102,743 research outputs found
Existence and stability of multiple spot solutions for the Gray-Scott model in R^2$
No full textExistence and Stability of Multiple Spot Solutions for the Gray-Scott Model in In this paper, we rigorously
prove the existence and stability of multiple spot patterns for the Gray-Scott system in a two dimensional domain
which are far from
spatial homogeneity.
The Green's function and its derivatives
together with two nonlocal eigenvalue problems
both play a major role in the analysis.
We establish a threshold behavior for stability:
If a certain inequality for the parameters holds
then we get stability, otherwise we get instability of multiple spot solutions.
The exact asymptotics of the critical thresholds are obtained
Gray, R J, VX46535
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/388770Surname: GRAY. Given Name(s) or Initials: R J. Military Service Number or Last Known Location: VX46535. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 1783.211687
Item: [2016.0049.21063] "Gray, R J, VX46535
Existence and stability of multiple spot solutions for the gray-scott model in R^2
No full textWe study the Gray-Scott model in a bounded two dimensional domain and establish the existence and stability of {\bf symmetric} and {\bf asymmetric} multiple spotty patterns. The Green's function and its derivatives
together with two nonlocal eigenvalue problems
both play a major role in the analysis.
For symmetric spots, we establish a threshold behavior for stability:
If a certain inequality for the parameters holds
then we get stability, otherwise we get instability of multiple spot solutions.
For asymmetric spots, we show that they can be stable within a narrow parameter range
Leucocarbo chalconotus G. R. Gray 1845
No full textLEUCOCARBO CHALCONOTUS (G. R. GRAY, 1845) OTAGO SHAG. Graucalus auritus Lesson, 1831: G. R. Gray, 1843, in E. Dieffenbach, Travels in N. Z. 2: 201. Not Carbo auritus Lesson, 1831. Gracalus chalconotus G. R. Gray, 1845; in Richardson & J. E. Gray (eds), Zool. Voy. Erebus & Terror: Birds 1 (8): 20, pl. 21 – Otago Province, possibly Karitane (Scofield et al., 2012). Graculus glaucus ‘Gray’: Reichenbach, 1850, Nov. Syn. Avium; pl. 49, fig. 2553 – Otago. Phalacrocorax glaucus Hombron & Jacquinot, 1853, in Dumont d’Urville, Voyage ˆ Sud, Zoologie 3: 127. Graculus chalconotus (G. R. Gray): G. R. Gray, 1862, Ibis 4: 252. Graculus glaucus (Hombron & Jacquinot, 1853): Bonaparte, 1855, Consp. Gen. Avium 2: 171. Phalacrocorax chalconotus (G. R. Gray): Buller, 1873, Hist. Birds N. Z. (1 st ed.), 334. Buller, 1888, Hist. Birds N. Z. (2 nd ed.) 2: 162. Phalacrocorax carunculatus (Gmelin): Buller, 1888, Hist. Birds N. Z. (2 nd ed.) 2: 155. In part. Phalacrocorax chalconotus (G. R. Gray): Buller, 1888, Hist. Birds N. Z. (2 nd ed.) 2: 162. Phalacrocorax glaucus Hombron & Jacquinot: Buller, 1888, Hist. Birds N. Z. (2 nd ed.) 2: 163. Phalacrocorax huttoni Buller, 1888: Hist. Birds N. Z. (2 nd ed.) 2: 174 – ocean beach near Dunedin, most likely Ocean Beach at Saint Clair, Dunedin (this study). Phalacrocorax chalconotus (G. R. Gray): Ogilvie- Grant, 1898, Cat. Birds Brit. Mus. 26: 369. In part. Hypoleucus campbelli stewarti (Ogilvie-Grant): Mathews & Iredale, 1913, Ibis 1 (10 th Ser.): 413. In part. Hypoleucus chalconotus (G. R. Gray): Mathews & Iredale, 1913, Ibis 1 (10 th Ser.): 413. In part. Hypoleucus chalconotus (G. R. Gray): Mathews, 1927, Syst. Avium Australasianarum 1: 227. In part. Phalacrocorax chalconotus (G. R. Gray): Oliver, 1930, N. Z. Birds (1 st ed.): 192. In part. Phalacrocorax huttoni Buller: Oliver, 