scholarly journals Nonlinear Compartment Models with Time-Dependent Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1657
Author(s):  
Jochen Merker ◽  
Benjamin Kunsch ◽  
Gregor Schuldt
Keyword(s):  
Stable Equilibrium ◽  
Compartment Model ◽  
Basins Of Attraction ◽  
Dynamical Behaviour ◽  
Time Dependent ◽  
Compartment Models ◽  
Autonomous Case ◽  
Hyperbolic Equilibrium ◽  
Interior Points ◽  
Two Parameter

A nonlinear compartment model generates a semi-process on a simplex and may have an arbitrarily complex dynamical behaviour in the interior of the simplex. Nonetheless, in applications nonlinear compartment models often have a unique asymptotically stable equilibrium attracting all interior points. Further, the convergence to this equilibrium is often wave-like and related to slow dynamics near a second hyperbolic equilibrium on the boundary. We discuss a generic two-parameter bifurcation of this equilibrium at a corner of the simplex, which leads to such dynamics, and explain the wave-like convergence as an artifact of a non-smooth nearby system in C0-topology, where the second equilibrium on the boundary attracts an open interior set of the simplex. As such nearby idealized systems have two disjoint basins of attraction, they are able to show rate-induced tipping in the non-autonomous case of time-dependent parameters, and induce phenomena in the original systems like, e.g., avoiding a wave by quickly varying parameters. Thus, this article reports a quite unexpected path, how rate-induced tipping can occur in nonlinear compartment models.

scholarly journals Two-Parameter Dynamics of An Autonomous Mechanical Governor System With Time Delay

2021 ◽  
Author(s):  
Shuning Deng ◽  
Jinchen Ji ◽  
Guilin Wen ◽  
Huidong Xu
Keyword(s):  
Time Delay ◽  
Dynamical Behavior ◽  
Evolutionary Process ◽  
Basins Of Attraction ◽  
Poincaré Section ◽  
Poincare Section ◽  
Interesting Phenomenon ◽  
Computing Technique ◽  
Intersection Points ◽  
Two Parameter

Abstract Understanding of dynamical behavior in the parameter-state space plays a vital role in the optimal design and motion control of mechanical governor systems. By combining the GPU parallel computing technique with two determinate indicators, namely, the Lyapunov exponents and Poincaré section, this paper presents a detailed study on the two-parameter dynamics of a mechanical governor system with different time delays. By identifying different system responses in two-parameter plane, it is shown that the complexity of evolutionary process can increase significantly with the increase of time delay. The path-following strategy and the time domain collocation method are used to explore the details of the evolutionary process. An interesting phenomenon is found in the dynamical behavior of the delayed governor system, which can cause the inconsistency between the number of intersection points of certain periodic response on Poincaré section and the actual period characteristic. For example, the commonly exhibited period-1 orbit may have two or more intersection points on the Poincaré section instead of one point. Furthermore, the variations of basins of attraction are also discussed in the plane of initial history conditions to demonstrate the observed multistability phenomena and chaotic transitions.

scholarly journals Automated Compartment Model Development Based on Data from Flow-Following Sensor Devices

Processes ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1651
Author(s):  
Jonas Bisgaard ◽  
Tannaz Tajsoleiman ◽  
Monica Muldbak ◽  
Thomas Rydal ◽  
Tue Rasmussen ◽  
...  
Keyword(s):  
Large Scale ◽  
Model Development ◽  
Axial Flow ◽  
Compartment Model ◽  
Mixing Times ◽  
Flow Rates ◽  
Stirred Vessel ◽  
Compartment Models ◽  
Flow Models ◽  
Sensor Devices

