1,834 research outputs found
Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx âc/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 PenmanâMonteith 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 (ââwet bulb approachâ). In this study, and for five different forest types and climate conditions, interception loss measurements were compared to modelled values (Gashâs interception model) based on estimates of E by the PenmanâMonteith 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 PenmanâMonteith 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 Gashâs 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; nâ=â213) or carotid endarterectomy (nâ=â211) 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 â„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), Pâ=â0.02] and carotid endarterectomy [2.43 (1.03-5.73), Pâ=â0.04], and with increased long-term risk of restenosis in endovascular treatment [hazard ratio 1.68 (1.12-2.53), Pâ=â0.01]. 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 Pâ=â0.003). 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 âFuji Supremaâ.
O objetivo deste trabalho foi avaliar a eficiĂȘncia de embalagens de diferentes materiais para a proteção contra pragas e doenças e seu efeito sobre a qualidade fĂsico-quĂmica, maturação e teor de cĂĄlcio (Ca) em maçãs âFuji Supremaâ. O experimento foi desenvolvido nas safras de 2007/2008 e 2008/2009, em pomar manejado sob o sistema orgĂąnico, localizado na regiĂŁo de SĂŁo Joaquim (SC). O pomar era composto por plantas de dez anos de idade da cultivar Fuji Suprema, sobre porta-enxerto âMarubakaidoâ, com interenxerto âEM-9â. Depois do raleio manual, aproximadamente 40 dias apĂłs a plena floração, os frutos foram ensacados com embalagens plĂĄsticas transparentes microperfuradas ou de tecido nĂŁo texturizado (TNT). Os frutos foram mantidos ensacados atĂ© a colheita. A testemunha foi constituĂda por frutos nĂŁo 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 incidĂȘncia de sarna da macieira (Venturia inaequalis), podridĂŁo amarga (Colletotrichum gloeosporioides) e podridĂŁo carpelar (Alternaria sp., Fusarium sp.). TambĂ©m foi avaliada a incidĂȘncia de distĂșrbios fisiolĂłgicos ârussetingâ e âbitter pitâ, atributos fĂsico-quĂmicos de maturação e qualidade e o teor de Ca nos frutos. Independentemente do tipo de embalagem verificou-se que o ensacamento Ă© prĂĄtica eficaz na proteção contra o ataque de insetos, mas nĂŁo reduz a incidĂȘncia e o desenvolvimento de doenças nos frutos. Na safra de 2008/2009, o ensacamento dos frutos aumentou o teor de Ca e reduziu a incidĂȘncia de âbitter pitâ, e aumentou a incidĂȘncia do ârussetingâ. O ensacamento dos frutos antecipou a maturação, especialmente com embalagem plĂĄstica transparente microperfurada, e reduziu a coloração vermelha, especialmente com embalagem TNT
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