1995
DOI: 10.1029/95wr01396
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Nonlocal Reactive Transport with Physical and Chemical Heterogeneity: Localization Errors

Abstract: The origin of nonlocality in "macroscale" models for subsurface chemical transport is illustrated. It is argued that media that are either nonperiodic (e.g., media with evolving heterogeneity) or periodic viewed on a scale wherein a unit cell is discernible must display some nonlocality in the mean. A metaphysical argument suggests that owing to the scarcity of information on natural scales of heterogeneity and on scales of observation associated with an instrument window, constitutive theories for the mean co… Show more

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Cited by 94 publications
(56 citation statements)
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“…We focus our attention on the problem given in (5) - (8). Following the standard procedure of HAM, according to (5) and based on the method of linear partition matching [23], we choose the linear operator…”
Section: Homotopy Analysis Methods For the Telegraph Equationmentioning
confidence: 99%
“…We focus our attention on the problem given in (5) - (8). Following the standard procedure of HAM, according to (5) and based on the method of linear partition matching [23], we choose the linear operator…”
Section: Homotopy Analysis Methods For the Telegraph Equationmentioning
confidence: 99%
“…al., , 1997aHuang and Hu, 2000) frameworks. Cushman et al (1995) argue that media which are either nonperiodic (e.g. media with evolving heterogeneity) or periodic media, viewed on a scale wherein a unit cell is discernible, must display nonlocality in the mean.…”
Section: Nonlocal Models Of Transportmentioning
confidence: 99%
“…Such theories have been derived from both Lagrangian (e.g., Cushman, 1991;Cushman and Ginn, 1993;Cushman et al, 1994) and Eulerian (e.g., Koch and Brady, 1988;Deng et al, 1993;Cushman et al, 1995;Hu et. al., , 1997aHuang and Hu, 2000) frameworks.…”
Section: Nonlocal Models Of Transportmentioning
confidence: 99%
“…In most of the conventional methods, the modeling parameters/coefficients were usually specified as deterministic. However, in realistic energy management systems, many parameters/coefficients as well as the irrelations may have uncertain natures with multiple dimensions and layers [9,10,[179][180][181][182][183]. Over the past decades, the most common approaches for dealing with uncertainties in optimization modeling included interval, stochastic, and fuzzy-set-based methods as well as their hybrids [9][10][11][184][185][186][187][188].…”
Section: Inexact Optimization Modelingmentioning
confidence: 99%