scholarly journals IDENTIFICATION OF A TEMPERATURE DEPENDENT FITZHUGH–NAGUMO MODEL FOR THE BELOUSOV–ZHABOTINSKII REACTION

2011 ◽  
Vol 21 (11) ◽  
pp. 3249-3258 ◽  
Author(s):  
Y. ZHAO ◽  
S. A. BILLINGS ◽  
D. COCA ◽  
Y. GUO ◽  
R. I. RISTIC ◽  
...  
Keyword(s):  
Oscillation Frequency ◽  
Propagation Speed ◽  
Oscillatory Behavior ◽  
Steady States ◽  
Model Parameters ◽  
Good Representation ◽  
Temperature Dependent ◽  
Control Variables ◽  
The Stability ◽  
Belousov Zhabotinskii Reaction

This paper describes the identification of a temperature dependent FitzHugh–Nagumo model directly from experimental observations with controlled inputs. By studying the steady states and the trajectory of the phase of the variables, the stability of the model is analyzed and a rule to generate oscillation waves is proposed. The dependence of the oscillation frequency and propagation speed on the model parameters is then investigated to seek the appropriate control variables, which then become functions of temperature in the identified model. The results show that the proposed approach can provide a good representation of the dynamics of the oscillatory behavior of a Belousov–Zhabotinskii reaction.

scholarly journals A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1393
Author(s):  
Xiaochang Duan ◽  
Hongwei Yuan ◽  
Wei Tang ◽  
Jingjing He ◽  
Xuefei Guan
Keyword(s):  
Composite Materials ◽  
Constitutive Model ◽  
Model Parameters ◽  
Temperature Dependent ◽  
Stress Strain ◽  
Proposed Model ◽  
Single Temperature ◽  
Testing Data ◽  
Bonded Composite ◽  
Tension And Compression

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Da Yang ◽  
Liling Zhu ◽  
Yun Pu
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Model Parameters ◽  
Optimal Velocity ◽  
Stability Functions ◽  
Car Following Model ◽  
Traffic Wave ◽  
The Stability ◽  
Different Characteristics ◽  
Stationary Velocity

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

scholarly journals A Theoretical Model for the Transmission Dynamics of the Buruli Ulcer with Saturated Treatment

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ebenezer Bonyah ◽  
Isaac Dontwi ◽  
Farai Nyabadza
Keyword(s):  
Human Population ◽  
Reproduction Number ◽  
Buruli Ulcer ◽  
Coupled System ◽  
Model Parameters ◽  
The Public ◽  
Treatment Function ◽  
Medical Facilities ◽  
The Stability ◽  
Saturated Treatment

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

Sensitivity Analysis for Nonlinear Heat Conduction

2000 ◽  
Vol 123 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Kevin J. Dowding ◽  
Bennie F. Blackwell
Keyword(s):  
Heat Conduction ◽  
General Procedure ◽  
Model Parameters ◽  
Nonlinear Heat Conduction ◽  
Temperature Dependent ◽  
Sensitivity Equations ◽  
Verification Problem ◽  
Temperature Variable ◽  
Numerical Solver ◽  
Temperature Dependent Properties

Parameters in the heat conduction equation are frequently modeled as temperature dependent. Thermal conductivity, volumetric heat capacity, convection coefficients, emissivity, and volumetric source terms are parameters that may depend on temperature. Many applications, such as parameter estimation, optimal experimental design, optimization, and uncertainty analysis, require sensitivity to the parameters describing temperature-dependent properties. A general procedure to compute the sensitivity of the temperature field to model parameters for nonlinear heat conduction is studied. Parameters are modeled as arbitrary functions of temperature. Sensitivity equations are implemented in an unstructured grid, element-based numerical solver. The objectives of this study are to describe the methodology to derive sensitivity equations for the temperature-dependent parameters and present demonstration calculations. In addition to a verification problem, the design of an experiment to estimate temperature variable thermal properties is discussed.

scholarly journals Using the LIST model to Estimate the Effects of Contact Tracing on COVID-19 Endemic Equilibria in England and its Regions

