scholarly journals A phenomenological model of the time course of maximal voluntary isometric contraction force for optimization of complex loading schemes

2018 ◽  
Author(s):  
Johannes L. Herold ◽  
Christian Kirches ◽  
Johannes P. Schlöder
Keyword(s):  
Isometric Contraction ◽  
Time Course ◽  
Complex Loading ◽  
Equation Model ◽  
Limiting Factor ◽  
Published Data ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Maximal Voluntary Isometric Contraction ◽  
Time Courses

AbstractWe construct a simple and predictive ordinary differential equation model to describe the time course of maximal voluntary isometric contraction (MVIC) force during voluntary isometric contractions and at rest. These time courses are of particular interest whenever force capacities are a limiting factor, e.g. during heavy manual work or resistance training (RT) sessions. Our model is able to describe MVIC force under complex loading schemes and is validated with a comprehensive set of published data from the elbow flexors. We use the calibrated model to analyze fatigue and recovery patterns observed in the literature. Due to the model’s structure, it can be efficiently employed to optimize complex loading schemes. We demonstrate this by computing a work-rest schedule that minimizes fatigue and an optimal isometric RT session as examples.

scholarly journals A Stochastic TB Model for a Crowded Environment

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Sibaliwe Maku Vyambwera ◽  
Peter Witbooi
Keyword(s):  
Compartmental Model ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Equation Model ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
The Stability ◽  
Crowded Environments ◽  
Disease Free

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

The half-life of the cytochrome bf complex in leaves of pea plants after transfer from moderately-high growth light to low light

2017 ◽  
Vol 44 (3) ◽  
pp. 351 ◽  
Author(s):  
Hui Zhu ◽  
Ling-Da Zeng ◽  
Xiao-Ping Yi ◽  
Chang-Lian Peng ◽  
Wang-Feng Zhang ◽  
...  
Keyword(s):  
Half Life ◽  
Time Course ◽  
Photosynthetic Capacity ◽  
High Growth ◽  
Limiting Factor ◽  
Low Light ◽  
High Photosynthetic Capacity ◽  
Growth Irradiance ◽  
The Difference ◽  
Time Courses

The content of cytochrome (cyt) bf complex is the main rate-limiting factor that determines light- and CO2-saturated photosynthetic capacity. A study of the half-life of the cyt f content in leaves was conducted whereby Pisum sativum L. plants, grown in moderately high light (HL), were transferred to low light (LL). The cyt f content in fully-expanded leaves decreased steadily over the 2 weeks after the HL-to-LL transfer, whereas control leaves in HL retained their high contents. The difference between the time courses of HL-to-LL plants and control HL plants represents the time course of loss of cyt f content, with a half-life of 1.7 days, which is >3-fold shorter than that reported for tobacco leaves at constant growth irradiance using an RNA interference approach (Hojka et al. 2014). After transfer to LL (16 h photoperiod), pea plants were re-exposed to HL for 0, 1.5 h or 5 h during the otherwise LL photoperiod, but the cyt f content of fully-expanded leaves declined practically at the same rate regardless of whether HL was re-introduced for 0, 1.5 h or 5 h during each 16 h LL photoperiod. It appears that fully-expanded leaves, having matured under HL, were unable to increase their cyt f content when re-introduced to HL. These findings are relevant to any attempts to maintain a high photosynthetic capacity when the growth irradiance is temporarily decreased by shading or overcast weather.

scholarly journals Reduced ODE dynamics as formal relativistic asymptotics of a Peierls–Nabarro model

2014 ◽  
Vol 25 (4) ◽  
pp. 511-529
Author(s):  
H. IBRAHIM ◽  
R. MONNEAU
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Half Plane ◽  
Displacement Field ◽  
Equation Model ◽  
Linear Wave ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Linear Wave Equation ◽  
Total Displacement

In this paper, we consider a scalar Peierls--Nabarro model describing the motion of dislocations in the plane (x1,x2) along the linex2=0. Each dislocation can be seen as a phase transition and creates a scalar displacement field in the plane. This displacement field solves a simplified elasto-dynamics equation, which is simply a linear wave equation. The total displacement field creates a stress which makes move the dislocation itself. By symmetry, we can reduce the system to a wave equation in the half planex2>0 coupled with an equation for the dynamics of dislocations on the boundary of the half plane, i.e. onx2=0. Our goal is to understand the dynamics of well-separated dislocations in the limit when the distance between dislocations is very large, of order 1/ɛ. After rescaling, this corresponds to introduce a small parameter ɛ in the system. For the limit ɛ → 0, we are formally able to identify a reduced ordinary differential equation model describing the dynamics of relativistic dislocations if a certain conjecture is assumed to be true.

scholarly journals Experimental and mathematical insights on the interactions between poliovirus and a defective interfering genome

2021 ◽  
Vol 17 (9) ◽  
pp. e1009277
Author(s):  
Yuta Shirogane ◽  
Elsa Rousseau ◽  
Jakub Voznica ◽  
Yinghong Xiao ◽  
Weiheng Su ◽  
...  
Keyword(s):  
Rna Viruses ◽  
Equation Model ◽  
Critical Parameters ◽  
Model Parameters ◽  
Experimental Measurements ◽  
Genome Replication ◽  
Virus Population ◽  
Wild Type ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model

During replication, RNA viruses accumulate genome alterations, such as mutations and deletions. The interactions between individual variants can determine the fitness of the virus population and, thus, the outcome of infection. To investigate the effects of defective interfering genomes (DI) on wild-type (WT) poliovirus replication, we developed an ordinary differential equation model, which enables exploring the parameter space of the WT and DI competition. We also experimentally examined virus and DI replication kinetics during co-infection, and used these data to infer model parameters. Our model identifies, and our experimental measurements confirm, that the efficiencies of DI genome replication and encapsidation are two most critical parameters determining the outcome of WT replication. However, an equilibrium can be established which enables WT to replicate, albeit to reduced levels.

scholarly journals Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 663
Author(s):  
Ying Yang ◽  
Daqing Jiang ◽  
Donal O’Regan ◽  
Ahmed Alsaedi
Keyword(s):  
Chemical Reaction ◽  
Existence And Uniqueness ◽  
Reaction Model ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Chemical Reaction Model ◽  
Theoretical Results

In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.

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