The existence and stability of nontrivial steady-state for a delay competition-diffusion model

1999 ◽  
Vol 4 (4) ◽  
pp. 377-381 ◽  
Author(s):  
Zhou Li ◽  
Shawgy Hussein
Keyword(s):  
Steady State ◽  
Diffusion Model ◽  
Existence And Stability ◽  
Competition Diffusion

scholarly journals Carbon cycle at steady state in an ocean. Simulation using a box diffusion model.

1990 ◽  
Vol 16 (6) ◽  
pp. 1195-1202
Author(s):  
Atsushi Inaba ◽  
Yuji Shindo ◽  
Hiroshi Komiyama
Keyword(s):  
Steady State ◽  
Carbon Cycle ◽  
Diffusion Model ◽  
Ocean Simulation

Spherical Diffusion Model of Interspecies Hydrogen Transfer in Steady-State Methanogenic Reactors

1992 ◽  
Vol 26 (9-11) ◽  
pp. 2389-2392 ◽  
Author(s):  
D. P. Smith
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Diffusion Model ◽  
Hydrogen Concentration ◽  
Hydrogen Transfer ◽  
Solution Concentration ◽  
Bulk Solution ◽  
Transfer Resistance ◽  
Concentration Difference ◽  
Spherical Diffusion

A previously developed spherical diffusion model of interspecies molecular hydrogen transfer was applied to a mathematical model of ethanol and propionate methanogenesis in a dispersed-growth, continuously stirred tank reactor (CSTR). Steady-state methanogenesis at a 0.10 day−1 space velocity required a hydrogen concentration difference of 1.12 × 10−5 aim (8.4 × 10−12 moles/cm3) between the surface of the propionate organisms and the bulk solution. The total difference in hydrogen concentration between source organism and sink organism Ihydrogenotrophic methanogenstwas 2.1 × 10−5 atm (1.6 × 10−11 moles/cm3). Steep gradients in hydrogen concentration existed only at close proximity to the bacterial spheres, with hydrogen concentration approaching bulk solution concentration at distances greater than 10 microns. Small hydrogen gradients and the bulk solution concentration prevailed through the majority of the reactor aqueous volume. Overall, the incorporation of hydrogen mass transfer resistance into the mathematical model had only a slight effect on hydrogen partial pressure, organic substrate levels, and bacterial mass concentrations predicted by the steady-state solution.

scholarly journals Existence and stability of steady-state solutions of the shallow-ice-sheet equation by an energy-minimization approach

2011 ◽  
Vol 57 (202) ◽  
pp. 345-354 ◽  
Author(s):  
Guillaume Jouvet ◽  
Jacques Rappaz ◽  
Ed Bueler ◽  
Heinz Blatter
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Mass Balance ◽  
Energy Minimization ◽  
Existence Of Solutions ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Existence And Stability ◽  
Steady State Solutions ◽  
Minimization Approach

AbstractThe existence of solutions of the non-sliding shallow-ice-sheet equation on a flat horizontal bed with a mass balance linearly depending on altitude is proven for fixed margins. Free-margin solutions for the same mass balance do not exist. Fixed-margin solutions show unbounded shear stress and nonzero mass flux at the margin. Steady-state solutions with realistic margins, vanishing ice flux and vanishing shear stress are found numerically for ice sheets with Weertman-type sliding.

scholarly journals Steady state analysis of a syntrophic model: the effect of a new input substrate concentration

2018 ◽  
Vol 13 (3) ◽  
pp. 31
Author(s):  
Y. Daoud ◽  
N. Abdellatif ◽  
T. Sari ◽  
J. Harmand
Keyword(s):  
Steady State ◽  
Methanogenic Bacteria ◽  
Stable Steady State ◽  
Operating Parameters ◽  
Steady State Analysis ◽  
Bacteria Growth ◽  
Digestion Process ◽  
Acetogenic Bacteria ◽  
Existence And Stability ◽  
Exponentially Stable

In this work, we are interested in a reduced and simplified model of the anaerobic digestion process. We focus on the acetogenesis and hydrogenetrophic methanogenesis phases. The model describes a syntrophic relashionship between two microbial species (the acetogenic bacteria and the hydrogenetrophic methanogenic bacteria) with two input substrates (the fatty acids and the hydrogen) including both decay terms and inhibition of the acetogenic bacteria growth by an excess of hydrogen in the system. The existence and stability analysis of the steady states of the model points out the existence of a new equilibrium point which can be stable according to the operating parameters of the system. By means of operating diagrams, we show that, whatever the region of space considered, there exists only one locally exponentially stable steady state.

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