1930, N. Z. Birds (1 st ed.): 190. In part. Hypoleucus chalconotus (G. R. Gray): Mathews, 1931, List Birds Australasia: 146. In part. Phalacrocorax (Leucocarbo) huttoni Buller: Falla, 1932, Rec. Auck. Inst. Mus. 1: 147. In part. Phalacrocorax (Leucocarbo) chalconotus (G. R. Gray): Falla, 1932, Rec. Auck. Inst. Mus. 1: 148. In part. Hypoleucus chalconotus (G. R. Gray): Mathews, 1936, Suppl. Birds Norfolk & Lord Howe Islands: 142. In part. Hypoleucus huttoni (Buller): Mathews, 1936, Suppl. Birds Norfolk & Lord Howe Islands: 141. In part. Phalacrocorax (Leucocarbo) carunculatus chalconotus (G. R. Gray): Checklist Committee Ornithological Society of New Zealand, 1953, Checklist N. Z. Birds: 29. In part. Leucocarbo carunculatus chalconotus (G. R. Gray): Checklist Committee OSNZ, 1970, Annot. Checklist Birds N. Z. (2 nd ed.): 32. In part. Leucocarbo chalconotus (G. R. Gray): van Tets, 1976, Proc. 16 th Int. Ornith. Cong.: 122. In part. Phalacrocorax carunculatus chalconotus (G. R. Gray): Dorst & Mougin, 1979, in Peters, Check-list Birds World 1 (2 nd ed.): 176. In part. Euleucocarbo chalconotus (G. R. Gray): Siegel-Causey, 1988, Condor 90: 892. In part. Leucocarbo chalconotus (G. R. Gray): Checklist Committee OSNZ, 1990, Checklist Birds N. Z. (3 rd ed.): 83. In part. Phalacrocorax chalconotus (G. R. Gray): O’Brien, 1990, in Marchant & Higgins, Handbook Aust. N. Z. Antarct. Birds: 876. In part. Leucocarbo (carunculatus) chalconotus (G. R. Gray): Johnsgard, 1993, Cormorants, Darters and Pelicans World: 271. In part. Leucocarbo chalconotus (G. R. Gray): Checklist Committee OSNZ, 2010, Checklist Birds N. Z. (4 th ed.): 147. In part. Leucocarbo chalconotus ‘Otago’: Rawlence et al., 2014, PLoS ONE 9: e 90769: 1.Published as part of Nicolas J. Rawlence, R. Paul Scofield, Hamish G. Spencer, Chris Lalas, Luke J. Easton, Alan J. D. Tennyson, Mark Adams, Eric Pasquet, Cody Fraser, Jonathan M. Waters & Martyn Kennedy, 2016, Genetic and morphological evidence for two species of Leucocarbo shag (Aves, Pelecaniformes, Phalacrocoracidae) from southern South Island of New Zealand, pp. 676-694 in Zoological Journal of the Linnean Society 177 on page 693, DOI: 10.1111/zoj.12376, http://zenodo.org/record/27031
Asymmetric spotty patterns for the Gray-Scott model in R^2
No full textIn this paper, we rigorously
prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain.
We show that given any two positive integers k_1,\,k_2,
there are asymmetric solutions with k_1 large spots (type A) and k_2 small spots (type B).
We also give conditions for their location and calculate their heights.
Most of these asymmetric solutions are shown
to be unstable. However, in a narrow range of parameters,
asymmetric solutions may be stable
Letter from J. R. Eakin to Arthur G. Ringland
No full textLetter (copy) from J. R. Eakin to Arthur C. Ringland about the alignment of 40 acres near the Buggeln ranch
Letter from Arno B. Cammerer to J. R. Eakin
No full textLetter from Arno B. Cammerer to J. R. Eakin describing the procedure for purchasing Bright Angel Trail
Letter from J. R. Eakin to Carl Hayden
No full textLetter from J. R. Eakin to Carl T. Hayden concerning access to Rowe Well and the canyon
Letter from J. R. Eakin to Stephen Mather
No full textLetter from J. R. Eakin to Stephen T. Mather about expenses and reconstruction of the Kaibab Trail
Letter from Carl Hayden to J. R. Eakin
No full textLetter from Carl T. Hayden to J. R. Eakin regarding changes to the Grand Canyon National Park boundaries and the purchase of lands from William Randolph Hearst
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