A MATHEMATICAL MODEL FOR TRAINING IMPULSE AND LACTATE INFLUX AND OUTFLUX DURING EXERCISE

2009 ◽  
Vol 20 (01) ◽  
pp. 147-177 ◽  
Author(s):  
JOHN F. MOXNES ◽  
KJELL HAUSKEN
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Lactate Concentration ◽  
Lactate Production ◽  
Published Data ◽  
Interval Exercise ◽  
Common Concept ◽  
Training Impulse ◽  
The Mathematical Model ◽  
Upper Boundary

This paper provides a mathematical description based on the theory of differential equations, for the dynamics of lactate production and removal. Analytical and numerical results for training/exercise of endurance of athletes are presented based on the common concept of training impulse (Trimp). The relationships between activity, production rate, and removal strategies of lactate are studied. Parameters are estimated from published data. A model for optimum removal of lactate after exercise is developed. The model provides realistic predictions when compared with experimental results. We show some specific examples for the usefulness of the mathematical model by studying some recent problems discussed in the literature. (a) Is interval exercise more beneficial than steady-state exercise? (b) What is the optimum aerobic power during recovery? We discuss whether steady-state exercise gives higher Trimp than interval exercise, when imposing an upper boundary for the lactate concentration as a constraint. The model allows for testing all imaginable kinds of steady-state and interval exercises in search of the optimal exercise regime for individuals with various kinds of characteristics. In general, the dynamic model constitute a powerful tool describing the processes by which the concentration of lactate can be studied and controlled to decrease fatigue and increase endurance.

scholarly journals New “Full-Bridge Buck Inverter–DC Motor” System: Steady-State and Dynamic Analysis and Experimental Validation

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1216 ◽  
Author(s):  
Eduardo Hernández-Márquez ◽  
Carlos Alejandro Avila-Rea ◽  
José Rafael García-Sánchez ◽  
Ramón Silva-Ortigoza ◽  
Magdalena Marciano-Melchor ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Motor System ◽  
Circuit Simulation ◽  
Dc Motor ◽  
Matlab Simulink ◽  
Duty Cycles ◽  
System Variables ◽  
The Mathematical Model ◽  
Steady State Stability

A mathematical model of a new “full-bridge Buck inverter–DC motor” system is developed and experimentally validated. First, using circuit theory and the mathematical model of a DC motor, the dynamic behavior of the system under study is deduced. Later, the steady-state, stability, controllability, and flatness properties of the deduced model are described. The flatness property, associated with the mathematical model, is then exploited so that all system variables and the input can be differentially parameterized in terms of the flat output, which is determined by the angular velocity. Then, when a desired trajectory is proposed for the flat output, the input signal is calculated offline and is introduced into the system. In consequence, the validation of the mathematical model for constant and time-varying duty cycles is possible. Such a validation of this mathematical model is tackled from two directions: (1) by circuit simulation through the SimPowerSystems toolbox of Matlab-Simulink and (2) via a prototype of the system built by using Matlab-Simulink and a DS1104 board. The good similarities between the circuit simulation and the experimental results allow satisfactorily validating the mathematical model.

VALIDATION OF THEIN VITROINCUBATION OF EXTENSOR DIGITORUM LONGUS MUSCLE FROM MICE WITH A MATHEMATICAL MODEL

2010 ◽  
Vol 18 (03) ◽  
pp. 687-707
Author(s):  
PETER SOGAARD ◽  
MIKAEL HARLÉN ◽  
YUN CHAU LONG ◽  
FERENC SZEKERES ◽  
BRIAN R. BARNES ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Experimental Method ◽  
Glycogen Content ◽  
Lactate Concentration ◽  
Lactate Production ◽  
Measuring Method ◽  
High Rate ◽  
Diabetes Research ◽  
Spatial Differences

In vitro incubation of tissues; in particular, skeletal muscles from rodents, is a widely-used experimental method in diabetes research. This experimental method has previously been validated, both experimentally and theoretically. However, much of the method's experimental data remains unclear, including the high-rate of lactate production and the lack of an observable increase in glycogen content, within a given time. The predominant hypothesis explaining the high-rate of lactate production is that this phenomenon is dependent on a mechanism in glycolysis that works as a safety valve, producing lactate when glucose uptake is super-physiological. Another hypothesis is that existing anoxia forces more ATP to be produced from glycolysis, leading to an increased lactate concentration. The lack of an observable increase in glycogen content is assumed to be dependent on limitations in sensitivity of the measuring method used. We derived a mathematical model to investigate which of these hypotheses is most likely to be correct. Using our model, data analysis indicates that the in vitro incubated muscle specimens, most likely are sensing the presence of existing anoxia, rather than an overflow in glycolysis. The anoxic milieu causes the high lactate production. The model also predicts an increased glycogenolysis. After mathematical analyses, an estimation of the glycogen concentration could be made with a reduced model. In conclusion, central anoxia is likely to cause spatial differences in glycogen concentrations throughout the entire muscle. Thus, data regarding total glycogen levels in the incubated muscle do not accurately represent the entire organ. The presented model allows for an estimation of total glycogen, despite spatial differences present in the muscle specimen.

