scholarly journals Alan Turing-ek morfogenesiaren inguruan egindako ikerketaren analisi matematikoa

2021 ◽  
Author(s):  
Jone Apraiz Iza ◽  
Idoia Marauri Bernedo
Keyword(s):  
Continuous Ring ◽  
Chemical Basis ◽  
Alan Turing ◽  
And Diffusion

Artikulu honetan, Alan Turing matematikariak 1952an morfogenesiaren inguruan aurkeztu zuen «The Chemical Basis of Morphogenesis» lanaren zati bat aurkeztu eta matematikoki garatuko dugu. Horretarako, beharrezkoak diren matematikako kontzeptuak eta baliabideak azalduko ditugu. Konkretuki, Alan Turingek lan horretako “Reactions and Diffusion in a Ring of Cells” (eraztun diskretuko eremua) eta “Continuous Ring of Tissue” (eraztun jarraituko eremua) ataletan gehiegi sakondu edo zehaztu gabe erabili zituen ekuazio diferentzialak, erreakzio-difusio ekuazioak, Fourier-en serieak eta funtzioen linealizazioa azalduko ditugu eta bi eremu horietan planteatutako ekuazio sistemen soluzioak bilatzeko erabiliko ditugu. Artikulu hau UPV/EHUko Idoia Marauri ikasle ohiaren Gradu Amaierako Lanean oinarrituta dago.

scholarly journals Forging patterns and making waves from biology to geology: a commentary on Turing (1952) ‘The chemical basis of morphogenesis’

2015 ◽  
Vol 370 (1666) ◽  
pp. 20140218 ◽  
Author(s):  
Philip Ball
Keyword(s):  
Royal Society ◽  
Natural Process ◽  
Substantial Impact ◽  
Sand Ripples ◽  
Chemical Basis ◽  
Spontaneous Formation ◽  
Alan Turing ◽  
Random Fluctuations ◽  
And Diffusion ◽  
350Th Anniversary

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, ‘The chemical basis of morphogenesis’, on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of ‘Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society .

scholarly journals Towards an integrated experimental–theoretical approach for assessing the mechanistic basis of hair and feather morphogenesis

2012 ◽  
Vol 2 (4) ◽  
pp. 433-450 ◽  
Author(s):  
K. J. Painter ◽  
G. S. Hunt ◽  
K. L. Wells ◽  
J. A. Johansson ◽  
D. J. Headon
Keyword(s):  
Pattern Formation ◽  
Theoretical Approach ◽  
Spatial Patterning ◽  
Biological Processes ◽  
Chemical Basis ◽  
Alan Turing ◽  
Theoretical Approaches ◽  
Simple Demonstration ◽  
Mechanistic Basis ◽  
Elegant Solution

In his seminal 1952 paper, ‘The Chemical Basis of Morphogenesis’, Alan Turing lays down a milestone in the application of theoretical approaches to understand complex biological processes. His deceptively simple demonstration that a system of reacting and diffusing chemicals could, under certain conditions, generate spatial patterning out of homogeneity provided an elegant solution to the problem of how one of nature's most intricate events occurs: the emergence of structure and form in the developing embryo. The molecular revolution that has taken place during the six decades following this landmark publication has now placed this generation of theoreticians and biologists in an excellent position to rigorously test the theory and, encouragingly, a number of systems have emerged that appear to conform to some of Turing's fundamental ideas. In this paper, we describe the history and more recent integration between experiment and theory in one of the key models for understanding pattern formation: the emergence of feathers and hair in the skins of birds and mammals.

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

Renilla Bioluminescence: A Morphologic Approach to the Location of Photocytes

1974 ◽  
Vol 32 ◽  
pp. 208-209
Author(s):  
Ben O. Spurlock ◽  
Milton J. Cormier
Keyword(s):  
Excited State ◽  
Ground State ◽  
Molecular Basis ◽  
Light Emission ◽  
Chemical Basis ◽  
Electronic Excited State ◽  
Colonial Form ◽  
The Common ◽  
Eighteenth And Nineteenth Centuries ◽  
Catalyzed Oxidation

The phenomenon of bioluminescence has fascinated layman and scientist alike for many centuries. During the eighteenth and nineteenth centuries a number of observations were reported on the physiology of bioluminescence in Renilla, the common sea pansy. More recently biochemists have directed their attention to the molecular basis of luminosity in this colonial form. These studies have centered primarily on defining the chemical basis for bioluminescence and its control. It is now established that bioluminescence in Renilla arises due to the luciferase-catalyzed oxidation of luciferin. This results in the creation of a product (oxyluciferin) in an electronic excited state. The transition of oxyluciferin from its excited state to the ground state leads to light emission.

Ordering and diffusion in II-VI/III-VI alloys with structural vacancies

1997 ◽  
Vol 101-103 (1-2) ◽  
pp. 479-487
Author(s):  
H v. Wensierski
Keyword(s):  
And Diffusion
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