usefulness with examples of use in ongoing LA adoption processes in Australia, Spain and Estonia

Biohydrogen production from diary processing wastewater by anaerobic biofilm reactors

Fermentative hydrogen production was studied in packed bed batch reactors to assess the influence of environmental factors over yield hydrogen production from dairy wastewater. Dried stems of Opuntia imbricata were used as substratum adding a pretreated mixed culture for biofilm formation. Experimental results showed that, yield hydrogen production was significantly affected by initial COD concentration, temperature and dairy wastewater pH. Maximum yield obtained was 12.73 mM H2/g CODc when initial COD concentration was 21.1 g COD, dairy wastewater pH with no adjustment (11.32) and room temperature of 16 ± 3°C. Methane production was completely inhibit at an initial pH of 4 at all temperature studied (final pH 4.06), meanwhile, with an initial pH of 11.32, with exception for 16°C, methanogenic activity was not completely inhibit when final pH was over 5, showing an increase in methane production of 0.35 to 0.75 g CH4/l for 35 to 55°C.Key words: Biofilm, dairy wastewater, hydrogen, Opuntia imbricat