A bistable kinetic system with oscillations on the thermodynamic and flow-through branches

1987 ◽  
Vol 52 (10) ◽  
pp. 2365-2374 ◽  
Author(s):  
Antonín Tockstein
Keyword(s):  
Characteristic Equation ◽  
Parameter Dependence ◽  
Fourth Degree ◽  
Stationary Concentration ◽  
Competitive Reactions ◽  
Stirred Reactor ◽  
Kinetic System ◽  
Oscillatory Character ◽  
Flow Through ◽  
Parallel Reactions

A model of a flow-through perfectly stirred reactor comprising three consecutive competitive reactions with parallel reactions of some intermediates and exhibiting bistable behaviour and possessing regions with an oscillatory character on the thermodynamic branch is treated. The stationary concentration vs parameter dependence is of the fourth degree and the characteristic equation, of the fifth degree.

scholarly journals Does denitrification occur within porous carbonate sand grains?

2017 ◽  
Vol 14 (18) ◽  
pp. 4061-4069 ◽  
Author(s):  
Perran Louis Miall Cook ◽  
Adam John Kessler ◽  
Bradley David Eyre
Keyword(s):  
Grain Size ◽  
Habitat Type ◽  
Carbonate Sediments ◽  
Carbonate Sand ◽  
Sediment Grain Size ◽  
Stirred Reactor ◽  
Sediment Fraction ◽  
Consumption Rates ◽  
Flow Through ◽  
Oxygen Concentrations

Abstract. Permeable carbonate sands form a major habitat type on coral reefs and play a major role in organic matter recycling. Nitrogen cycling within these sediments is likely to play a major role in coral reef productivity, yet it remains poorly studied. Here, we used flow-through reactors and stirred reactors to quantify potential rates of denitrification and the dependence of denitrification on oxygen concentrations in permeable carbonate sands at three sites on Heron Island, Australia. Our results showed that potential rates of denitrification fell within the range of 2–28 µmol L−1 sediment h−1 and were very low compared to oxygen consumption rates, consistent with previous studies of silicate sands. Denitrification was observed to commence at porewater oxygen concentrations as high as 50 µM in stirred reactor experiments on the coarse sediment fraction (2–10 mm) and at oxygen concentrations of 10–20 µM in flow-through and stirred reactor experiments at a site with a median sediment grain size of 0.9 mm. No denitrification was detected in sediments under oxic conditions from another site with finer sediment (median grain size: 0.7 mm). We interpret these results as confirmation that denitrification may occur within anoxic microniches present within porous carbonate sand grains. The occurrence of such microniches has the potential to enhance denitrification rates within carbonate sediments; however further work is required to elucidate the extent and ecological significance of this effect.

On the subject of influence of dissipative and permanent momentums on stability of uniform rotations of two elastically connected free gyroscopes of Lagrange

2019 ◽  
Vol 33 ◽  
pp. 132-141
Author(s):  
Yuri Kononov ◽  
Yaroslav Sviatenko
Keyword(s):  
Asymptotic Stability ◽  
Characteristic Equation ◽  
Joint Stiffness ◽  
Quadratic Equation ◽  
Stability Conditions ◽  
Spherical Joint ◽  
Fourth Degree ◽  
Left Hand ◽  
Resisting Medium ◽  
Complex Coefficients

In many works, there are studies of the asymptotic stability of rotation of a free Lagrange gyroscope in a resisting medium. This article generalizes this problem to the case of uniform rotations of two free Lagrange gyroscopes connected by an elastic restoring spherical hinge. The rotation of each gyroscope is maintained by a constant moment in an inertial coordinate system. The characteristic equation of the perturbed motion is presented in the form of an algebraic equation of the fourth degree with complex coefficients. Based on the innor approach, conditions of asymptotic stability are obtained in the form of a system of three inequalities. The left-hand side of these inequalities is represented, respectively, in the form of determinants of the third, fifth, and seventh orders. Up to first-order values of smallness, relative to the reciprocal of the stiffness coefficient, a study is made of the effect of the joint stiffness on stability conditions. From the conditions of positivity of the highest coefficients in three inequalities, it is shown that for a sufficiently large rigidity, the stability conditions are determined by only one inequality. Cases of degeneration of an elastic spherical joint into a spherical inelastic, cylindrical, and universal elastic joint (Hooke's joint) are considered. In the case of an inelastic spherical joint, the system of three inequalities is slightly simplified. The greatest simplification arises in the case of a cylindrical hinge. In this case, the characteristic equation is represented as a quadratic equation with complex coefficients. According to the innoric approach, the conditions of asymptotic stability are written in the form of a single inequality, the left side of which is presented in the form of third-order determinants. It is shown that this inequality coincides with the inequality obtained earlier for the case of a sufficiently large rigidity of the hinge. If the angular velocities of the proper rotations of the gyroscopes coincide, the inequality obtained for the cylindrical hinge coincides with the well-known inequality for one gyroscope. In the case of a universal elastic hinge (Hooke's hinge), the first inequality is represented as a square inequality with respect to the angular velocity of proper rotation.

