Matches in SemOpenAlex for { <https://semopenalex.org/work/W2084450456> ?p ?o ?g. }
Showing items 1 to 82 of
82
with 100 items per page.
- W2084450456 endingPage "26" @default.
- W2084450456 startingPage "1" @default.
- W2084450456 abstract "The optical caustics associated with a number of higher umbilic catastrophes have been studied experimentally by passing light through drops of water resting on a horizontal glass slide. When the perimeters of the drops were constrained to have the symmetry of a square (4mm), the caustics were organized by X 9 , which is the lowest catastrophe of corank 2 to possess a modulus. Changing the shape of the perimeter of a thin drop of this symmetry that is large enough to be affected by gravity has the effect of sweeping the modulus K through its complete range -6 to +2; in particular, one can study the physical caustics as K passes through the special value -2, which is mathematically excluded from X 9 . Similar variations of K are produced by varying the size of thin drops with square outlines, or simply by adding water to a drop of fixed outline so that its profile becomes highly curved. Twofold (2mm) and fourfold (4mm) symmetries are the only ones that allow X 9 , with its full range of moduli, to participate. However, the range of caustics produced by drops with these symmetries cannot be understood in terms of X 9 alone; to explain the observed details it is necessary to take account of the fact that X 9 is embedded in the higher catastrophe Y 1 / 2 , 2 . A theory of the drop profile under the combined effects of surface tension and gravity, valid for small slopes, leads to a calculation of the caustics in the paraxial approximation. This is completely adequate to explain the observations, for thin drops, but, as a surprising example of structural stability, it also suffices when the drops are highly curved and the paraxial approximation breaks down. However, the paraxial theory does fail, as expected, when highly curved drops are inverted so that they hang from the lower surface of the glass slide. Then the X 9 patterns due to gravity are opposed to those due to non-paraxiality; for a drop of square outline, filled nearly to the point where it is about to detach itself, and illuminated from below, the two effects exactly cancel when the side is 7.3 mm. Analysis of these patterns of fourfold symmetry helps in understanding the caustic patterns produced by drops having other symmetries, or no symmetry at all." @default.
- W2084450456 created "2016-06-24" @default.
- W2084450456 creator A5012158588 @default.
- W2084450456 date "1986-01-08" @default.
- W2084450456 modified "2023-10-02" @default.
- W2084450456 title "The catastrophe optics of liquid drop lenses" @default.
- W2084450456 cites W1975383406 @default.
- W2084450456 cites W1998979822 @default.
- W2084450456 cites W2021487384 @default.
- W2084450456 cites W2030901336 @default.
- W2084450456 cites W2031323400 @default.
- W2084450456 cites W2060333113 @default.
- W2084450456 cites W2076050576 @default.
- W2084450456 doi "https://doi.org/10.1098/rspa.1986.0001" @default.
- W2084450456 hasPublicationYear "1986" @default.
- W2084450456 type Work @default.
- W2084450456 sameAs 2084450456 @default.
- W2084450456 citedByCount "39" @default.
- W2084450456 countsByYear W20844504562012 @default.
- W2084450456 countsByYear W20844504562015 @default.
- W2084450456 countsByYear W20844504562016 @default.
- W2084450456 countsByYear W20844504562017 @default.
- W2084450456 countsByYear W20844504562018 @default.
- W2084450456 countsByYear W20844504562019 @default.
- W2084450456 countsByYear W20844504562020 @default.
- W2084450456 countsByYear W20844504562021 @default.
- W2084450456 countsByYear W20844504562022 @default.
- W2084450456 crossrefType "journal-article" @default.
- W2084450456 hasAuthorship W2084450456A5012158588 @default.
- W2084450456 hasConcept C110277352 @default.
- W2084450456 hasConcept C120665830 @default.
- W2084450456 hasConcept C121089165 @default.
- W2084450456 hasConcept C121332964 @default.
- W2084450456 hasConcept C168834538 @default.
- W2084450456 hasConcept C2524010 @default.
- W2084450456 hasConcept C2781345722 @default.
- W2084450456 hasConcept C33923547 @default.
- W2084450456 hasConcept C41008148 @default.
- W2084450456 hasConcept C56034020 @default.
- W2084450456 hasConcept C57879066 @default.
- W2084450456 hasConcept C62520636 @default.
- W2084450456 hasConcept C74650414 @default.
- W2084450456 hasConcept C76155785 @default.
- W2084450456 hasConcept C8892853 @default.
- W2084450456 hasConcept C96469262 @default.
- W2084450456 hasConceptScore W2084450456C110277352 @default.
- W2084450456 hasConceptScore W2084450456C120665830 @default.
- W2084450456 hasConceptScore W2084450456C121089165 @default.
- W2084450456 hasConceptScore W2084450456C121332964 @default.
- W2084450456 hasConceptScore W2084450456C168834538 @default.
- W2084450456 hasConceptScore W2084450456C2524010 @default.
- W2084450456 hasConceptScore W2084450456C2781345722 @default.
- W2084450456 hasConceptScore W2084450456C33923547 @default.
- W2084450456 hasConceptScore W2084450456C41008148 @default.
- W2084450456 hasConceptScore W2084450456C56034020 @default.
- W2084450456 hasConceptScore W2084450456C57879066 @default.
- W2084450456 hasConceptScore W2084450456C62520636 @default.
- W2084450456 hasConceptScore W2084450456C74650414 @default.
- W2084450456 hasConceptScore W2084450456C76155785 @default.
- W2084450456 hasConceptScore W2084450456C8892853 @default.
- W2084450456 hasConceptScore W2084450456C96469262 @default.
- W2084450456 hasIssue "1824" @default.
- W2084450456 hasLocation W20844504561 @default.
- W2084450456 hasOpenAccess W2084450456 @default.
- W2084450456 hasPrimaryLocation W20844504561 @default.
- W2084450456 hasRelatedWork W1992297007 @default.
- W2084450456 hasRelatedWork W2015787458 @default.
- W2084450456 hasRelatedWork W2080504126 @default.
- W2084450456 hasRelatedWork W2084450456 @default.
- W2084450456 hasRelatedWork W2111830442 @default.
- W2084450456 hasRelatedWork W2128588006 @default.
- W2084450456 hasRelatedWork W2168009170 @default.
- W2084450456 hasRelatedWork W2735336642 @default.
- W2084450456 hasRelatedWork W3101202789 @default.
- W2084450456 hasRelatedWork W2149136543 @default.
- W2084450456 hasVolume "403" @default.
- W2084450456 isParatext "false" @default.
- W2084450456 isRetracted "false" @default.
- W2084450456 magId "2084450456" @default.
- W2084450456 workType "article" @default.