On the Stability Intervals of the Hill Equation

1959 ◽  
Vol 7 (1) ◽  
pp. 101-106
Author(s):  
C. R. Putnam
Keyword(s):  
Hill Equation ◽  
Stability Intervals ◽  
The Stability ◽  
The Hill

scholarly journals Floquet Theory for Discontinuously Supported Waveguides

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
A. Sorzia
Keyword(s):  
Floquet Theory ◽  
Periodic Coefficient ◽  
Fundamental Solutions ◽  
Hill Equation ◽  
Elastic Waveguide ◽  
Elastic String ◽  
Winkler Elastic Foundation ◽  
The Stability ◽  
The Hill ◽  
Band Gap Structure

We apply Floquet theory of periodic coefficient second-order ODEs to an elastic waveguide. The waveguide is modeled as a uniform elastic string periodically supported by a discontinuous Winkler elastic foundation and, as a result, a Hill equation is found. The fundamental solutions, the stability regions, and the dispersion curves are determined and then plotted. An asymptotic approximation to the dispersion curve is also given. It is further shown that the end points of the band gap structure correspond to periodic and semiperiodic solutions of the Hill equation.

STABILITY BOUNDARY AND DURATION TIME OF SYNCHRONIZATION FOR COUPLED CHAOTIC MATHIEU–DUFFING OSCILLATORS

2008 ◽  
Vol 22 (27) ◽  
pp. 4817-4831
Author(s):  
JIANHE SHEN ◽  
JIANPING CAI ◽  
SHUHUI CHEN ◽  
KECHANG LIN
Keyword(s):  
Coupling Strength ◽  
Stability Boundary ◽  
Hill Equation ◽  
Critical Values ◽  
Stability Boundaries ◽  
Synchronization Time ◽  
Duration Time ◽  
Error System ◽  
The Stability ◽  
The Hill

The stability boundaries and behaviors of the duration time of synchronization for chaotic Mathieu–Duffing oscillators are investigated. Based on the unidirectional or bidirectional linear state error feedback coupled scheme, the error system is derived. After replacing the chaotic orbit by a regular orbit containing multi-harmonics, we analyze the asymptotic stability of the error system, which leads to a Hill equation. According to Floquet theory and the properties of the Hill equation, the evolution of the discriminant of the Hill equation with respect to the coupling strength is traced to determine the stability boundaries between the synchronization and desynchronization domains. Thus, the critical values of coupling strength are obtained. These critical values are in good agreement with those from numerical simulations. The behaviors of the synchronization time are numerically investigated in the synchronization domain. It is found that the synchronization time reaches an asymptotic minimal value when the oscillators are unidirectionally or bidirectionally coupled, and the two asymptotic minimal values are almost the same. It is also noted that the slowing down behavior of the synchronization time can occur inside the synchronization domain when the coupling is bidirectional.

scholarly journals Resonance tongues for the Hill equation with Duffing coefficients and instabilities in a nonlinear beam equation

2017 ◽  
Vol 20 (01) ◽  
pp. 1750022 ◽  
Author(s):  
Carlo Gasparetto ◽  
Filippo Gazzola
Keyword(s):  
Nauk Sssr ◽  
Elliptic Functions ◽  
Periodic Coefficient ◽  
Hill Equation ◽  
Beam Equation ◽  
Stability And Instability ◽  
Beam Equations ◽  
Akad Nauk Sssr ◽  
The Stability ◽  
The Hill

We consider a class of Hill equations where the periodic coefficient is the squared solution of some Duffing equation plus a constant. We study the stability of the trivial solution of this Hill equation and we show that a criterion due to Burdina [Boundedness of solutions of a system of differential equations, Dokl. Akad. Nauk. SSSR 92 (1953) 603–606] is very helpful for this analysis. In some cases, we are also able to determine exact solutions in terms of Jacobi elliptic functions. Overall, we obtain a fairly complete picture of the stability and instability regions. These results are then used to study the stability of nonlinear modes in some beam equations.

scholarly journals Pharmacodynamics of Daptomycin against Enterococcus faecium and Enterococcus faecalis in the Murine Thigh Infection Model

2018 ◽  
Vol 62 (10) ◽  
Author(s):  
James M. Kidd ◽  
Kamilia Abdelraouf ◽  
Tomefa E. Asempa ◽  
Romney M. Humphries ◽  
David P. Nicolau
Keyword(s):  
Enterococcus Faecalis ◽  
Enterococcus Faecium ◽  
Hill Equation ◽  
Infection Model ◽  
Free Drug Concentration ◽  
Time Curve ◽  
Content Type ◽  
Concentration Time ◽  
The Hill ◽  
Susceptibility Breakpoint

