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## ‣ Difusão de spins nucleares em meios porosos - uma abordagem computacional da RMN; Nuclear spin diffusion in porous media - a computational approach of NMR

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 19/02/2015
Português

Relevância na Pesquisa

67.71082%

#Computational modeling#Diffusion#Difusão#Modelagem computacional#NMR in porous media#Nuclear relaxation#Relaxação nuclear#RMN em meios porosos

A Ressonância Magnética Nuclear (RMN) é uma importante técnica empregada nas principais áreas de conhecimento, tais como, Física, Química e Medicina. Importantes trabalhos da RMN aplicada ao estudo da dinâmica de moléculas em fluidos presentes em meios porosos permitiram que esta técnica ganhasse também notoriedade na indústria do petróleo. O presente projeto é fundamentado em alguns destes trabalhos seminais, reproduzindo, através de modelos físico-computacionais, os principais efeitos físicos da difusão e a consequente relaxação dos spins dos núcleos atômicos presentes nas moléculas dos fluidos imersos nos meios porosos. Os métodos teóricos utilizados para a interpretação dos parâmetros de relaxação transversal (T2) e longitudinal (T1), levam em consideração as propriedades macroscópicas da dinâmica de um ensemble de spins nucleares. Para a compreensão da difusão e relaxação nuclear em meios porosos, é de fundamental importância o emprego de métodos físico-computacionais que levam em consideração tanto a microestrutura quanto a difusão translacional dos spins nucleares através desses meios. Dentro dos modelos propostos nesta dissertação, foram utilizados conceitos básicos de mecânica estatística e de relaxação nuclear...

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## ‣ Processamento digital de sinais aplicado a análise de distribuição de tempos de relaxação em sinais de ressonância magnética nuclear; Digital signal processing applied to relaxation times distribution analysis in nuclear magnetic resonance signals

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 03/06/2015
Português

Relevância na Pesquisa

68.373364%

#Digital signal processing#Equações integrais de Fredholm#Fredholm integral equations#Meios porosos#Nuclear magnetic ressonance#Porous media#Processamento digital de sinais#Ressonância magnética nuclear

Sabe-se que a relaxação de líquidos em meios porosos envolve três mecanismos principais: relaxação bulk, relaxação de superfície e difusão. Muitas vezes, os processos de relaxação de líquidos confinados em meios porosos são dominados pelo processo de relaxação de superfície e difusão do fluído. No chamado regime de difusão rápida, a relaxação de um único poro é comandada por uma função mono exponencial que depende, principalmente, da relação superfície-volume do poro, de modo que em um material poroso, isto é, contendo uma distribuição ampla de tamanho de poros, o sinal de decaimento de magnetização obtido por meio da ressonância magnética nuclear é formado pela soma de exponenciais com diferentes tempos de relaxação. O problema-chave abordado neste trabalho consiste, portanto, em obter por meio desse sinal de magnetização a distribuição dos tempos de relaxação que controlam o decaimento das funções mono-exponenciais. Matematicamente...

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## ‣ Fractal approach to ac impedance spectroscopy studies of ceramic materials

Fonte: Universidade Estadual Paulista
Publicador: Universidade Estadual Paulista

Tipo: Artigo de Revista Científica
Formato: 89-94

Português

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67.81127%

#Ceramics#Fractal#Grain boundary#Impedance spectroscopy#Model#Calculations#Carrier mobility#Charge carriers#Electric conductivity of solids#Electric impedance#Fractals

A novel fractal model for grain boundary regions of ceramic materials was developed. The model considers laterally inhomogeneous distribution of charge carriers in the vicinity of grain boundaries as the main cause of the non-Debye behaviour and distribution of relaxation times in ceramic materials. Considering the equivalent circuit the impedance of the grain boundary region was expressed. It was shown that the impedance of the grain boundary region has the form of the Davidson-Cole equation. The fractal dimension of the inhomogeneous distribution of charge carriers in the region close to the grain boundaries could be calculated based on the relation ds = 1 + β, where β is the constant from the Davidson-Cole equation.