2020 ◽  
Author(s):  
Rosalyn J. Moran ◽  
Alexander J. Billig ◽  
Maell Cullen ◽  
Adeel Razi ◽  
Jean Daunizeau ◽  
...  
Keyword(s):  
Endemic Equilibrium ◽  
Contact Tracing ◽  
Model Parameters ◽  
Infection Rates ◽  
Stable States ◽  
Medium Term ◽  
The Stability ◽  
Lower Death Rate ◽  
The Impact ◽  
List Model

AbstractGovernments across Europe are preparing for the emergence from lockdown, in phases, to prevent a resurgence in cases of COVID-19. Along with social distancing (SD) measures, contact tracing – find, track, trace and isolate (FTTI) policies are also being implemented. Here, we investigate FTTI policies in terms of their impact on the endemic equilibrium. We used a generative model – the dynamic causal ‘Location’, ‘Infection’, ‘Symptom’ and ‘Testing’ (LIST) model to identify testing, tracing, and quarantine requirements. We optimised LIST model parameters based on time series of daily reported cases and deaths of COVID-19 in England— and based upon reported cases in the nine regions of England and in all 150 upper tier local authorities. Using these optimised parameters, we forecasted infection rates and the impact of FTTI for each area—national, regional, and local. Predicting data from early June 2020, we find that under conditions of medium-term immunity, a ‘40%’ FTTI policy (or greater), could reach a distinct endemic equilibrium that produces a significantly lower death rate and a decrease in ICU occupancy. Considering regions of England in isolation, some regions could substantially reduce death rates with 20% efficacy. We characterise the accompanying endemic equilibria in terms of dynamical stability, observing bifurcation patterns whereby relatively small increases in FTTI efficacy result in stable states with reduced overall morbidity and mortality. These analyses suggest that FTTI will not only save lives, even if only partially effective, and could underwrite the stability of any endemic steady-state we manage to attain.

scholarly journals Estimation of Rate Constants for Nutrient Transformations

2019 ◽  
Vol 8 (3) ◽  
pp. 2437-2441
Keyword(s):  
Water Quality ◽  
Rate Constants ◽  
High Water ◽  
Model Parameters ◽  
Success Factor ◽  
Point Source Pollution ◽  
Temperature Dependent ◽  
Phosphate Nitrate ◽  
Simulation Errors ◽  
Key Success Factor

Non-point source pollution of surface water is a major impediment to meet water quality objectives. Managing such pollution sources in a sustainable way is a key success factor in maintaining high water quality and to prevent eutrophication. Mathematical models are widely used to simulate ecological and water quality interactions in surface waters. Simulation errors may arise due to uncertainties of the structure, input data and the model parameters. In this study, an attempt has been made to estimate the rate constants for nutrient transformations in Kabini River located in Southern part of Karnataka state in India. The experimental results demonstrated both ammonia and nitrite oxidation. In the river water, DO concentration was 5.2 mg/L. After addition of pollutants it reduced to 3.9 mg/L. EC changed from 370 to 550 µS/cm. pH remained almost the same. At 320C, the rate constants for phosphate, nitrate, nitrite, potassium and ammonia were found to be 0.165, 0.21, 0.077, 0.0777 and 0.078/hr respectively. The results obtained clearly specify that the rate constants are concentration and temperature dependent.

Temperature Field Simulation of Anode Erosion in Electric Discharge Machining

2010 ◽  
Vol 455 ◽  
pp. 345-349
Author(s):  
B.C. Xie ◽  
Zhen Long Wang ◽  
Yu Kui Wang ◽  
Jing Zhi Cui
Keyword(s):  
Temperature Field ◽  
Electric Discharge ◽  
Material Removal ◽  
Machining Process ◽  
Model Parameters ◽  
Temperature Dependent ◽  
Electric Discharge Machining ◽  
Field Simulation ◽  
Simulation And Experiment ◽  
Anode Erosion

In this paper, a thermo-physical model of the electric discharge machining process using finite element method is presented. In this model, parameters such as convection, the latent heat and the thermal properties based on temperature dependent etc. are studied to predict the temperature distribution in the workpiece. The temperature field simulation and experiment were carried out by adopting parameters through optimum pulse curve, and amending the effects of recast layer, the simulation results amended shows a better agreement with experimental results, indicating a theoretical foundation for mechanism of material removal in EDM machining.

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