Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0

A detailed study of the group of symmetries of the time-dependent free particle Schrödinger equation in one space dimension is presented. An orbit analysis of all first order symmetries is seen to correspond in a well-defined manner to the separation of variables of this equation. The study gives a unified treatment of the harmonic oscillator (both attractive and repulsive), Stark effect, and free particle Hamiltonians in the time dependent formalism. The case of a potential c/x2 is also discussed in the time dependent formalism. Use of representation theory for the symmetry groups permits simple derivation of expansions relating various solutions of the Schrödinger equation, several of which are new

Models of electron transport in single layer graphene

The main features of the conductivity of doped single layer graphene are analyzed, and models for different scattering mechanisms are presented.Comment: 15 pages. Submitted to the Proceedings of the ULTI symposium on Quantum Phenomena and Devices at Low Temperatures, Espoo, Finland, to be published in the Journ. of Low. Temp. Phy

Adaptation of the generic PDE's results to the notion of prevalence

Many generic results have been proved, especially concerning the qualitative behaviour of solutions of partial differential equations. Recently, a new notion of "almost always", the prevalence, has been developped for vectorial spaces. This notion is interesting since, for example, prevalence sets are equivalent to the full Lebesgue measure sets in finite dimensional spaces. The purpose of this article is to adapt the generic PDE's results to the notion of prevalence. In particular, we consider the cases where Sard-Smale theorems or arguments of analytic perturbations of the parameters are used

Rainfall interception modelling: is the wet bulb approach adequate to estimate mean evaporation rate from wet/saturated canopies in all forest types?

The Penman–Monteith equation has been widely used to estimate the maximum evaporation rate (E) from wet/saturated forest canopies, regardless of canopy cover fraction. Forests are then represented as a big leaf and interception loss considered essentially as a one-dimensional process. With increasing forest sparseness the assumptions behind this big leaf approach become questionable. In sparse forests it might be better to model E and interception loss at the tree level assuming that the individual tree crowns behave as wet bulbs (‘‘wet bulb approach”). In this study, and for five different forest types and climate conditions, interception loss measurements were compared to modelled values (Gash’s interception model) based on estimates of E by the Penman–Monteith and the wet bulb approaches. Results show that the wet bulb approach is a good, and less data demanding, alternative to estimate E when the forest canopy is fully ventilated (very sparse forests with a narrow canopy depth). When the canopy is not fully ventilated, the wet bulb approach requires a reduction of leaf area index to the upper, more ventilated parts of the canopy, needing data on the vertical leaf area distribution, which is seldom-available. In such cases, the Penman–Monteith approach seems preferable. Our data also show that canopy cover does not per se allow us to identify if a forest canopy is fully ventilated or not. New methodologies of sensitivity analyses applied to Gash’s model showed that a correct estimate of E is critical for the proper modelling of interception loss

Photoionization of ultracold and Bose-Einstein condensed Rb atoms

Photoionization of a cold atomic sample offers intriguing possibilities to observe collective effects at extremely low temperatures. Irradiation of a rubidium condensate and of cold rubidium atoms within a magneto-optical trap with laser pulses ionizing through 1-photon and 2-photon absorption processes has been performed. Losses and modifications in the density profile of the remaining trapped cold cloud or the remaining condensate sample have been examined as function of the ionizing laser parameters. Ionization cross-sections were measured for atoms in a MOT, while in magnetic traps losses larger than those expected for ionization process were measured.Comment: 9 pages, 7 figure

Klein tunneling in graphene: optics with massless electrons

This article provides a pedagogical review on Klein tunneling in graphene, i.e. the peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two simple situations in detail: a massless Dirac electron incident either on a potential step or on a potential barrier and use elementary quantum wave mechanics to obtain the transmission probability. We emphasize the connection to related phenomena in optics, such as the Snell-Descartes law of refraction, total internal reflection, Fabry-P\'erot resonances, negative refraction index materials (the so called meta-materials), etc. We also stress that Klein tunneling is not a genuine quantum tunneling effect as it does not necessarily involve passing through a classically forbidden region via evanescent waves. A crucial role in Klein tunneling is played by the conservation of (sublattice) pseudo-spin, which is discussed in detail. A major consequence is the absence of backscattering at normal incidence, of which we give a new shorten proof. The current experimental status is also thoroughly reviewed. The appendix contains the discussion of a one-dimensional toy model that clearly illustrates the difference in Klein tunneling between mono- and bi-layer graphene.Comment: short review article, 18 pages, 14 figures; v3: references added, several figures slightly modifie

Kaluza-Klein Cosmology With Modified Holographic Dark Energy

We investigate the compact Kaluza-Klein cosmology in which modified holographic dark energy is interacting with dark matter. Using this scenario, we evaluate equation of state parameter as well as equation of evolution of the modified holographic dark energy. Further, it is shown that the generalized second law of thermodynamics holds without any constraint.Comment: 13 pages, accepted for publication in Gen. Relativ. Gravi

Length of carotid stenosis predicts peri-procedural stroke or death and restenosis in patients randomized to endovascular treatment or endarterectomy.

