20,204 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
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
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
Pleasant and Hannah Gray Biographical Info
No full textA xeroxed copy of a page out of the book: Walker County, Texas: a History. The section included is written by Shirley Scott Dye about Pleasant and Hannah Gray
Pleasant and Hannah Gray Biographical Info
No full textA xeroxed copy of a page out of the book: Walker County, Texas: a History. The section included is written by Shirley Scott Dye about Pleasant and Hannah Gray
William Scott Southgate to Hannah Hughes Gray, 1891
No full textOne letter from William Scott Southgate to Hannah Hughes Gray, December 28, 1891
Depression and Gender: The Expression and Experience of Melancholy in the Eighteenth Century
No full textThis thesis investigates the life and work of six eighteenth-century writers, two male and four female. It explores their experience of depression through their letters and other autobiographical material, and examines the ways in which they represent melancholy in their poetry and prose. The subject of Chapter Two is Thomas Gray, whose real life persona as the lonely intellectual is also identifiable in his poetry. The Scottish poet Robert Fergusson is studied in Chapter Three. Fergusson’s lively and vigorous mind was shattered in the months leading up to his death, during which time some of his writing became darkly nihilistic. Chapter Four looks at Anne Finch, Countess of Winchilsea, a lifelong depressive who often wrote about her feelings of despair in her poetry. Chapter Five explores Lady Mary Wortley Montagu. She was a courageous and controversial figure, but despite her resilience, on occasion in her letters she reveals her vulnerability and susceptibility to low spirits, a mood which is sometimes expressed in her creative writing. Sarah Scott, whose life and work have not yet been considered in relation to the subject of melancholy, is examined in Chapter Six. Her novel includes several low-spirited and depressed female characters who are continually seeking asylum from a hostile world. Chapter Seven analyses Charlotte Smith, a mother of twelve children whose unhappy marriage ended in separation. Smith wrote extensively about her depression in her letters, prefaces, poetry and novels.
This study shows that the women in particular use their writing on melancholy and depression to express their discontent with the confined way in which they are often expected to live out their lives
An innocent at home: Scott Pilgrim and his Canadian multicultural contexts
No full textbook chapterThe chapter, "An innocent at home: Scott Pilgrim and his Canadian multicultural contexts" was written by the listed authors Brenna Clarke Gray and Peter Wilkins (Douglas College Faculty). Part of the Routledge research in cultural and media studies series.Published
A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates
No full textWe consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with
fractional reaction rates such as the Sel'kov model, the
Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt
system.
We give some sufficient and explicit conditions for stability
by studying the corresponding nonlocal eigenvalue problem in a new
range of parameters
Compromise between minimization and maximization of entropy production in reversible Gray-Scott model
No full text
In this work, the evolution of entropy production in the Gray-Scott model (P. Gray and S. K. Scott, Chemical Engineering Science 38 (1983) 29-43) is investigated for four representative cases within three regimes. It is revealed that the extremal trends of entropy production for these cases are regime-dependent. In the monostable regime without heterogeneous structures, the steady state follows the minimization of entropy production. For the bistable uniform regime, the steady state with higher entropy production prevails over that with lower entropy production. As to the heterogeneous states that emerge around the bifurcation curves, the entropy production varies in both space and time, showing alternate appearance of states corresponding to minimum and maximum values of entropy production, respectively. The spatiotemporal compromise between maximization and minimization of entropy production appears to govern the corresponding steady states in different regimes. (C) 2016 Elsevier Ltd. All rights reserved.</p
- …
