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

Biomass accumulation in mombasa guineagrass plants under different levels of nitrogen supply and plant densities

The objective of this study was to evaluate the effect of different levels of nitrogen supply and plants densities in the productivity of mombasa guineagrass (Panicum maximum) in the period of establishment. The design was of completely randomized blocks, with 12 treatments and three repetitions, with four nitrogen supplies (absence of application, 80, 160 and 320 kg/ha.year) and three plant densities (9, 25 and 49 plants/m²). The plot was cut at 30 cm from the ground when the sward high intercepted 95% of light. The following items were evaluated: sward height at 95% light interception, interval and number of cuts, dry mass production, total dry mass of leaves, stems and dead material and the morphologic composition. Nitrogen increased the dry mass production and the dry mass of stem in winter and summer, and decreased in the fall. The total dry mass of leaf presented decrease of 19% in the summer between the smallest and biggest densities in the 320 kg/ha. The dry mass of dead material had negative effect of the density in the fall. The leaf percentage increased 88% between the smallest and largest nitrogen level at the plant density of 49 plants/m². Only density influenced the sward height in the condition of 95% of light interception. The number of cuts increased with nitrogen levels in the fall, spring and summer, while the interval of cuts decreased with fertilization in the spring and summer. Nitrogen increases the production of mombasa guineagrass in each cycle

Características morfogênicas e estruturais do capim-tifton 85 sob doses de nitrogênio e alturas de corte

Objetivou-se avaliar características morfogênicas e estruturais do capim-tifton 85 adubado com nitrogênio nas doses de 0, 33, 66, 100 ou 133 kg/ha.ano em três alturas à data de corte (30, 40 ou 50 cm). O delineamento foi inteiramente casualizado em esquema de parcelas subdivididas com três repetições. As doses de nitrogênio (N) corresponderam às parcelas e as alturas ao tempo de corte, às subparcelas. A taxa de aparecimento foliar do capim-tifton 85 foi influenciada de forma negativa pela altura da planta na época do corte e de maneira positiva pela dose de nitrogênio. A taxa de senescência foliar e o número total de folhas por perfilho diminuíram, enquanto a taxa de alongamento foliar aumentou com a adubação nitrogenada. Por outro lado, a taxa de senescência foliar e o número total de folhas por perfilho aumentaram com a altura das plantas na época da colheita. Já o número de folhas vivas por perfilho não foi influenciado pela dose de nitrogênio nem pela altura da planta na época do corte. Para uma mesma altura do capim-tifton 85 na época da colheita, a adubação nitrogenada aumenta o fluxo de tecidos e a frequência de desfolhação. Na condição de desfolhação intermitente, o capim-tifton 85 deve ser colhido com altura de até 30 cm.The objective of this study was to evaluate the morphogenic and structural characteristics of tifton 85 bermudagrass under different nitrogen doses (0, 33, 66, 100 or 133 kg/ha.year of N) and three different plant heights (30, 40 or 50 cm) at harvesting time. A split plot scheme in a completely randomized design with three replications was used. The nitrogen (N) doses stood for the portions and the haversting heights, for the subportions. The leaf appearance rate of tifton 85 bermudagrass was negatively influenced by plant height at harvesting time, but positively influenced by N dose. Leaf senescence rate and total number of leaves per tiller decreased, whereas leaf elongation rate increased with nitrogen fertilization. On the other hand, leaf senescence rates and total leaf number per tiller increased according to the plant height at harvesting time. Contrarily, the number of green leaf per tiller was not influenced by N dose or plant height at harvesting time. For the same height of 'tifton 85' bermudagrass at harvesting time, nitrogen fertilization increases tissues flux and defoliation frequency. Under intermittent defoliation conditions, 'tifton 85' bermudagrass should be harvested at 30 cm of height

Crescimento do capim-tifton 85 sob doses de nitrogênio e alturas de corte

Objetivou-se avaliar os índices de crescimento do capim-tifton 85 adubado com quatro doses de nitrogênio (0, 33, 66, 100, e 133 kg/ha de N) e colhido em três alturas da planta (30, 40 e 50 cm). O delineamento experimental utilizado foi inteiramente casualizado em esquema de parcelas subdivididas com três repetições. As doses de nitrogênio corresponderam às parcelas e as alturas na data de corte, às subparcelas. Para todas as variáveis analisadas, a interação dose de N × altura da planta não foi significativa. A taxa assimilatória líquida e a taxa de crescimento relativo do capim-tifton 85 aumentaram com as doses de nitrogênio. A razão de área foliar (RAF) decresceu linearmente com a altura de corte das plantas, mas aumentou, também de forma linear, com a dose de nitrogênio. De modo linear, a razão de peso foliar decresceu com a altura de corte da planta forrageira e aumentou com a dose de nitrogênio. A área foliar específica do capim-tifton 85 foi influenciada de forma linear e positiva apenas pela adubação nitrogenada. O índice de área foliar (IAF) do capim-tifton 85 aumentou cerca de 0,05 unidade a cada centímetro de incremento na altura de corte das plantas. Houve resposta quadrática da dose de nitrogênio no IAF do capim-tifton 85. O acréscimo na altura do capim-tifton 85 na época do corte reduz a participação de lâmina foliar na forragem. A adubação nitrogenada aumenta a taxa de crescimento do capim-tifton 85, portanto, para assegurar colheita eficiente da forragem, ao aumentar a dose de nitrogênio, é necessário reduzir o intervalo de colheita.The objective this study was to evaluate the growth rates of Tifton 85 bermudagrass under four nitrogen levels (0, 33, 66, 100, and 133 kg/ha N) and harvested at three plant heights (30, 40 and 50 cm). The experimental design was completely randomized in a split plot scheme with three replications. Nitrogen rates were set in the plots and plants heights in the subplots. For all variables, the interaction N rate × plant height was not significant. The net assimilatory rate and relative growth rate of Tifton 85 increased with increasing N rates. The leaf area ratio (LAR) decreased linearly with plant height at harvesting. In contrast, the LAR increased linearly with N rate. Linearly, the leaf weight ratio decreased with plant height at harvesting, and increased with N rate. The specific leaf area of Tifton 85 bermudagrass was influenced linear and positively only by nitrogen fertilization. The leaf area index (LAI) of Tifton 85 bermudagrass increased by about 0.05 unit for each centimeter increase in plant height at harvesting. There was a quadratic response of N in LAI of Tifton 85 bermudagrass. The increase of bermudagrass height at harvesting season decreases the participation of leaf blade in the forage. The nitrogen increases the growth rate of Tifton 85 bermudagrass. To ensure efficient harvesting of forage, the increase of N rate for Tifton 85 Bermudagrass implies a reduction in the harvest interval