BACKGROUND: The anatomy of carotid stenosis may influence the outcome of endovascular treatment or carotid endarterectomy. Whether anatomy favors one treatment over the other in terms of safety or efficacy has not been investigated in randomized trials. METHODS: In 414 patients with mostly symptomatic carotid stenosis randomized to endovascular treatment (angioplasty or stenting; n = 213) or carotid endarterectomy (n = 211) in the Carotid and Vertebral Artery Transluminal Angioplasty Study (CAVATAS), the degree and length of stenosis and plaque surface irregularity were assessed on baseline intraarterial angiography. Outcome measures were stroke or death occurring between randomization and 30 days after treatment, and ipsilateral stroke and restenosis ≥50% during follow-up. RESULTS: Carotid stenosis longer than 0.65 times the common carotid artery diameter was associated with increased risk of peri-procedural stroke or death after both endovascular treatment [odds ratio 2.79 (1.17-6.65), P = 0.02] and carotid endarterectomy [2.43 (1.03-5.73), P = 0.04], and with increased long-term risk of restenosis in endovascular treatment [hazard ratio 1.68 (1.12-2.53), P = 0.01]. The excess in restenosis after endovascular treatment compared with carotid endarterectomy was significantly greater in patients with long stenosis than with short stenosis at baseline (interaction P = 0.003). Results remained significant after multivariate adjustment. No associations were found for degree of stenosis and plaque surface. CONCLUSIONS: Increasing stenosis length is an independent risk factor for peri-procedural stroke or death in endovascular treatment and carotid endarterectomy, without favoring one treatment over the other. However, the excess restenosis rate after endovascular treatment compared with carotid endarterectomy increases with longer stenosis at baseline. Stenosis length merits further investigation in carotid revascularisation trials

From thermal rectifiers to thermoelectric devices

We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.Comment: 42 pages, 22 figures, review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Efeito do ensacamento dos frutos no controle de pragas e doenças e na qualidade e maturação de maçãs ‘Fuji Suprema’.

O objetivo deste trabalho foi avaliar a eficiência de embalagens de diferentes materiais para a proteção contra pragas e doenças e seu efeito sobre a qualidade físico-química, maturação e teor de cálcio (Ca) em maçãs ‘Fuji Suprema’. O experimento foi desenvolvido nas safras de 2007/2008 e 2008/2009, em pomar manejado sob o sistema orgânico, localizado na região de São Joaquim (SC). O pomar era composto por plantas de dez anos de idade da cultivar Fuji Suprema, sobre porta-enxerto ‘Marubakaido’, com interenxerto ‘EM-9’. Depois do raleio manual, aproximadamente 40 dias após a plena floração, os frutos foram ensacados com embalagens plásticas transparentes microperfuradas ou de tecido não texturizado (TNT). Os frutos foram mantidos ensacados até a colheita. A testemunha foi constituída por frutos não ensacados. Na colheita, os frutos foram avaliados quanto aos danos provocados por mosca-das-frutas (Anastrepha fraterculus), mariposa oriental (Grapholita molesta) e lagarta enroladeira (Bonagota salubricola). As doenças foram avaliadas pela incidência de sarna da macieira (Venturia inaequalis), podridão amarga (Colletotrichum gloeosporioides) e podridão carpelar (Alternaria sp., Fusarium sp.). Também foi avaliada a incidência de distúrbios fisiológicos “russeting” e “bitter pit”, atributos físico-químicos de maturação e qualidade e o teor de Ca nos frutos. Independentemente do tipo de embalagem verificou-se que o ensacamento é prática eficaz na proteção contra o ataque de insetos, mas não reduz a incidência e o desenvolvimento de doenças nos frutos. Na safra de 2008/2009, o ensacamento dos frutos aumentou o teor de Ca e reduziu a incidência de “bitter pit”, e aumentou a incidência do “russeting”. O ensacamento dos frutos antecipou a maturação, especialmente com embalagem plástica transparente microperfurada, e reduziu a coloração vermelha, especialmente com embalagem TNT