ABSTRACT The Clinical and Laboratory Standards Institute (CLSI) daptomycin MIC susceptibility breakpoint for the treatment of enterococcal infections is ≤4 μg/ml. However, patients receiving daptomycin for the treatment of infections caused by enterococci with MICs of ≤4 μg/ml may experience treatment failures. We assessed the pharmacodynamics of daptomycin against enterococci in a neutropenic murine thigh infection model and determined the exposures necessary for bacteriostasis and a 1-log10-CFU reduction of Enterococcus faecalis and Enterococcus faecium. We further characterized daptomycin efficacy at clinically achievable exposures. Six E. faecium and 6 E. faecalis isolates (daptomycin MICs, 0.5 to 32 μg/ml) were studied. Daptomycin was administered at various doses over 24 h to achieve area under the free drug concentration-time curve-to-MIC ratios (fAUC0–24/MIC) ranging from 1 to 148. Daptomycin regimens that simulate mean human exposures following doses of 6, 8, and 10 mg/kg of body weight/day were also studied. Efficacy was assessed by the differences in the number of log10 CFU per thigh at 24 h. The Hill equation was used to estimate the fAUC0–24/MIC required to achieve bacteriostasis and a 1-log10-CFU reduction. For E. faecium, a 1-log10-CFU reduction required an fAUC0–24/MIC of 12.9 (R2 = 0.71). For E. faecalis, a 1-log10-CFU reduction was not achieved, while the fAUC0–24/MIC required for stasis was 7.2 (R2 = 0.8). With a human-simulated regimen of 6 mg/kg/day, a 1-log10-CFU reduction was observed in 3/3 E. faecium isolates with MICs of <4 μg/ml and 0/3 E. faecium isolates with MICs of ≥4 μg/ml; however, a 1-log10-CFU reduction was not achieved for any of the 6 E. faecalis isolates. These results, alongside clinical data, prompt a reevaluation of the current breakpoint.

Effect of osmotic swelling and shrinkage on Na(+)-K+ pump activity in mammalian cardiac myocytes

1993 ◽  
Vol 265 (5) ◽  
pp. C1201-C1210 ◽  
Author(s):  
D. W. Whalley ◽  
L. C. Hool ◽  
R. E. Ten Eick ◽  
H. H. Rasmussen
Keyword(s):  
Ventricular Myocytes ◽  
Pump Current ◽  
Hill Equation ◽  
Cell Swelling ◽  
Intracellular Na Activity ◽  
Single Ventricular Myocytes ◽  
Hyperosmolar Solutions ◽  
Hill Coefficients ◽  
The Hill ◽  
The Relationship

The effect on the sarcolemmal Na(+)-K+ pump of exposure to anisosmolar solutions was examined using whole cell patch clamping and ion-selective microelectrodes. Na(+)-K+ pump currents were measured in single ventricular myocytes by using pipette Na+ concentrations ([Na]pip) of 0-70 mM. The relationship between [Na]pip and pump current was well described by the Hill equation. The [Na]pip for half-maximal pump current (K0.5) was 21.4 mM in isosmolar (310 mosM) solution. K0.5 was 12.8 mM during cell swelling in hyposmolar solution (240 mosM) and 39.0 mM during cell shrinkage in hyperosmolar solution (464 mosM). The maximal pump currents, derived from the best fit of the Hill equation, and the Hill coefficients were similar in isosmolar, hyposmolar, and hyperosmolar solutions. A sustained (> 20 min) decrease in the intracellular Na+ activity developed during exposure of intact papillary muscles to hyposmolar solutions, and a sustained increase developed during exposure to hyperosmolar solutions. We conclude that osmotic myocyte swelling stimulates the sarcolemmal Na(+)-K+ pump at near-physiological levels of intracellular Na+, whereas shrinkage inhibits the pump. These changes are due to increases and decreases, respectively, in the apparent affinity of the pump for Na+.

Perspective on the relationship between GABAA receptor activity and the apparent potency of an inhibitor

2021 ◽  
Vol 19 ◽  
Author(s):  
Allison L. Germann ◽  
Spencer R. Pierce ◽  
Alex S. Evers ◽  
Joe Henry Steinbach ◽  
Gustav Akk
Keyword(s):  
Gabaa Receptor ◽  
Hill Equation ◽  
Response Relationship ◽  
Inhibition Concentration ◽  
Level Of Activity ◽  
Control Response ◽  
The Hill ◽  
The Relationship ◽  
Inhibition Curve ◽  
Receptor Channel

Background : In electrophysiological experiments inhibition of a receptor-channel, such as the GABAA receptor, is measured by co-applying an agonist producing a predefined control response with an inhibitor to calculate the fraction of the control response remaining in the presence of the inhibitor. The properties of the inhibitor are determined by fitting the inhibition concentration-response relationship to the Hill equation to estimate the midpoint (IC50) of the inhibition curve. Objective: We sought to estimate here the sensitivity of the fitted IC50 to the level of activity of the control response. Methods: The inhibition concentration-response relationships were calculated for models with distinct mechanisms of inhibition. In Model I, the inhibitor acts allosterically to stabilize the resting state of the receptor. In Model II, the inhibitor competes with the agonist for a shared binding site. In Model III, the inhibitor stabilizes the desensitized state. Results: The simulations indicate that the fitted IC50 of the inhibition curve is sensitive to the degree of activity of the control response. In Models I and II, the IC50 of inhibition was increased as the probability of being in the active state (PA) of the control response increased. In Model III, the IC50 of inhibition was reduced at higher PA. Conclusions: We infer that the apparent potency of an inhibitor depends on the PA of the control response. While the calculations were carried out using the activation and inhibition properties that are representative of the GABAA receptor, the principles and conclusions apply to a wide variety of receptor-channels.

