ELIZA

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290904 occurrences (No.84 in the rank) during 5 years in the PubMed. [no cache] 500 found

142) For a planar film, we find that this PDE can be reduced to an ordinary differential equation (ODE) that can be solved analytically or numerically.

--- ABSTRACT ---

PMID:24521538 DOI:10.1093/imammb/dqu001

2015 Mathematical medicine and biology : a journal of the IMA

* Modelling the evaporation of a tear film over a contact lens.

- A contact lens (CL) separates the tear film into a pre-lens tear film (PrLTF), the fluid layer between the CL and the outside environment, and a post-lens tear film (PoLTF), the fluid layer between the CL and the cornea. We examine a model for evaporation of a PrLTF on a modern permeable CL allowing fluid transfer between the PrLTF and the PoLTF. Evaporation depletes the PrLTF, and continued evaporation causes depletion of the PoLTF via fluid loss through the CL. Governing equations include Navier-Stokes, heat and Darcy's equations for the fluid flow and heat transfer in the PrLTF and porous layer. The PoLTF is modelled by a fixed pressure condition on the posterior surface of the CL. The original model is simplified using lubrication theory for the PrLTF and CL applied to a sagittal plane through the eye. We obtain a partial differential equation (PDE) for the PrLTF thickness that is first-order in time and fourth-order in space. This model incorporates evaporation, conjoining pressure effects in the PrLTF, capillarity and heat transfer. For a planar film, we find that this PDE can be reduced to an ordinary differential equation (ODE) that can be solved analytically or numerically. This reduced model allows for interpretation of the various system parameters and captures most of the basic physics contained in the model. Comparisons of ODE and PDE models, including estimates for the loss of fluid through the lens due to evaporation, are given.

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(1)66 the	(12)4 activity	(24)2 among	(35)2 interhemispheric
(2)30 in	(13)4 both	(25)2 availability	(36)2 it
(3)23 by	(14)4 cell	(26)2 blood	(37)2 likelihood
(4)13 null	(16)3 ability	(27)2 but	(38)2 number
(5)13 to	(17)3 after	(28)2 compared	(39)2 rates
(6)10 glutathione	(18)3 binding	(29)2 effortful	(40)2 stem
(7)8 and	(19)3 or	(30)2 ejection	(41)2 total
(8)8 expression	(20)3 risk	(31)2 following	(42)2 tumor
(9)5 levels	(21)3 sensitivity	(32)2 from	(43)2 which
(10)5 significantly	(22)2 (P	(33)2 glutathione,
(11)4 PGE2	(23)2 BRCA-1	(34)2 hippocampal

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--- WordNet output for reduced --- =>貧しい暮らし, 落ちぶれた生活 Overview of verb reduce The verb reduce has 20 senses (first 11 from tagged texts) 1. (102) reduce, cut down, cut back, trim, trim down, trim back, cut, bring down -- (cut down on; make a reduction in; "reduce your daily fat intake"; "The employer wants to cut back health benefits") 2. (9) reduce -- (make less complex; "reduce a problem to a single question") 3. (5) reduce -- (bring to humbler or weaker state or condition; "He reduced the population to slavery") 4. (3) reduce -- (simplify the form of a mathematical equation of expression by substituting one term for another) 5. (3) reduce -- (lower in grade or rank or force somebody into an undignified situation; "She reduced her niece to a servant") 6. (3) reduce, come down, boil down -- (be the essential element; "The proposal boils down to a compromise") 7. (2) shrink, reduce -- (reduce in size; reduce physically; "Hot water will shrink the sweater"; "Can you shrink this image?") 8. (1) reduce -- (lessen and make more modest; "reduce one's standard of living") 9. (1) reduce, scale down -- (make smaller; "reduce an image") 10. (1) deoxidize, deoxidise, reduce -- (to remove oxygen from a compound, or cause to react with hydrogen or form a hydride, or to undergo an increase in the number of electrons) 11. (1) reduce, tighten -- (narrow or limit; "reduce the influx of foreigners") 12. repress, quash, keep down, subdue, subjugate, reduce -- (put down by force or intimidation; "The government quashes any attempt of an uprising"; "China keeps down her dissidents very efficiently"; "The rich landowners subjugated the peasants working the land") 13. reduce -- (undergo meiosis; "The cells reduce") 14. reduce -- (reposition (a broken bone after surgery) back to its normal site) 15. reduce -- (destress and thus weaken a sound when pronouncing it) 16. abridge, foreshorten, abbreviate, shorten, cut, contract, reduce -- (reduce in scope while retaining essential elements; "The manuscript must be shortened") 17. boil down, reduce, decoct, concentrate -- (be cooked until very little liquid is left; "The sauce should reduce to one cup") 18. reduce, boil down, concentrate -- (cook until very little liquid is left; "The cook reduced the sauce by boiling it for a long time") 19. dilute, thin, thin out, reduce, cut -- (lessen the strength or flavor of a solution or mixture; "cut bourbon") 20. reduce, melt off, lose weight, slim, slenderize, thin, slim down -- (take off weight) Overview of adj reduced The adj reduced has 2 senses (first 2 from tagged texts) 1. (6) decreased, reduced -- (made less in size or amount or degree) 2. (1) reduced, rock-bottom -- (well below normal (especially in price)) --- WordNet end ---