3,883 research outputs found
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions
We derive the energy levels associated with the even-parity wave functions of
the harmonic oscillator with an additional delta-function potential at the
origin. Our results bring to the attention of students a non-trivial and
analytical example of a modification of the usual harmonic oscillator
potential, with emphasis on the modification of the boundary conditions at the
origin. This problem calls the attention of the students to an inaccurate
statement in quantum mechanics textbooks often found in the context of solution
of the harmonic oscillator problem.Comment: 9 pages, 3 figure
Argon assisted chemical vapor deposition of CrO: an efficient process leading to high quality epitaxial films
A comparative study of the structural, microstructural and magnetic
properties of CrO thin films grown onto (110) and (100) TiO rutile
single crystal substrates by chemical vapor deposition (CVD), using CrO as
chromium precursor and either oxygen or argon as carrier gas is presented. Our
results show that growth under argon carrier gas leads to high quality CrO
epilayers with structural and magnetic properties similar to those obtained
using the more standard oxygen carrier gas. Furthermore, we interpret the
larger magnetic coercivity observed for the (110) oriented films in terms of
their microstructure, in particular of the highest strain and edge roughness of
the building structures of the CrO epilayers, which are settled by the
substrate crystallographic orientation.Comment: 27 pages, 2 tables, 8 figure
Towards absolute calibration of optical tweezers
Aiming at absolute force calibration of optical tweezers, following a
critical review of proposed theoretical models, we present and test the results
of MDSA (Mie-Debye-Spherical Aberration) theory, an extension of a previous
(MD) model, taking account of spherical aberration at the glass/water
interface. This first-principles theory is formulated entirely in terms of
experimentally accessible parameters (none adjustable). Careful experimental
tests of the MDSA theory, undertaken at two laboratories, with very different
setups, are described. A detailed description is given of the procedures
employed to measure laser beam waist, local beam power at the transparent
microspheres trapped by the tweezers, microsphere radius and the trap
transverse stiffness, as a function of radius and height in the (inverted
microscope) sample chamber. We find generally very good agreement with MDSA
theory predictions, for a wide size range, from the Rayleigh domain to large
radii, including the values most often employed in practice, and at different
chamber heights, both with objective overfilling and underfilling. The results
asymptotically approach geometrical optics in the mean over size intervals, as
they should, and this already happens for size parameters not much larger than
unity. MDSA predictions for the trapping threshold, position of stiffness peak,
stiffness variation with height, multiple equilibrium points and `hopping'
effects among them are verified. Remaining discrepancies are ascribed to focus
degradation, possibly arising from objective aberrations in the infrared, not
yet included in MDSA theory.Comment: 15 pages, 20 figure
Identificação de modelos no conteúdo de estrutura atômica nos livros de Química geral do ensino superior
Na literatura científica poucos são os trabalhos que abordam Livros Textos nos cursos de Química Geral de diversas IES do Brasil, ao contrário do que ocorre com os Livros Didáticos no Ensino Médio. Este trabalho analisou os modelos apresentados no conteúdo de Estrutura da Matéria e como estes podem influenciar na formação dos modelos mentais dos alunos. Esta pesquisa foi realizada pela metodologia de Análise de Conteúdo e chegou-se a conclusão de que os Livros Texto utilizam muitos modelos porém de natureza diferente daqueles dos livros do ensino básico
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Aplicação de Análise e Modelagem Multidimensional para o Monitoramento de Resíduos Sólidos Industriais
Prominent effect of soil network heterogeneity on microbial invasion
Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil
Attractor Modulation and Proliferation in 1+ Dimensional Neural Networks
We extend a recently introduced class of exactly solvable models for
recurrent neural networks with competition between 1D nearest neighbour and
infinite range information processing. We increase the potential for further
frustration and competition in these models, as well as their biological
relevance, by adding next-nearest neighbour couplings, and we allow for
modulation of the attractors so that we can interpolate continuously between
situations with different numbers of stored patterns. Our models are solved by
combining mean field and random field techniques. They exhibit increasingly
complex phase diagrams with novel phases, separated by multiple first- and
second order transitions (dynamical and thermodynamic ones), and, upon
modulating the attractor strengths, non-trivial scenarios of phase diagram
deformation. Our predictions are in excellent agreement with numerical
simulations.Comment: 16 pages, 15 postscript figures, Late
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