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## ‣ Relaxation time distribution analysis of a polymer electrolyte fuel cell stack from its impedance response

Fonte: Laboratório Nacional de Energia e Geologia
Publicador: Laboratório Nacional de Energia e Geologia

Tipo: Conferência ou Objeto de Conferência

Publicado em 10/11/2011
Português

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#Distribution of relaxation times#Electrochemical impedance spectroscopy#Proton exchange membrane fuel cell

Electrochemical impedance spectroscopy (EIS) is an analysis technique that is commonly used as a base diagnostics technique for the in-situ analysis of the kinetic and transport properties of proton exchange membrane (PEM) fuel cells. This work proposes to use the distribution of relaxation times (DRT) as a complementary analysis technique for the interpretation of EIS data. For this purpose, the DRT is deduced for a modified Randles electric circuit composed of a constant phase element (CPE) connected in parallel with a resistance in series with a finite diffusion Warburg element. The experimental EIS data collected from an eight cell PEMFC with an open-air cathode was modeled through the use of two modified Randles circuit representing the fuel-cell electrodes. The analysis of the DRT allows to identify further characteristics of the individual processes that occur at both electrodes, while also being instrumental in detecting the effect on the fuel cell performance of some operating conditions, namely hydrogen flow-rate and current.

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## ‣ Assessing cell polarity reversal degradation phenomena in PEM fuel cells by electrochemical impedance sectroscopy

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

Publicado em //2013
Português

Relevância na Pesquisa

87.70699%

#PEM fuel cells#Degradation mechanisms#Fuel starvation#Catalyst loss#Electrochemical impedance#Spectroscopy#Distribution of relaxation times

Electrochemical impedance spectroscopy (EIS) is identified as one of the most promising in-situ diagnostics tools available for assessing fuel cell ageing and degradation.
In this work, the degradation phenomena caused by cell polarity reversal due to fuel starvation of an open cathode 16 membrane electrode assembly (MEA) – low power (PEM) fuel cell (15 W nominal power) – is reported using EIS as a base technique. Measuring the potential of individual cells, while the fuel cell is on load, was found instrumental in assessing the “state of health” of cells at fixed current. Location of affected cells, those farthest away from hydrogen entry in the stack, was revealed by very low or even negative potential values. EIS spectra were taken at selected break-in periods during fuel cell functioning. The analysis of impedance data was made using an a priori equivalent circuit describing the transfer function of the system in question –equivalent circuit elements were evaluated by a complex non-linear least square (CNLS) fitting algorithm, and by calculating and analyzing the corresponding distribution of relaxation times (DRT). Results and interpretation of cell polarity reversal due to hydrogen starvation were complemented with ex-situ MEA cross section analysis...

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## ‣ Modelling and identification of the dominant phenomena in hydrogen fuel-cells by the application of DRT analysis

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

Publicado em //2013
Português

Relevância na Pesquisa

77.69573%

This paper proposes the use of the distribution of relaxation times (DRT) for the analysis of the dynamic behavior of hydrogen fuel-cells. With this aim it
presents a new method to compute the DRT directly from electrochemical impedance spectroscopy (EIS) data. The method is formulated as a nonconvex complex domain
optimization problem where each EIS spectra is approximated by a general fractional-order Legendre basis. The DRT is computed directly from the Legendre basis functions and validated against the experimental data. The method is tested with real EIS data collected from an hydrogen polymer electrolyte fuel-cell under different operating conditions and the results are discussed.

