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.

scholarly journals Theta Method Dynamics

2000 ◽  
Vol 3 ◽  
pp. 27-43 ◽  
Author(s):  
Graeme J. Barclay ◽  
David F. Griffiths ◽  
Desmond J. Higham
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Lower Bounds ◽  
Nonlinear Differential Equations ◽  
Stable Steady State ◽  
Numerical Examples ◽  
Existence And Stability ◽  
Theta Method ◽  
Period Two Solutions

AbstractLong-term solutions of the theta method applied to scalar nonlinear differential equations are studied in this paper. In the case where the equation has a stable steady state, lower bounds on the basin of non-oscillatory, monotonic attraction for the theta method are derived. Spurious period two solutions are then analysed. Under mild assumptions, precise results are obtained concerning the generic nature and stability of these solutions for small timesteps. Particular problem classes are studied, and direct connections are made between the existence and stability of period two solutions and the dynamics of the theta method. The analysis is extended to a wide class of semi-discretized partial differential equations. Numerical examples are given.

The bacterial numeration and an observation of a new syntrophic association for granular sludge

1997 ◽  
Vol 36 (6-7) ◽  
pp. 133-140 ◽  
Author(s):  
Zhu Jianrong ◽  
Hu Jicui ◽  
Gu Xiasheng
Keyword(s):  
Anaerobic Bacteria ◽  
Granular Sludge ◽  
Methanogenic Bacteria ◽  
Uasb Reactor ◽  
Two Phase ◽  
Methanogenic Activity ◽  
Syntrophic Association ◽  
Group I ◽  
Acetogenic Bacteria ◽  
Fermentative Bacteria

The bacterial numeration and microbial observation were made on granular sludge from laboratory single and two-phase UASB reactors. It was shown that the fermentative bacteria (group I), H2-producing acetogenic bacteria (group II) and methanogenic bacteria (group III) of granular sludge in single UASB reactor were 9.3 × 108−4.3 × 109, 4.3 × 107−4.3 × 108, 2.0−4.3 × 108, respectively, during the granulation process. The sludge of methanogenic reactor exhibited the similar results. That indicates there is no big difference between suspended and granular sludge, and bacterial population for three groups of anaerobic bacteria are similar. The formation of granular sludge depends mainly on the organization and arrangement of bacteria. An observation of granular sludge using electron microscope revealed that the fermentative bacteria and hydrogenotrophic methanogens existed on outer surface of granules, and aceticlastic methanogens and H2-producing acetogenic bacteria occupied the inner layer. A new syntrophic association between Methanosaeta sp. and Syntrophomonas sp. (even plus Methanobrevibacter sp.) was observed. Because Methanosaeta can effectively convert the acetate (the end product of propionate and butyrate) to methane, such a new syntrophic association is supposed to support the degradation of short fatty acids and high methanogenic activity of granular sludge. Based on structural pattern, a hypothesis on mechanism of granulation called “crystallized nuclei formation” is proposed.

Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns

2018 ◽  
Vol 9 (1) ◽  
pp. 22-50 ◽  
Author(s):  
Thomas Y.S. Lee
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Repair Process ◽  
Polling System ◽  
Steady State Analysis ◽  
Relaxation System ◽  
Polling Model ◽  
State Dependent ◽  
Non Linear ◽  
State Analysis

Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.

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