Multiple steady states in combined buoyancy and wind driven natural ventilation: The conditions for multiple solutions and the critical point for initial conditions

2008 ◽  
Vol 43 (1) ◽  
pp. 62-69 ◽  
Author(s):  
Jinchao Yuan ◽  
Leon R. Glicksman
Keyword(s):  
Critical Point ◽  
Multiple Solutions ◽  
Natural Ventilation ◽  
Initial Conditions ◽  
Steady States ◽  
Multiple Steady States

scholarly journals Multiple steady-states in the terrestrial atmosphere-biosphere system: a result of a discrete vegetation classification?

2007 ◽  
Vol 4 (5) ◽  
pp. 707-714 ◽  
Author(s):  
A. Kleidon ◽  
K. Fraedrich ◽  
C. Low
Keyword(s):  
Land Surface ◽  
Initial Conditions ◽  
Steady States ◽  
Multiple Steady States ◽  
Atmospheric Conditions ◽  
Vegetation Productivity ◽  
Positive Feedbacks ◽  
Terrestrial Atmosphere ◽  
The Difference ◽  
Global Vegetation

Abstract. Multiple steady states in the atmosphere-biosphere system can arise as a consequence of interactions and positive feedbacks. While atmospheric conditions affect vegetation productivity in terms of available light, water, and heat, different levels of vegetation productivity can result in differing energy- and water partitioning at the land surface, thereby leading to different atmospheric conditions. Here we investigate the emergence of multiple steady states in the terrestrial atmosphere-biosphere system and focus on the role of how vegetation is represented in the model: (i) in terms of a few, discrete vegetation classes, or (ii) a continuous representation. We then conduct sensitivity simulations with respect to initial conditions and to the number of discrete vegetation classes in order to investigate the emergence of multiple steady states. We find that multiple steady states occur in our model only if vegetation is represented by a few vegetation classes. With an increased number of classes, the difference between the number of multiple steady states diminishes, and disappears completely in our model when vegetation is represented by 8 classes or more. Despite the convergence of the multiple steady states into a single one, the resulting climate-vegetation state is nevertheless less productive when compared to the emerging state associated with the continuous vegetation parameterization. We conclude from these results that the representation of vegetation in terms of a few, discrete vegetation classes can result (a) in an artificial emergence of multiple steady states and (b) in a underestimation of vegetation productivity. Both of these aspects are important limitations to be considered when global vegetation-atmosphere models are to be applied to topics of global change.

scholarly journals Multiple steady-states in the terrestrial atmosphere-biosphere system: a result of a discrete vegetation classification?

2007 ◽  
Vol 4 (1) ◽  
pp. 687-705 ◽  
Author(s):  
A. Kleidon ◽  
K. Fraedrich ◽  
C. Low
Keyword(s):  
Land Surface ◽  
Initial Conditions ◽  
Steady States ◽  
Multiple Steady States ◽  
Atmospheric Conditions ◽  
Vegetation Productivity ◽  
Positive Feedbacks ◽  
Terrestrial Atmosphere ◽  
The Difference ◽  
Global Vegetation

Abstract. Multiple steady states in the atmosphere-biosphere system can arise as a consequence of interactions and positive feedbacks. While atmospheric conditions affect vegetation productivity in terms of available light, water, and heat, different levels of vegetation productivity can result in differing energy- and water partitioning at the land surface, thereby leading to different atmospheric conditions. Here we investigate the emergence of multiple steady states in the terrestrial atmosphere-biosphere system and focus on the role of how vegetation is represented in the model: (i) in terms of a few, discrete vegetation classes, or (ii) a continuous representation. We then conduct sensitivity simulations with respect to initial conditions and to the number of discrete vegetation classes in order to investigate the emergence of multiple steady states. We find that multiple steady states occur in our model only if vegetation is represented by a few vegetation classes. With an increased number of classes, the difference between the number of multiple steady states diminishes, and disappears completely in our model when vegetation is represented by 8 classes or more. Despite the convergence of the multiple steady states into a single one, the resulting climate-vegetation state is nevertheless less productive when compared to the emerging state associated with the continuous vegetation parameterization. We conclude from these results that the representation of vegetation in terms of a few, discrete vegetation classes can result (a) in an artificial emergence of multiple steady states and (b) in a underestimation of vegetation productivity. Both of these aspects are important limitations to be considered when global vegetation-atmosphere models are to be applied to topics of global change.