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## ‣ Dispersed electrical-relaxation response: discrimination between conductive and dielectric relaxation processes

Fonte: Sociedade Brasileira de Física
Publicador: Sociedade Brasileira de Física

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/06/1999
Português

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Relations and distinctions which are relavant to small-signal electrical-relaxation behavior are reviewed and applied to the important problem of identifying the physical processes leading to dispersed relaxation response. Complex-nonlinear-least-squares fitting of a response model to frequency-response data is found not to allow one to distinguish unambiguously in most cases between conductive-system response of Wagner-Voigt type, which may be characterized by a distribution of conductive system relaxation times [DCRT], and dielectric- system response of Maxwell type, characterized by a distribution of dielectric-system relaxation times [DDRT]. In general, one must include a parallel conductivity element sCP, as well as a high-frequency-limiting dielectric constant, in a conductive-system fitting model used to represent dielectric-system data with non-zero dc conductivity. Contrary to earlier predictions of Gross and Meixner, accurate numerical inversion of a set of exact frequency- response data to estimate the distribution with which it is associated shows that no discrete line necessarily appears in a DCRT associated with a truncated continuous DDRT. A discrete line can appear in general, however, when sCP ¹ 0 and is unaccounted for in an inversion process. The novel result is established that a data set mathematically described in terms of a dielectric system with dc leakage and involving a Maxwell-circuit exponential distribution of relaxation times may be well represented within usual experimental error by a Wagner-Voigt conductive system involving a form of the important Kohlrausch-Williams-Watts response model.

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## ‣ Magnetic Resonance Studies on Membrane and Model Membrane Systems: Proton Magnetic Relaxation Rates in Sonicated Lecithin Dispersions*

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

Publicado em /03/1972
Português

Relevância na Pesquisa

58.237676%

We have used Fourier transform nuclear magnetic resonance methods to measure the spin-lattice and transverse relaxation times at 220 MHz of the choline N-methyl and the fatty-acid α-carbonyl, allyl, vinyl, methylene, and methyl protons of sonicated egg-yolk lecithin. Over the temperature range investigated the T1 values were, in general, similar to, but different from, one another, suggesting that the relaxation rates of all of the fatty-acid protons are not determined solely by spin-diffusion to a heat sink. Arrhenius plots of the T1 data gave activation energies similar to those for the barriers to internal rotation in alkanes. The values of the transverse relaxation rate, T2, showed a relatively large variation among the proton resonances; about 20% of the methylene protons had a T2 of 56 msec, while the remaining protons relaxed according to a distribution of values all shorter than 20 msec. Such a distribution of relaxation times is envisioned to arise from a distribution of correlation times stemming from complex motions in which extended angular excursions of the fatty acid chain are coupled to trans→gauche conformational transitions.

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## ‣ Dynamical characterization of residual and non-native structures in a partially folded protein by 15N NMR relaxation using a model based on a distribution of correlation times

Fonte: Cold Spring Harbor Laboratory Press
Publicador: Cold Spring Harbor Laboratory Press

Tipo: Artigo de Revista Científica

Publicado em /04/2002
Português

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68.09363%

A spectral density model based on a truncated lorentzian distribution of correlation times is used to analyze the nanosecond time-scale dynamics of the partially unfolded domain 2 of annexin I from its 15N NMR relaxation parameters measured at three magnetic field strengths. The use of a distribution of correlation times enables the characterization of the dynamical features of the NH bonds of the protein in terms of heterogeneity of dynamical states in the nanosecond range. The variation along the sequence of the two dynamical parameters introduced, namely the center and the width of the distribution, points out the different types of residual secondary structures present in the D2 domain. Moreover, it allows a physically sensible interpretation of the dynamical behavior of the different residual helices and of the non-native structures. Also, a striking correspondence is found between the parameters obtained using an extended Lipari and Szabo model and the parameters obtained using the distribution of correlation times. This result led us to propose a specific interpretation of the model-free order parameter for internal motions in the nanosecond range in the case of unfolded states.

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## ‣ Rigidity percolation and the spatial heterogeneity of soft modes in disordered materials

Fonte: National Academy of Sciences
Publicador: National Academy of Sciences

Tipo: Artigo de Revista Científica

Português

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67.30087%

We show how the spatial character of unconstrained motion in a network of bonds can be directly inferred from the topological arrangement of constraints. Relaxation time scales of these soft modes are determined, and from this information we generate spatial maps of the heterogeneous distribution of relaxation times in the disordered network. We show that the nature of the dynamic heterogeneity and its sensitivity to changes in bond configuration depends dramatically on the proximity of the system to the rigidity percolation point.

