scholarly journals Pattern formation of vascular network in a mathematical model of angiogenesis

2021 ◽  
Author(s):  
Jun Mada ◽  
Tetsuji Tokihiro
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Vascular Network

A mathematical model of self-organized pattern formation on the combs of honeybee colonies

1990 ◽  
Vol 147 (4) ◽  
pp. 553-571 ◽  
Author(s):  
Scott Camazine ◽  
James Sneyd ◽  
Michael J. Jenkins ◽  
J.D. Murray
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Self Organized

A model for the longitudinal patterns shaped by water on erodible rocks

2020 ◽  
Author(s):  
Matteo Bernard Bertagni ◽  
Carlo Camporeale
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Laminar Flow ◽  
Spatial Scales ◽  
Concentration Field ◽  
Water Film ◽  
Time And Space ◽  
Longitudinal Patterns ◽  
Flow Intensity ◽  
Alpine Environments

<p>The interactions between water and rocks create an extensive variety of marvelous patterns, which span on several classes of time and space scales. In this work, we provide a mathematical model for the formation of longitudinal erosive patterns commonly found in karst and alpine environments. The model couples the hydrodynamics of a laminar flow of water (Orr-Somerfield equation) to the concentration field of the eroded-rock chemistry. Results show that an instability of the plane rock wetted by the water film leads to a longitudinal channelization responsible for the pattern formation. The spatial scales predicted by the model span over different orders of magnitude depending on the flow intensity and this may explain why similar patterns of different sizes are observed in nature (millimetric microrills, centimetric rillenkarren, decametric solution runnels).</p>

scholarly journals Pattern Formation by Lateral Inhibition with Feedback: a Mathematical Model of Delta-Notch Intercellular Signalling

1996 ◽  
Vol 183 (4) ◽  
pp. 429-446 ◽  
Author(s):  
Joanne R. Collier ◽  
Nicholas A.M. Monk ◽  
Philip K. Maini ◽  
Julian H. Lewis
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Lateral Inhibition ◽  
Intercellular Signalling

A Mathematical Model of Pattern Formation by Swimming Microorganisms*

1975 ◽  
Vol 22 (2) ◽  
pp. 296-306 ◽  
Author(s):  
M. LEVANDOWSKY ◽  
W. S. CHILDRESS ◽  
E. A. SPIEGEL ◽  
S. H. HUTNER
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Swimming Microorganisms

A mathematical model of pattern formation

1986 ◽  
Vol 123 (1) ◽  
pp. 81-101 ◽  
Author(s):  
Eduardo J. Chichilnisky
Keyword(s):  
Mathematical Model ◽  
Pattern Formation

A new mathematical model for pattern formation by cranial sutures

2016 ◽  
Vol 408 ◽  
pp. 66-74 ◽  
Author(s):  
Kenji Yoshimura ◽  
Ryo Kobayashi ◽  
Tomohisa Ohmura ◽  
Yoshinaga Kajimoto ◽  
Takashi Miura
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Cranial Sutures
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