POVERTY TRAPS AND INFERIOR GOODS IN A DYNAMIC HECKSCHER–OHLIN MODEL

2012 ◽  
Vol 17 (6) ◽  
pp. 1227-1251 ◽  
Author(s):  
Eric W. Bond ◽  
Kazumichi Iwasa ◽  
Kazuo Nishimura
Keyword(s):  
Economic Theory ◽  
Steady State ◽  
World Economy ◽  
Steady States ◽  
The Other ◽  
Poverty Traps ◽  
Poverty Trap ◽  
Multiple Steady States ◽  
The World ◽  
State Capital

We extend the dynamic Heckscher–Ohlin model in Bond et al. [Economic Theory(48, 171–204, 2011)] and show that if the labor-intensive good is inferior, then there may exist multiple steady states in autarky and poverty traps can arise. Poverty traps for the world economy, in the form of Pareto-dominated steady states, are also shown to exist. We show that the opening of trade can have the effect of pulling the initially poorer country out of a poverty trap, with both countries having steady state capital stocks exceeding the autarky level. However, trade can also pull an initially richer country into a poverty trap. These possibilities are a sharp contrast with dynamic Heckscher–Ohlin models with normality in consumption, where the country with the larger (smaller) capital stock than the other will reach a steady state where the level of welfare is higher (lower) than in the autarkic steady state.

50 Multiple steady states in electrochemical reactors

1980 ◽  
Vol 35 (1-2) ◽  
pp. 396-404 ◽  
Author(s):  
George P. Sakellaropoulos ◽  
Brian G. Volintine
Keyword(s):  
Steady States ◽  
Multiple Steady States ◽  
Electrochemical Reactors

scholarly journals Intensification of Reactive Distillation for TAME Synthesis Based on the Analysis of Multiple Steady-State Conditions

Processes ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 241 ◽  
Author(s):  
Takehiro Yamaki ◽  
Keigo Matsuda ◽  
Duangkamol Na-Ranong ◽  
Hideyuki Matsumoto
Keyword(s):  
Liquid Flow ◽  
Reactive Distillation ◽  
Steady States ◽  
Vapor Flow ◽  
Multiple Steady States ◽  
Reflux Ratio ◽  
Flow Rates ◽  
Reaction Conversion ◽  
Reaction Performance ◽  
Separation Performances

Our previous study reported that operation in multiple steady states contributes to an improvement in reaction conversion, making it possible to reduce the energy consumption of the reactive distillation process for tert-amyl methyl ether (TAME) synthesis. This study clarified the factors responsible for an improvement in the reaction conversion for operation in the multiple steady states of the reactive distillation column used in TAME synthesis. The column profiles for those conditions, in which multiple steady states existed and those in which they did not exist, were compared. The vapor and liquid flow rates with the multiple steady states were larger than those when the multiple steady states did not exist. The effect of the duty of the intermediate condenser, which was introduced at the top of the reactive section, on the liquid flow rate for a reflux ratio of 1 was examined. The amount of TAME production increased from 55.2 to 72.1 kmol/h when the intermediate condenser was operated at 0 to −5 MW. Furthermore, the effect of the intermediate reboiler duty on the reaction performance was evaluated. The results revealed that the liquid and vapor flow rates influenced the reaction and separation performances, respectively.

The NO + CO reaction on clean Pt(lOO): Multiple steady states and oscillations

1988 ◽  
Vol 206 (1-2) ◽  
pp. 169-186 ◽  
Author(s):  
S.B. Schwartz ◽  
L.D. Schmidt
Keyword(s):  
Steady States ◽  
Multiple Steady States
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