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## ‣ Broadband Dielectric Spectroscopy of Mixed Betaine Phosphate Betaine Phosphite, CuInP_2(S_xSe_{1-x})_6 crystals and PMN-PSN-PZN Ceramics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/12/2010
Português

Relevância na Pesquisa

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TIn the first chapter, the current ideas about crystalline disordered system
are surveyed and exemplified by the results allowing for the most
straightforward interpretation. Exclusive consideration is intended for
broadband dielectric spectroscopy results. Several critical remarks are
presented about various predefined forms of the distribution of relaxation
times and it physical meaning.
The second chapter is devoted to the experimental and theoretical methods of
the broadband dielectric spectroscopy, which have been applied by the author to
collect the original data personally.
The third chapter contains results of investigations of the mixed
hydrogen-bond betaine phosphite betaine phosphate phase transitions dynamics.
Here distribution of the relaxation times, double well potential parameters,
local polarization distributions of the investigated crystals are presented. In
the fourth chapter the dielectric spectroscopy results of mixed
CuInP2(SxSe1-x)6 crystals are presented, phase diagram of these crystals is
discussed. The fifth chapter contains the dielectric spectra of PMN-PSN-PZN
relaxor ferroelectrics in a very wide frequency range. Formation of the polar
nanoregions below the Burns temperature (700-800 K) is manifested by the
appearance of the dielectric relaxation in the THz range and by splitting of
polar modes in the infrared spectra. Dielectric spectra are analyzed in terms
of distribution of relaxation times using the Tichonov regularization method.
The distributions splits in two components near room temperature and the origin
of both components are discussed. In the infrared spectra interesting phonon
anomalies are observed.

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## ‣ Resolving distribution of relaxation times in Poly(propylene glycol) on the crossover region

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/03/2004
Português

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In this paper, a recently developed numerical technique [{\em Tuncer E and
Guba{\'n}ski S M, IEEE Trans Diel El Insul {\bf 8}(3)(2001) 310-320}] is
applied to poly(propylene glycol) complex dielectric data to extract more
information about the molecular relaxation processes. The method is based on a
constrained-least-squares (\clsq) data fitting procedure together with the
Monte Carlo (\mc) method. We preselect the number of relaxation times with no
{\em a-priori} physical assumption, and use the Debye single relaxation as
``kernel'', then the obtained weighting factors at each \mc step from the \clsq
method builds up a relaxation time spectrum. When the analysis is repeated for
data at different temperatures a {\em relaxation-image} is created. The
obtained relaxation are analyzed using the Lorentz (Cauchy) distribution, which
is a special form of the L{\'e}vy statistics. In the present report the $\beta$
and $\alpha$ relaxations are resolved for the \ppg. A comparison of the
relaxations to those earlier reported in the literature indicate that the
presented method provides additional information compared to methods based on
empirical formulas. The distribution of relaxation times analysis is especially
useful to probe the crossover region where the $\alpha$- and $\beta$-
relaxations merge and the results show that the relaxation after the crossover
region at higher temperatures is Arrhenius-type as the $\beta$-relaxation.
Moreover...

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## ‣ Relaxation time distributions for an anomalously diffusing particle

