Accurate determination of the stability exponent and eigenvalue abscissas in a linear delay — Differential system

1997 ◽  
Author(s):  
James Louisell
Keyword(s):  
Differential System ◽  
Accurate Determination ◽  
Linear Delay ◽  
Delay Differential System ◽  
The Stability ◽  
Delay Differential

STABILITY AND HOPF BIFURCATION OF A DELAY DIFFERENTIAL SYSTEM IN MICROBIAL CONTINUOUS CULTURE

2009 ◽  
Vol 02 (03) ◽  
pp. 321-328 ◽  
Author(s):  
XIAOFANG LI ◽  
RONGNING QU ◽  
ENMIN FENG
Keyword(s):  
Hopf Bifurcation ◽  
Continuous Culture ◽  
Differential System ◽  
Center Manifold ◽  
Continuous Fermentation ◽  
Transversality Condition ◽  
Discrete Time Delay ◽  
Delay Differential System ◽  
The Stability ◽  
Delay Differential

Introducing discrete time delay into the model for producing 1, 3-propanediol by microbial continuous fermentation, the stability and Hopf bifurcation of a delay differential system for microorganisms in continuous culture are considered in this paper, including the changing regularity of bifurcation value and oscillating period. Algebraic criteria for absolute stability, as well as the transversality condition for Hopf bifurcation of this kind system are obtained. Explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and center manifold. Finally, numerical simulations show the effectiveness of our results. The pictures of periodic solutions and phase planes with specified parameters suggest that our results can qualitatively describe oscillatory phenomena occurring in experiments.

New Methodology for the Determination of the Vertical Center of Gravity of In-Service Semisubmersibles: Proposal and Numerical Assessment

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Ivan N. Porciuncula ◽  
Claudio A. Rodríguez ◽  
Paulo T. T. Esperança
Keyword(s):  
Accurate Determination ◽  
Center Of Gravity ◽  
Practical Implementation ◽  
Numerical Assessment ◽  
Neutral Equilibrium ◽  
Inclination Angles ◽  
Numerical Tools ◽  
The Stability ◽  
Metacentric Height

Along its lifetime, an offshore unit is subjected to several equipment interventions. These modifications may include large conversions in loco that usually are not adequately documented. Hence, the accurate determination of the platform's center of gravity (KG) is not possible. For vessels with low metacentric height (GM), such as semisubmersibles, Classification Societies penalize the platform's KG, inhibiting the installation of new equipment until an accurate measurement of KG is provided, i.e., until an updated inclining test is performed. For an operating semisubmersible, the execution of this type of test is not an alternative because it implies in removing the vessel from its in-service location to sheltered waters. Relatively recently, some methods have been proposed for the estimation of KG for in-service vessels. However, as all of the methods depend on accurate measurements of inclination angles and, eventually, on numerical tools for the simulation of vessel dynamics onboard, they are not straightforward for practical implementation. The objective of the paper is to present a practical methodology for the experimental determination of KG, without the need of accurate measurements of inclinations and/or complex numerical simulations, but based on actual operations that can be performed onboard. Indeed, the proposed methodology relies on the search, identification, and execution of a neutral equilibrium condition where, for instance, KG = KM. The method is exemplified using actual data of a typical semisubmersible. The paper also numerically explores and discusses the stability of the platform under various conditions with unstable initial GM, as well as the effect of mooring and risers.

scholarly journals Applications of Legendre spectral collocation method for solving system of time delay differential equations

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402092211
Author(s):  
Sami Ullah Khan ◽  
Ishtiaq Ali
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Collocation Method ◽  
Differential System ◽  
Numerical Test ◽  
Spectral Collocation Method ◽  
Numerical Techniques ◽  
Spectral Collocation ◽  
Delay Differential System ◽  
Delay Differential

The numerical techniques are regarded as the backbone of modern research. In literature, the exact solution of time delay differential models are hardly achievable or impossible. Therefore, numerical techniques are the only way to find their solution. In this article, a novel numerical technique known as Legendre spectral collocation method is used for the approximate solution of time delay differential system. Legendre spectral collocation method and their properties are applied to determined the general procedure for solving time delay differential system with detail error and convergence analysis. The method first convert the proposed system to a system of ordinary differential equations and then apply the Legendre polynomials to solve the resultant system efficiently. Finally, some numerical test problems are given to confirm the efficiency of the method and were compared with other available numerical schemes in the literature.

Factors affecting constancy of acetate concentration and correct determination of methanogenic activity in pH-stat experiments

2003 ◽  
Vol 48 (6) ◽  
pp. 111-118
Author(s):  
M. Mösche ◽  
U. Meyer
Keyword(s):  
Accurate Determination ◽  
Original Method ◽  
Experimental Conditions ◽  
Methanogenic Activity ◽  
Factors Affecting ◽  
Acetate Concentration ◽  
Correct Determination ◽  
Ph Stat ◽  
The Stability

The determination of methanogenic activity with a pH-stat titration bioassay is evaluated utilising a mathematical model of this system. For given kinetic parameters and experimental conditions the model calculates the development of titrant flow and acetate concentration during experiments. Simulations of experiments under various conditions are compared. They show that the original method inherently causes a strong drift of acetate concentration during the experiments and a misestimation of methanogenic activity. As a solution to these disadvantages the addition of sodium hydroxide to the titrant and a careful control of pH during flushing the reactor with gas prior to the experiment are recommended. In this way a better constancy of acetate concentration and a more accurate determination of methanogenic activity should be achievable. The accuracy of this method is limited by the stability of pH-electrode calibration parameters.

Factors affecting the stability and estimation of carotene in artificially dried grass and hays

1940 ◽  
Vol 30 (4) ◽  
pp. 622-638 ◽  
Author(s):  
S. K. Kon ◽  
S. Y. Thompson
Keyword(s):  
Chromatographic Analysis ◽  
Accurate Determination ◽  
Total Loss ◽  
Carotene Content ◽  
Factors Affecting ◽  
Ordinary Temperature ◽  
Initial Drop ◽  
The Difference ◽  
The Stability

1. The influence of storage in the light and in the dark at ordinary temperature and in a heated room at 70–80° F. on the carotene content of finely ground artificially dried grass stored in paper sacks and jute sacks was studied. There was an initial drop in carotene content from 61·1 to 46·5 mg./100 g., i.e. 23·9%, in the first month, and a total loss of 31·4% during 6 months' storage (August to February). No difference could be detected either between treatments or types of containers.2. There was a marked loss of carotene during 13 months' storage of baled artificially dried grass and of hays, amounting to 30–40% of the original value.3. Two methods of estimating carotene were compared. The method of Ferguson & Bishop (1936) gave higher results than the method of Peterson, Hughes & Freéman (1937). The difference is probably due to incomplete extraction in the latter method.4. Chromatographic analyses of “carotene” fractions from the above grasses showed the presence of coloured impurities amounting to 20·5–33·8% of the total recovered pigments.5. As these impurities are biologically inactive, chromatographic analysis or the use of special solvents are probably necessary for the accurate determination of carotene in forage.

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