Due to the heterogeneous nature of large-scale fermentation processes they cannot be modelled as ideally mixed reactors, and therefore flow models are necessary to accurately represent the processes. Computational fluid dynamics (CFD) is used more and more to derive flow fields for the modelling of bioprocesses, but the computational demands associated with simulation of multiphase systems with biokinetics still limits their wide applicability. Hence, a demand for simpler flow models persists. In this study, an approach to develop data-based flow models in the form of compartment models is presented, which utilizes axial-flow rates obtained from flow-following sensor devices in combination with a proposed procedure for automatic zoning of volume. The approach requires little experimental effort and eliminates the necessity for computational determination of inter-compartmental flow rates and manual zoning. The concept has been demonstrated in a 580 L stirred vessel, of which models have been developed for two types of impellers with varying agitation intensities. The sensor device measurements were corroborated by CFD simulations, and the performance of the developed compartment models was evaluated by comparing predicted mixing times with experimentally determined mixing times. The data-based compartment models predicted the mixing times for all examined conditions with relative errors in the range of 3–27%. The deviations were ascribed to limitations in the flow-following behavior of the sensor devices, whose sizes were relatively large compared to the examined system. The approach provides a versatile and automated flow modelling platform which can be applied to large-scale bioreactors.

scholarly journals Modeling Growth, Containment and Decay of the COVID-19 Epidemic in Italy

2020 ◽  
Vol 8 ◽  
Author(s):  
Francesco Capuano
Keyword(s):  
Exponential Growth ◽  
Compartment Model ◽  
Growth Behavior ◽  
Time Dependent ◽  
Model Parameters ◽  
Susceptible Population ◽  
Dependent Rate ◽  
Slow Decay ◽  
Cumulative Curve ◽  
Modeling Growth

A careful inspection of the cumulative curve of confirmed COVID-19 infections in Italy and in other hard-hit countries reveals three distinct phases: i) an initial exponential growth (unconstrained phase), ii) an algebraic, power-law growth (containment phase), and iii) a relatively slow decay. We propose a parsimonious compartment model based on a time-dependent rate of depletion of the susceptible population that captures all such phases for a plausible range of model parameters. The results suggest an intimate interplay between the growth behavior, the timing and implementation of containment strategies, and the subsequent saturation of the outbreak.

scholarly journals Comparisons of two-, three-, and four-compartment models of body composition analysis in men and women

1998 ◽  
Vol 85 (1) ◽  
pp. 238-245 ◽  
Author(s):  
R. T. Withers ◽  
J. LaForgia ◽  
R. K. Pillans ◽  
N. J. Shipp ◽  
B. E. Chatterton ◽  
...  
Keyword(s):  
Body Composition ◽  
Compartment Model ◽  
Dry Mass ◽  
Fat Free Mass ◽  
Composition Analysis ◽  
Compartment Models ◽  
Bone Mineral Mass ◽  
Body Composition Measurement ◽  
Composition Measurement ◽  
Total Body

This study compared the traditional two-compartment (fat mass or FM; fat free mass or FFM) hydrodensitometric method of body composition measurement, which is based on body density, with three (FM, total body water or TBW, fat free dry mass)- and four (FM, TBW, bone mineral mass or BMM, residual)-compartment models in highly trained men ( n = 12), sedentary men ( n = 12), highly trained women ( n = 12), and sedentary women ( n = 12). The means and variances for the relative body fat (%BF) differences between the two- and three-compartment models [2.2 ± 1.6 (SD) % BF; n = 48] were significantly greater ( P ≤ 0.02) than those between the three- and four-compartment models (0.2 ± 0.3% BF; n = 48) for all four groups. The three-compartment model is more valid than the two-compartment hydrodensitometric model because it controls for biological variability in TBW, but additional control for interindividual variability in BMM via the four-compartment model achieves little extra accuracy. The combined group ( n = 48) exhibited greater ( P < 0.001) FFM densities (1.1075 ± 0.0049 g/cm3) than the hydrodensitometric assumption of 1.1000 g/cm3, which is based on analyses of three male cadavers aged 25, 35, and 46 yr. This was primarily because their FFM hydration (72.4 ± 1.1%; n = 48) was lower ( P ≤ 0.001) than the hydrodensitometric assumption of 73.72%.