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/05/2011
Português

Relevância na Pesquisa

58.135796%

As well known, the generalized Langevin equation with a memory kernel
decreasing at large times as an inverse power law of time describes the motion
of an anomalously diffusing particle. Here, we focus attention on some new
aspects of the dynamics, successively considering the memory kernel, the
particle's mean velocity, and the scattering function. All these quantities are
studied from a unique angle, namely, the discussion of the possible existence
of a distribution of relaxation times characterizing their time decay. Although
a very popular concept, a relaxation time distribution cannot be associated
with any time-decreasing quantity (from a mathematical point of view, the decay
has to be described by a completely monotonic function). Technically, we use a
memory kernel decaying as a Mittag-Leffler function (the Mittag-Leffler
functions interpolate between stretched or compressed exponential behaviour at
short times and inverse power law behaviour at large times). We show that, in
the case of a subdiffusive motion, relaxation time distributions can be defined
for the memory kernel and for the scattering function, but not for the
particle's mean velocity. The situation is opposite in the superdiffusive case.; Comment: 17 pages

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## ‣ Segmental relaxation in semicrystalline polymers: a mean field model for the distribution of relaxation times in confined regimes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/02/2009
Português

Relevância na Pesquisa

67.8163%

The effect of confinement in the segmental relaxation of polymers is
considered. On the basis of a thermodynamic model we discuss the emerging
relevance of the fast degrees of freedom in stimulating the much slower
segmental relaxation, as an effect of the constraints at the walls of the
amorphous regions. In the case that confinement is due to the presence of
crystalline domains, a quasi-poissonian distribution of local constraining
conditions is derived as a result of thermodynamic equilibrium. This implies
that the average free energy barrier $\Delta F$ for conformational
rearrangement is of the same order of the dispersion of the barrier heights,
$\delta (\Delta F)$, around $\Delta F$. As an example, we apply the results to
the analysis of the $\alpha$-relaxation as observed by dielectric broad band
spectroscopy in semicrystalline poly(ethylene terephthalate) cold-crystallized
from either an isotropic or an oriented glass. It is found that in the latter
case the regions of cooperative rearrangement are significantly larger than in
the former.; Comment: 10 pages, 4 figures .eps

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## ‣ Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

67.515244%

We consider the long-ranged Ising spin-glass with random couplings decaying
as a power-law of the distance, in the region of parameters where the
spin-glass phase exists with a positive droplet exponent. For the Metropolis
single-spin-flip dynamics near zero temperature, we construct via real-space
renormalization the full hierarchy of relaxation times of the master equation
for any given realization of the random couplings. We then analyze the
probability distribution of dynamical barriers as a function of the spatial
scale. This real-space renormalization procedure represents a simple explicit
example of the droplet scaling theory, where the convergence towards local
equilibrium on larger and larger scales is governed by a strong hierarchy of
activated dynamical processes, with valleys within valleys.; Comment: v2=final version

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## ‣ Distribution of relaxation times in $\alpha$-phase polyvinylidene fluoride

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/09/2004
Português

Relevância na Pesquisa

87.8562%

In this paper, a recently developed numerical method to analyze
dielectric-spectroscopy data is applied to $\alpha$-phase polyvinylidene
fluoride (PVDF). The numerical procedure is non-parametric and does not contain
any of the extensively used empirical formulas mentioned in the literature. The
method basically recovers the unknown distribution of relaxation times of the
generalized dielectric function representation by simultaneous application of
the Monte Carlo integration method and of the constrained least-squares
optimization. The relaxation map constructed after the numerical analysis is
compared to $\alpha$-phase PVDF data presented in the literature and results of
the parametric analysis with a well-known empirical formula.; Comment: 4 figures, 1 table

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## ‣ Comparison of methods for estimating continuous distributions of relaxation times

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/04/2005
Português

Relevância na Pesquisa

77.970044%

The nonparametric estimation of the distribution of relaxation times approach
is not as frequently used in the analysis of dispersed response of dielectric
or conductive materials as are other immittance data analysis methods based on
parametric curve fitting techniques. Nevertheless, such distributions can yield
important information about the physical processes present in measured
material. In this letter, we apply two quite different numerical inversion
methods to estimate the distribution of relaxation times for glassy \lila\
dielectric frequency-response data at $225 \kelvin$. Both methods yield unique
distributions that agree very closely with the actual exact one accurately
calculated from the corrected bulk-dispersion Kohlrausch model established
independently by means of parametric data fit using the corrected modulus
formalism method. The obtained distributions are also greatly superior to those
estimated using approximate functions equations given in the literature.; Comment: 4 pages and 4 figures

