FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2045807767> ?p ?o ?g. }

• W2045807767 endingPage "19323" @default.
• W2045807767 startingPage "19301" @default.
• W2045807767 abstract "Gombosi et al. (1993) recently derived a modified telegrapher's equation for charged particle transport under the influence of isotropic scattering. This equation obeys causality and disallows upstream diffusion for particles with random velocities smaller than the bulk flow velocity. The acausal diffusion equation was obtained to lowest order in the expansion of smallness parameters. The paper by Gombosi et al. (1993) prompted responses from Pauls et al. (1993) and Earl (1993). This paper is written to explain the differences between the methods, assumptions, and results of Gombosi et al. (1993), Pauls et al. (1993), and Earl (1993) and presents a new method of obtaining approximate solutions. It is shown that the assumptions used by Gombosi et al. (1993) and Pauls et al. (1993) are physically equivalent. In these papers, a second‐order expansion is made by introducing smallness parameters, not by truncating an eigenfunction series. Earl (1993) estimates the overall behavior of a dispersion relation for the two lowest‐frequency modes by truncating an eigenfunction series and by using empirical approximations motivated by a Monte Carlo simulation. Earl's (1993) approximations are mathematically not equivalent to the smallness parameter expansion introduced by Gombosi et al. (1993). We have developed a new solution method which is both functionally consistent with Earl's (1993) solutions and with the smallness parameter expansion. Because the new solution method involves both causal telegrapher's equation propagation and diffusion, it becomes clear that Earl's (1993) coherent pulse velocity is smaller than the modified telegrapher's coherent velocity because diffusion limits the efficiency of coherent propagation. In our solution method, the solution of the modified telegrapher's equation is obtained as the causal limit of solutions accurate to second order in the smallness parameter expansion. In order to investigate the coherent velocity, we have also developed “wavenumber eigenfunctions” which account for all the pitch angle dependence in our Boltzmann equation. Using truncation, Earl (1993) obtains approximations for the wavenumber dependence of the lowest two frequency modes, which correspond to two of the wavenumber eigenmodes. We find that a consequence of including only two wavenumber eigenmodes is that one obtains solutions which disobey causality at sufficiently short times. Furthermore, the coherent velocity of the two eigenmodes is strongly dependent on wavenumber and approaches the particle velocity in the limit of large wavenumber for both isotropic and anisotropic scattering processes. We conclude that Earl's (1993) solutions and solutions obtained using the new solution method implicitly assume weak acausality and reasonable behavior in the temporal regime, t < 4τ. The solutions are not strictly consistent with the behavior of the lowest two frequency modes but have similar behavior in the regime of low wavenumber." @default.
• W2045807767 created "2016-06-24" @default.
• W2045807767 creator A5018406009 @default.
• W2045807767 creator A5053795386 @default.
• W2045807767 date "1994-10-01" @default.
• W2045807767 modified "2023-09-27" @default.
• W2045807767 title "A unifying comparison of nearly scatter free transport models" @default.
• W2045807767 cites W1963701191 @default.
• W2045807767 cites W1974332423 @default.
• W2045807767 cites W1992040778 @default.
• W2045807767 cites W2008277413 @default.
• W2045807767 cites W2031277212 @default.
• W2045807767 cites W2044591190 @default.
• W2045807767 cites W2050062367 @default.
• W2045807767 cites W2055023831 @default.
• W2045807767 cites W2060078125 @default.
• W2045807767 cites W2061485921 @default.
• W2045807767 cites W2063717068 @default.
• W2045807767 cites W2086573375 @default.
• W2045807767 cites W2087364146 @default.
• W2045807767 cites W2087464258 @default.
• W2045807767 cites W3181001136 @default.
• W2045807767 doi "https://doi.org/10.1029/94ja01737" @default.
• W2045807767 hasPublicationYear "1994" @default.
• W2045807767 type Work @default.
• W2045807767 sameAs 2045807767 @default.
• W2045807767 citedByCount "15" @default.
• W2045807767 countsByYear W20458077672013 @default.
• W2045807767 countsByYear W20458077672014 @default.
• W2045807767 countsByYear W20458077672015 @default.
• W2045807767 countsByYear W20458077672016 @default.
• W2045807767 countsByYear W20458077672017 @default.
• W2045807767 countsByYear W20458077672019 @default.
• W2045807767 countsByYear W20458077672020 @default.
• W2045807767 countsByYear W20458077672021 @default.
• W2045807767 crossrefType "journal-article" @default.
• W2045807767 hasAuthorship W2045807767A5018406009 @default.
• W2045807767 hasAuthorship W2045807767A5053795386 @default.
• W2045807767 hasConcept C105795698 @default.
• W2045807767 hasConcept C121332964 @default.
• W2045807767 hasConcept C121864883 @default.
• W2045807767 hasConcept C128803854 @default.
• W2045807767 hasConcept C134306372 @default.
• W2045807767 hasConcept C143724316 @default.
• W2045807767 hasConcept C151730666 @default.
• W2045807767 hasConcept C158693339 @default.
• W2045807767 hasConcept C184050105 @default.
• W2045807767 hasConcept C186080144 @default.
• W2045807767 hasConcept C19499675 @default.
• W2045807767 hasConcept C33923547 @default.
• W2045807767 hasConcept C62520636 @default.
• W2045807767 hasConcept C69357855 @default.
• W2045807767 hasConcept C86803240 @default.
• W2045807767 hasConceptScore W2045807767C105795698 @default.
• W2045807767 hasConceptScore W2045807767C121332964 @default.
• W2045807767 hasConceptScore W2045807767C121864883 @default.
• W2045807767 hasConceptScore W2045807767C128803854 @default.
• W2045807767 hasConceptScore W2045807767C134306372 @default.
• W2045807767 hasConceptScore W2045807767C143724316 @default.
• W2045807767 hasConceptScore W2045807767C151730666 @default.
• W2045807767 hasConceptScore W2045807767C158693339 @default.
• W2045807767 hasConceptScore W2045807767C184050105 @default.
• W2045807767 hasConceptScore W2045807767C186080144 @default.
• W2045807767 hasConceptScore W2045807767C19499675 @default.
• W2045807767 hasConceptScore W2045807767C33923547 @default.
• W2045807767 hasConceptScore W2045807767C62520636 @default.
• W2045807767 hasConceptScore W2045807767C69357855 @default.
• W2045807767 hasConceptScore W2045807767C86803240 @default.
• W2045807767 hasIssue "A10" @default.
• W2045807767 hasLocation W20458077671 @default.
• W2045807767 hasOpenAccess W2045807767 @default.
• W2045807767 hasPrimaryLocation W20458077671 @default.
• W2045807767 hasRelatedWork W1662757438 @default.
• W2045807767 hasRelatedWork W1985146289 @default.
• W2045807767 hasRelatedWork W1997850781 @default.
• W2045807767 hasRelatedWork W1999657763 @default.
• W2045807767 hasRelatedWork W2045807138 @default.
• W2045807767 hasRelatedWork W2049570251 @default.
• W2045807767 hasRelatedWork W2072690751 @default.
• W2045807767 hasRelatedWork W2131885480 @default.
• W2045807767 hasRelatedWork W3023975926 @default.
• W2045807767 hasRelatedWork W4293919821 @default.
• W2045807767 hasVolume "99" @default.
• W2045807767 isParatext "false" @default.
• W2045807767 isRetracted "false" @default.
• W2045807767 magId "2045807767" @default.
• W2045807767 workType "article" @default.