Nonlinear Methods and Chaos

Arfken, George B.; Weber, H. J.

doi:10.1016/b978-0-12-059815-1.50023-2

Cited by 170 publications

(236 citation statements)

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“…The validity of the infinite product expansion follows from general properties of entire functions [12]. Let us then define the generalized Rayleigh function ‡…”

Section: Generalized Rayleigh Functionsmentioning

confidence: 99%

“…To the best of the author's knowledge, this questions has never been raised before. The derivation outlined in this article is based on the expansion of entire functions as an infinite product [12]. This approach, originally developed by Euler and Rayleigh [13], has been extended recently by Muldoon and collaborators to derive convolution formulas for Rayleigh functions [14,15].…”

Section: Introductionmentioning

confidence: 99%

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A note on confined diffusion

Bickel

2007

Physica A: Statistical Mechanics and its Applications

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Abstract.The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion operator. Unfortunately, the latter depend on space dimensionality and on the particular shape of the domain, and an analytical expression is in most circumstances not available. In this article, it is shown that the series may in some circumstances sum up exactly. Explicit calculations are performed for 2D diffusion restricted to a circular domain and 3D diffusion inside a sphere. In both cases, the short-time behaviour of the mean square displacement is obtained.

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“…The validity of the infinite product expansion follows from general properties of entire functions [12]. Let us then define the generalized Rayleigh function ‡…”

Section: Generalized Rayleigh Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A note on confined diffusion

Bickel

2007

Physica A: Statistical Mechanics and its Applications

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“…The problem can thus be treated in this approach only numerically, which requires a long computation time. Similar difficulties are encountered in other methods that directly solve Maxwell's equations, such as the finite element method (FEM) [22][23][24], finite-difference time-domain (FDTD) method [25,26], small perturbation method (SPM) [27]. Moreover, taking into account the interaction between a layer of nanoparticles and the substrate adds considerable complexity to the computation process or requires a number of approximations, e.g., averaging of the refractive indices of the substrate and environment [28], which can be done by different procedures, or the introduction of an imaginary nanostructured layer, a reflection of the real layer [18].…”

Section: Introductionmentioning

confidence: 83%

“…In this case, to calculate the reflection and transmission spectra of the system with these parameters, the exact electrodynamics finite element method [22][23][24][25][26][27][28][29][30][31][32][33][34] is used in order to exclude the effect of made approximation (2) and the absence of multipole terms in the nanoparticle interaction tensor (6) (which are significant for the considered case of touching spheres) on the result. According to [29], for such geometrical parameters of the nanoaggregate, the considered analytical approach can be used only for estimating investigations.…”

Section: Condition Of the Total Blooming Of A Substratementioning

confidence: 99%

Optical Antireflection of a Medium by Nanostructural Layers

Shalin¹

2011

PIER B

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Abstract-This work examines reflection of a light from a semiinfinite medium which is modified with an ordered monolayer of spherical nanoparticles placed on or under its surface. We derive analytical expressions for the electric fields within and outside such structures and verify them with help of strict numerical simulations. We show that nanoparticles layer acts as an imaginary zero-thickness surface having complicated non-Fresnel reflection coefficients with wavelength dependent phase shift. It is shown that such monolayers may reduce reflection relative to reflection from a pure substrate surface. We derive and analyse a zero-reflection condition in the simple intuitive form. It is shown that a single layer of nanocavities near the medium-vacuum interface may increase the transparency of a dielectric medium to values close to 100% in a wide wavelength range.

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“…24 The spectra were then range autoscaled and truncated to select the region around the amide I band (~1680 cm -1 ), the principal region of interest for 2D analyses. 25,26 Computer programs…”

Section: Spectra Pre-processingmentioning

confidence: 99%

Two-dimensional low resolution raman spectroscopy applied to fast discrimination of clinically relevant microorganisms: a whole-organism fingerprinting approach

Mello¹,

Ciuffi²,

Nassar³

et al. 2006

J. Braz. Chem. Soc.

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A diferenciação de bactérias causadoras de gastrenterites através de métodos microbiológicos clássicos é muito eficiente, na maior parte dos casos. Todavia, o elevado custo dos reagentes e o tempo necessário para tais determinações, cerca de 4 dias, podem causar sérias conseqüências, quando os pacientes são crianças, idosos ou adultos com baixa resistência imunológica. Assim, a pesquisa por métodos espectroscópicos de baixo custo, que permitam tais determinações com pouco uso de reagentes e em curtos intervalos de tempo é extremamente relevante. Neste trabalho os principais microrganismos causadores de gastrenterites, E. coli, S. chroleraesuis, S. flexneri foram avaliados. Foram preparadas sessenta dispersões para cada um dos microrganismos, usando solução fisiológica como solvente, e seus espectros adquiridos. Os espectros obtidos foram muito similares, tornando muito difícil a diferenciação dos microrganismos. Entretanto, aplicando a teoria de correlação generalizada em 2D, foi possível diferenciar os microrganismos avaliados usando o espectro síncrono como "impressão digital do organismo" em um curto intervalo de tempo (~10h).The discrimination of the bacteria that cause gastroenteritis through classical microbiological methods is very efficient in the great majority of the cases. However, the high cost of chemicals and the time spent for such identifications, about four days, could generate serious consequences for the patients. Thus, the search for low cost spectroscopic methods which would allow a fast and reagentless discrimination of these microorganisms is extremely relevant. In this work the main microorganisms that cause gastroenteritis: E. coli, S. chroleraesuis, S. flexneri were studied. For each of the microorganisms sixty different dispersions were prepared using physiological solution as solvent and its Raman spectra recorded. The 1D spectra obtained were similar, making it very difficult to differentiate the microorganisms. However, applying the 2D correlation method, it was possible to identify the microorganisms evaluated using the synchronous spectrum as "whole-organism fingerprinting" in a reduced time interval (~10 h).

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Nonlinear Methods and Chaos

Cited by 170 publications

References 1 publication

A note on confined diffusion

A note on confined diffusion

Optical Antireflection of a Medium by Nanostructural Layers

Two-dimensional low resolution raman spectroscopy applied to fast discrimination of clinically relevant microorganisms: a whole-organism fingerprinting approach

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