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## ‣ Point process model of 1/f noise versus a sum of Lorentzians

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/04/2005
Português

Relevância na Pesquisa

58.21367%

#Condensed Matter - Statistical Mechanics#Astrophysics#Condensed Matter - Disordered Systems and Neural Networks#Computer Science - Computational Engineering, Finance, and Science#Mathematics - Statistics Theory#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Physics - Data Analysis, Statistics and Probability#Quantitative Biology - Neurons and Cognition

We present a simple point process model of $1/f^{\beta}$ noise, covering
different values of the exponent $\beta$. The signal of the model consists of
pulses or events. The interpulse, interevent, interarrival, recurrence or
waiting times of the signal are described by the general Langevin equation with
the multiplicative noise and stochastically diffuse in some interval resulting
in the power-law distribution. Our model is free from the requirement of a wide
distribution of relaxation times and from the power-law forms of the pulses. It
contains only one relaxation rate and yields $1/f^ {\beta}$ spectra in a wide
range of frequency. We obtain explicit expressions for the power spectra and
present numerical illustrations of the model. Further we analyze the relation
of the point process model of $1/f$ noise with the Bernamont-Surdin-McWhorter
model, representing the signals as a sum of the uncorrelated components. We
show that the point process model is complementary to the model based on the
sum of signals with a wide-range distribution of the relaxation times. In
contrast to the Gaussian distribution of the signal intensity of the sum of the
uncorrelated components, the point process exhibits asymptotically a power-law
distribution of the signal intensity. The developed multiplicative point
process model of $1/f^{\beta}$ noise may be used for modeling and analysis of
stochastic processes in different systems with the power-law distribution of
the intensity of pulsing signals.; Comment: 23 pages...

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## ‣ A Comparison of Pore Size Distributions Derived by NMR and X-ray-CT Techniques

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Keywords: Computer simulation#Computerized tomography#Diffusion in liquids#Eigenvalues and eigenfunctions#Laplace transforms#Magnetic fields#Mathematical models#Nuclear magnetic resonance#Pore size#Relaxation processes#Rocks

High resolution micro-X-ray-CT data is used as a "gold standard" to define the morphology of a number of sandstones as well as a carbonate rock. From these micro-CT images the NMR responses to surface relaxation and restricted diffusion in the internal magnetic field are calculated numerically. The NMR response is decomposed into a distribution of relaxation times by an inverse Laplace transformation. By interpreting the relaxation time distributions in terms of relaxation and diffusion modes pore size distributions are derived from the NMR responses. The pore size distributions obtained from an interpretation of the NMR data are compared with corresponding measures derived directly from the X-ray-CT images.

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## ‣ Electrochemical impedance spectroscopy modeling using the dis-tribution of relaxation times and error analysis for fuel cells

Fonte: Laboratório Nacional de Energia e Geologia
Publicador: Laboratório Nacional de Energia e Geologia

Tipo: Conferência ou Objeto de Conferência

Publicado em //2013
Português

Relevância na Pesquisa

118.13361%

#Fuel-cell #Impedance spectroscopy#Distribution of relaxation times#Parameter estimation#Residuals bootstrap

This paper proposes a new approach to determine the distribution of relaxation times (DRT) directly from the electro-chemical impedance spectroscopy (EIS) data, i.e. without the use of an equivalent electrical circuit model. The method uses a generalized fractional-order Laguerre basis to represent EIS where both the parameters of the basis and their co-efficients are estimated by solving a nonconvex minimization problem. Furthermore, the DRT confidence region is de-termined to assess the accuracy and precision of the DRT estimate. The approach is applied to analyze the dominant dynamic properties of an open-cathode hydrogen fuel-cell under different current and air-flow conditions. Results showed that the estimated DRT closely reconstructs EIS data even when there is a higher variance at smaller relaxation times.

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