scholarly journals Kinetic studies on two isoforms of acetyl-CoA carboxylase from maize leaves

1996 ◽  
Vol 318 (3) ◽  
pp. 997-1006 ◽  
Author(s):  
Derek HERBERT ◽  
Lindsey J PRICE ◽  
Claude ALBAN ◽  
Laure DEHAYE ◽  
Dominique JOB ◽  
...  
Keyword(s):  
Kinetic Studies ◽  
Product Inhibition ◽  
Hill Equation ◽  
Acetyl Coa Carboxylase ◽  
Acetyl Coa ◽  
Maize Leaves ◽  
Ic50 Values ◽  
A Minor ◽  
The Hill

The steady-state kinetics of two multifunctional isoforms of acetyl-CoA carboxylase (ACCase) from maize leaves (a major isoform, ACCase1 and a minor isoform, ACCase2) have been investigated with respect to reaction mechanism, inhibition by two graminicides of the aryloxyphenoxypropionate class (quizalofop and fluazifop) and some cellular metabolites. Substrate interaction and product inhibition patterns indicated that ADP and Pi products from the first partial reaction were not released before acetyl-CoA bound to the enzymes. Product inhibition patterns did not match exactly those predicted for an ordered Ter Ter or a random Ter Ter mechanism, but were close to those postulated for an ordered mechanism. ACCase2 was about 1/2000 as sensitive as ACCase1 to quizalofop but only about 1/150 as sensitive to fluazifop. Fitting inhibition data to the Hill equation indicated that binding of quizalofop or fluazifop to ACCase1 was non-cooperative, as shown by the Hill constant (napp) values of 0.86 and 1.16 for quizalofop and fluazifop respectively. Apparent inhibition constant values (K´ from the Hill equation) for ACCase1 were 0.054 µM for quizalofop and 21.8 µM for fluazifop. On the other hand, binding of quizalofop or fluazifop to ACCase2 exhibited positive co-operativity, as shown by the napp values of 1.85 and 1.59 for quizalofop and fluazifop respectively. K´ values for ACCase2 were 1.7 mM for quizalofop and 140 mM for fluazifop. Kinetic parameters for the co-operative binding of quizalofop to maize ACCase2 were close to those of another multifunctional ACCase of limited sensitivity to graminicide, ACC220 from pea. Inhibition of ACCase1 by quizalofop was mixed-type with respect to acetyl-CoA or ATP, but the concentration of acetyl-CoA had the greater effect on the level of inhibition. Neither ACCase1 nor ACCase2 was appreciably sensitive to CoA esters of palmitic acid (16:0) or oleic acid (18:1). Approximate IC50 values were 10 µM (ACCase2) and 50 µM (ACCase1) for both CoA esters. Citrate concentrations up to 1 mM had no effect on ACCase1 activity. Above this concentration, citrate was inhibitory. ACCase2 activity was slightly stimulated by citrate over a broad concentration range (0.25–10 mM). The significance of possible effects of acyl-CoAs or citrate in vivo is discussed.

scholarly journals Integrated Simulation Modeling Approach for Investigating Pore Water Pressure Induced Landslides

2022 ◽  
Author(s):  
Sahila Beegum ◽  
P J Jainet ◽  
Dawn Emil ◽  
K P Sudheer ◽  
Saurav Das
Keyword(s):  
Pore Water ◽  
Factor Of Safety ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Simulation Models ◽  
Integrated Simulation ◽  
Hill Slope ◽  
Slope Factor ◽  
The Stability ◽  
The Hill

Abstract Soil pore water pressure analysis is crucial for understanding landslide initiation and prediction. However, field-scale transient pore water pressure measurements are complex. This study investigates the integrated application of simulation models (HYDRUS-2D/3D and GeoStudio–Slope/W) to analyze pore water pressure-induced landslides. The proposed methodology is illustrated and validated using a case study (landslide in India, 2018). Model simulated pore water pressure was correlated with the stability of hillslope, and simulation results were found to be co-aligned with the actual landslide that occurred in 2018. Simulations were carried out for natural and modified hill slope geometry in the study area. The volume of water in the hill slope, temporal and spatial evolution of pore water pressure, and factor of safety were analysed. Results indicated higher stability in natural hillslope (factor of safety of 1.243) compared to modified hill slope (factor of safety of 0.946) despite a higher pore water pressure in the natural hillslope. The study demonstrates the integrated applicability of the physics-based models in analyzing the stability of hill slopes under varying pore water pressure and hill slope geometry and its accuracy in predicting future landslides.

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