An Improved Method for Numerical Inversion of Laplace Transforms

Hoog, Frank de; Knight, J. H.; Stokes, A. N.

doi:10.1137/0903022

Cited by 730 publications

(389 citation statements)

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“…Figure 2 shows graphs of the functions h 1 (t), H 1 (t), and > t 0 H 1 (s) ds for c=0.6; these curves were obtained by numerically inverting the Laplace transform. (10) In Fig. 3 we show bs QQ (t) and bs PP (t), given by (4.10).…”

Section: And the Variance Of Q(t) And P(t) Is Given Bymentioning

confidence: 99%

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Fractional Kinetics in Kac–Zwanzig Heat Bath Models

Kupferman

2004

Journal of Statistical Physics

143

135

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We study a variant of the Kac-Zwanzig model of a particle in a heat bath. The heat bath consists of n particles which interact with a distinguished particle via springs and have random initial data. As n Q . the trajectories of the distinguished particle weakly converge to the solution of a stochastic integro-differential equation-a generalized Langevin equation (GLE) with power-law memory kernel and driven by 1/f a -noise. The limiting process exhibits fractional sub-diffusive behaviour. We further consider the approximation of nonMarkovian processes by higher-dimensional Markovian processes via the introduction of auxiliary variables and use this method to approximate the limiting GLE. In contrast, we show the inadequacy of a so-called fractional Fokker-Planck equation in the present context. All results are supported by direct numerical experiments.

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Section: And the Variance Of Q(t) And P(t) Is Given Bymentioning

confidence: 99%

“…where 10) are the centered joint moments of degree 2b of h(w j , t p ). Since w j and w i are independent for j ] i, then many of these moments vanish; every V j 1 ,..., j 2b (t 1 ,..., t b ) that contains an index j which appears only once vanishes.…”

Section: Fractional Kinetics In Kac-zwanzig Heat Bath Modelsmentioning

confidence: 99%

Fractional Kinetics in Kac–Zwanzig Heat Bath Models

Kupferman

2004

Journal of Statistical Physics

143

135

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“…et e sont succéssivement la conductivité thermique et Après l'inversion numérique de cette expression par l'algorithme de De Hoog [9], on obtient l'expression théorique de la température. L'algorithme de Levenberg Marquardt [10][11] est utilisé pour l'estimation des paramètres a, ∅  et h par minimisation de l'erreur quadratique entre le thermogramme expérimental représentant l'évolution de la température de la face arrière de l'échantillon et l'expression théorique de la température.…”

Section: Méthode Flashunclassified

“…La aplace inverse de la relation (8) est sant l'algorithme de De Hoog [9]. Nous constatons que la masse volumique apparente ne varie pratiquement pas en fonction de la taille.…”

Section: 8unclassified

Thermal characterization of a new effective building material based on clay and olive waste

et al. 2018

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Abstract. The influence of thermophysical properties of wall materials on energy performance and comfort in traditional building was investigated. The clay is the most commonly used sustainable building material. The study looked at the effects of the addition of pomace olive on the thermophysical properties of clay bricks to improve the energy efficiency of this ecological material. An experimental measurement of thermal properties of clay mixed with pomace olive was carried out by using the transient and steady state hot-plate and flash methods. The experimental methods are applied to measure the thermal properties of the composite material. The estimation of these thermal characteristics is based on a one dimensional model and the experimental errors are found less than 3%. The composite samples were prepared with different granular classes and mass fractions of the pomace olive in the mixture. The results show that the density of the new material was not substantially influenced by the size of the pomace olive. However, the thermal conductivity and diffusivity decrease from 0.65 W.m -1 .K -1 and 4.21×10 -7 m 2 .s -1 to 0.29 W.m -1 .K -1 and 2.47×10 -7 m 2 .s -1 , respectively, according to the variation of the volume fraction of pomace olive from 0 (pure clay) to 71% showing that the olive pomace can be used as effective secondary raw materials in the making of clay bricks.

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“…Eqs. (1) and (2) were solved in Laplace space for a timedependent Dirichlet-type boundary condition before being returned to the time domain by numerical inversion using the method of De Hoog et al (1982). According to filtration theory, k c may be determined as follows (Tien and Payatakes, 1979):…”

Section: Numerical Interpretationmentioning

confidence: 99%

Bacteriophage transport through a fining-upwards sedimentary sequence: laboratory experiments and simulation

Flynn

Cornaton

Hunkeler

et al. 2004

Journal of Contaminant Hydrology

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A column containing four concentric layers of progressively finer-grained glass beads (graded column) was used to study the transport of the bacteriophage T7 in water flowing parallel to layering through a fining-upwards (FU) sedimentary structure. By passing a pulse of T7, and a conservative solute tracer upwards through a column packed with a single bead size (uniform column), the capacity of each bead type to attenuate the bacteriophage was determined. Solute and bacteriophage responses were modelled using an analytical solution to the advection -dispersion equation, with first-order kinetic deposition simulating bacteriophage attenuation. Resulting deposition constants for different flow velocities indicated that filtration theory-determined values differed from experimentally determined values by less than 10%. In contrast, the responses of solute and bacteriophage tracers passing upwards through graded columns could not be reproduced with a single analytical solution. However, a flux-weighted summation of four one-dimensional advectivedispersive analytical terms approximated solute breakthrough curves. The prolonged tailing observed in the resulting curve resembled that typically generated from field-based tracer test data, reflecting the potential importance of textural heterogeneity in the transport of dissolved substances in groundwater. Moreover, bacteriophage deposition terms, determined from filtration theory, reproduced the T7 breakthrough curve once desorption and inactivation on grain surfaces were incorporated. To evaluate the effect of FU sequences on mass transport processes in more detail, bacteriophage passage through sequences resembling those sampled from a FU bed in a fluvioglacial gravel pit were carried out using an analogous approach to that employed in the laboratory. Both solute and bacteriophage breakthrough responses resembled those generated from field-based test data and in the graded column experiments. Comparisons with the results of * Corresponding author. Fax: +41-32-718-26-03.E-mail address: ray.flynn@unine.ch (R. Flynn).simulations using averaged hydraulic conductivities show that simulations employing averaged parameters overestimate bacteriophage travel times and underestimate masses recovered and peak concentrations.

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An Improved Method for Numerical Inversion of Laplace Transforms

Cited by 730 publications

References 8 publications

Fractional Kinetics in Kac–Zwanzig Heat Bath Models

Fractional Kinetics in Kac–Zwanzig Heat Bath Models

Thermal characterization of a new effective building material based on clay and olive waste

Bacteriophage transport through a fining-upwards sedimentary sequence: laboratory experiments and simulation

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