scholarly journals Analytical modeling of the binary dynamic circuit motion

2021 ◽  
Vol 9 (5) ◽  
pp. 23-32
Author(s):  
Anatolii Alpatov ◽  
Victor Kravets ◽  
Volodymyr Kravets ◽  
Erik Lapkhanov
Keyword(s):  
Characteristic Equation ◽  
Initial Phase ◽  
Analytical Modeling ◽  
Phase State ◽  
Translational Motion ◽  
Elastic Interaction ◽  
Dissipative Function ◽  
Fourth Degree ◽  
Phase Coordinates ◽  
Particular Solution

The binary dynamic circuit, which can be a design scheme for a number of technical systems is considered in the paper. The dynamic circuit is characterized by the kinetic energy of the translational motion of two masses, the potential energy of these masses’ elastic interaction and the dissipative function of energy dissipation during their motion. The free motion of a binary dynamic circuit is found according to a given initial phase state. A mathematical model of the binary dynamic circuit motion in the canonical form and the corresponding characteristic equation of the fourth degree are compiled. Analytical modeling of the binary dynamic circuit is carried out on the basis of the proposed particular solution of the complete algebraic equation of the fourth degree. A homogeneous dynamic circuit is considered and the reduced coefficients of elasticity and damping are introduced. The dependence of the reduced coefficients of elasticity and damping is established, which provides the required class of solutions to the characteristic equation. An ordered form of the analytical representation of a dynamic process is proposed in symmetric determinants, which is distinguished by the conservatism of notation with respect to the roots of the characteristic equation and phase coordinates.

Development of apical pits in chloride cells of the gills of Pimephales promelas after chronic exposure to acid water

1983 ◽  
Vol 41 ◽  
pp. 462-463
Author(s):  
Richard L. Leino ◽  
Jon G. Anderson ◽  
J. Howard McCormick
Keyword(s):  
Confidence Interval ◽  
Chronic Exposure ◽  
Lake Superior ◽  
Pimephales Promelas ◽  
Chloride Cells ◽  
Fathead Minnows ◽  
Secondary Lamellae ◽  
Untreated Water ◽  
Water Ph ◽  
Flow Through

Groups of 12 fathead minnows were exposed for 129 days to Lake Superior water acidified (pH 5.0, 5.5, 6.0 or 6.5) with reagent grade H2SO4 by means of a multichannel toxicant system for flow-through bioassays. Untreated water (pH 7.5) had the following properties: hardness 45.3 ± 0.3 (95% confidence interval) mg/1 as CaCO3; alkalinity 42.6 ± 0.2 mg/1; Cl- 0.03 meq/1; Na+ 0.05 meq/1; K+ 0.01 meq/1; Ca2+ 0.68 meq/1; Mg2+ 0.26 meq/1; dissolved O2 5.8 ± 0.3 mg/1; free CO2 3.2 ± 0.4 mg/1; T= 24.3 ± 0.1°C. The 1st, 2nd and 3rd gills were subsequently processed for LM (methacrylate), TEM and SEM respectively.Three changes involving chloride cells were correlated with increasing acidity: 1) the appearance of apical pits (figs. 2,5 as compared to figs. 1, 3,4) in chloride cells (about 22% of the chloride cells had pits at pH 5.0); 2) increases in their numbers and 3) increases in the % of these cells in the epithelium of the secondary lamellae.

Flow Through Heterogeneous Geologic Media

2015 ◽  
Author(s):  
Tian-Chyi Yeh ◽  
Raziuddin Khaleel ◽  
Kenneth C. Carroll
Keyword(s):  
Flow Through ◽  
Geologic Media
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