The evolution of slender inviscid drops in an axisymmetric straining flow

1980 ◽  
Vol 101 (3) ◽  
pp. 545-553 ◽  
Author(s):  
E. J. Hinch
Keyword(s):  
Global Stability ◽  
Stable Equilibrium ◽  
Stability Result ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Initial Shape ◽  
Low Reynolds Numbers ◽  
Long Wavelength ◽  
Shape Equation ◽  
Low Reynolds

The evolution of the shape of a slender inviscid drop in an axisymmetric straining motion is studied at low Reynolds numbers. It is found that the shape equation can be solved by polynommals with time-dependent coefficients. A global stability result can be used to show simply that only one possible equilibrium is stable. It is further shown that if the slender drop starts with a long-wavelength waist then it cannot go to this stable equilibrium and must either extend indefinitely or burst. In the class of trinomial shapes, it is shown that the drop either bursts or goes to the stable equilibrium, depending on whether or not the initial shape has a waist.

scholarly journals CMEs ‘en rafale’ observations and simulations

2008 ◽  
Vol 4 (S257) ◽  
pp. 251-255
Author(s):  
Cristiana Dumitrache
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Solar Disk ◽  
Large Scale ◽  
Stable Equilibrium ◽  
Time Dependent ◽  
Kink Mode ◽  
Mhd Equilibrium ◽  
Ideal Mhd ◽  
Slow Evolution

AbstractA CME is triggered by the disappearance of a stable equilibrium as a result of the slow evolution of the photospheric magnetic field. This disappearance may be due to a loss of ideal-MHD equilibrium or stability as in the kink mode, or to a loss of resistive-MHD equilibrium as a result of magnetic reconnection. We have obtained CMEs in sequence by a time dependent magnetohydrodynamic computation performed on three solar radii. These successive CMEs resulted from a prominence eruption. Velocities of these CMEs decrease in time, from a CME to another. We present observational evidences for large-scale magnetic reconnections that caused the destabilization of a sigmoid filament. These reconnections covered half of the solar disk and produced CMEs in squall (sequential CMEs).

Determination of digesta fill and passage rate from nonabsorbed particulate phase markers using the single dosing method

1989 ◽  
Vol 67 (2) ◽  
pp. 488-494 ◽  
Author(s):  
D. F. Holleman ◽  
R. G. White
Keyword(s):  
Compartment Model ◽  
Time Dependent ◽  
Passage Rate ◽  
Fecal Output ◽  
Two Compartment Model ◽  
Significant Difference ◽  
Single Marker ◽  
Dependent Model ◽  
Digesta Passage

A method is given for analyzing particulate digestive marker data in terms of digesta fill, fecal output, and digesta passage times. The method applies the Stewart – Hamilton Principle to data obtained from a single marker dosing followed by feces sampling; it assumes steady-state conditions for the digesta, but makes no assumptions concerning compartmentalization of digesta. Data analyses are presented for an experiment with sheep in which a particle phase marker, cerium-141 chloride, was used. The estimate of fecal output obtained was 1.8 ± 2.2% (mean percent difference ± SE) greater than the actual fecal output; the in vivo estimate of total digesta fill was 3.3 ± 3.4% less than measured digesta fill. For comparison, the present data were also analyzed using two established compartment modeling approaches, namely a time-independent and a time-dependent two-compartment model. The only significant difference between the estimated parameters as obtained from the Stewart – Hamilton method and the compartmental models was a significantly shorter transit time as estimated by the time-dependent model.

scholarly journals A theoretical connection between the Noisy Leaky integrate-and-fire and the escape rate models: The non-autonomous case

2020 ◽  
Vol 15 ◽  
pp. 59
Author(s):  
Grégory Dumont ◽  
Jacques Henry ◽  
Carmen Oana Tarniceriu
Keyword(s):  
Mathematical Model ◽  
General Framework ◽  
Time Dependent ◽  
Escape Rate ◽  
Neural Dynamics ◽  
General View ◽  
Integrate And Fire ◽  
Autonomous Case ◽  
Stochastic Framework ◽  
Statistical Similarity

Finding a mathematical model that incorporates various stochastic aspects of neural dynamics has proven to be a continuous challenge. Among the different approaches, the noisy leaky integrate-and-fire and the escape rate models are probably the most popular. These two models are generally thought to express different noise action over the neural cell. In this paper we investigate the link between the two formalisms in the case of a neuron subject to a time dependent input. To this aim, we introduce a new general stochastic framework. As we shall prove, our general framework entails the two already existing ones. Our results have theoretical implications since they offer a general view upon the two stochastic processes mostly used in neuroscience, upon the way they can be linked, and explain their observed statistical similarity.

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