The Effect of Leakage on Railroad Brake Pipe Steady State Behavior

1988 ◽  
Vol 110 (3) ◽  
pp. 329-335 ◽  
Author(s):  
K. Abdol-Hamid ◽  
D. E. Limbert ◽  
G. A. Chapman
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Transmission Lines ◽  
Computation Time ◽  
State Behavior ◽  
Implicit Finite Difference Scheme ◽  
Inlet Flow Rate ◽  
Model Equations ◽  
The Mathematical Model ◽  
Steady State Behavior

A mathematical model for pneumatic transmission lines containing leakage is developed. This model is used to show the effect of leakage size and distribution on the steady state behavior of the brake pipe on a train brake system. The model equations are solved using the implicit finite difference scheme without neglecting any terms. The model is presented in a nonlinear continuous network form, consisting of N sections. Each of the network sections represents one car and may contain one leakage. A computer program was developed to solve the model equations. This program is capable of simulating a train with cars of various lengths and takes a minimum amount of computation time as compared with previous methods. Through analysis and experimentation, the authors have demonstrated that pressure gradient and inlet flow rate are very sensitive to leakage locations as compared with leakage size. The results, generated by the mathematical model, are compared with the experimental data of two different brake pipe set-ups having different dimensions.

scholarly journals Mass transfer during electrodeposition of metals at a periodically changing rate

1999 ◽  
Vol 64 (5-6) ◽  
pp. 317-340 ◽  
Author(s):  
Miodrag Maksimovic ◽  
Konstantin Popov
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Steady State ◽  
Layer 4 ◽  
Millisecond Range ◽  
The Mathematical Model ◽  
Pulsating Current ◽  
Pulsating Overpotential ◽  
Changing Rate ◽  
Electrodeposition Of Metals

1. Introduction 2. Mass transfer in the steady state periodic condition 2.1. Reversing current 2.2. Pulsating current 2.3. Alternating current superimposed on direct current 3. The influence of the charge and discharge of the electrical double layer 4. The validity of the mathematical model 4.1. Reversing current in the millisecond range 4.2. Reversing current in the second range 4.3. Pulsating current 4.4. Pulsating overpotential 5. Conclusion

scholarly journals On the global attractors in one mathematical model of antiviral immunity

2020 ◽  
Author(s):  
Alexei Tsygvintsev
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Immune System ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Antiviral Immunity ◽  
Global Attractors ◽  
Viral Pathogens ◽  
Basic Reproductive Ratio ◽  
The Mathematical Model

AbstractWe consider the mathematical model introduced by Batholdy et al. [1] describing the interaction between viral pathogens and immune system. We prove the global asymptotic stability of the infection steady-state if the basic reproductive ratio R0 is greater than unity. That solves the conjecture announced in [7].

The Simulation of Six Phase PMSM Taking Iron Loss into Account

2012 ◽  
Vol 433-440 ◽  
pp. 7535-7540
Author(s):  
Dong Xing ◽  
Xiao Ning Zhang ◽  
Yong Ling Fu ◽  
Hai Tao Qi
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Dynamic Response ◽  
Iron Loss ◽  
Field Oriented Control ◽  
Three Phase ◽  
Simulation Results ◽  
Set Up ◽  
The Mathematical Model ◽  
Fast Dynamic

This paper studies the mathematical model considering iron loss in the d-q axis of six phase permanent magnetic synchronous motor (PMSM), through the expansion of Field-Oriented Control (FOC) based on three phase PMSM, the simulation model of six phase PMSM under environment of simulink7.0 is set up, which has fast dynamic response, high steady-state precision, and has no problems about current balance compared to dual three phase PMSM. In order to get an accurate simulation results, this mathematical model takes iron loss into account. The simulation results show that iron loss have bad effects on the performance of PMSM especially affect the dynamic response, and to reduce the bad effects, the resistance of the motor core should be increased.

scholarly journals STUDY OF TRANSIENT AND STATIONARY OPERATION MODES OF SYNCHRONOUS SYSTEM CONSISTING IN TWO MACHINES

2017 ◽  
Vol 60 (3) ◽  
pp. 228-236
Author(s):  
V. S. Safaryan
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Power System ◽  
Mathematical Models ◽  
Coordinate System ◽  
Electric Power ◽  
Electric Power System ◽  
Machine System ◽  
Transient Regimes ◽  
The Mathematical Model

The solution of the problem of reliable functioning of an electric power system (EPS) in steady-state and transient regimes, prevention of EPS transition into asynchronous regime, maintenance and restoration of stability of post-emergency processes is based on formation and realization of mathematical models of an EPS processes. During the functioning of electric power system in asynchronous regime, besides the main frequencies, the currents and voltages include harmonic components, the frequencies of which are multiple of the difference of main frequencies. At the two-frequency asynchronous regime the electric power system is being made equivalent in a form of a two-machine system, functioning for a generalized load. In the article mathematical models of transient process of a two-machine system in natural form and in d–q coordinate system are presented. The mathematical model of two-machine system is considered in case of two windings of excitement at the rotors. Also, in the article varieties of mathematical models of EPS transient regimes (trivial, simple, complete) are presented. Transient process of a synchronous two-machine system is described by the complete model. The quality of transient processes of a synchronous machine depends on the number of rotor excitation windings. When there are two excitation windings on the rotor (dual system of excitation), the mathematical model of electromagnetic transient processes of a synchronous machine is represented in a complex form, i.e. in coordinate system d, q, the current of rotor being represented by a generalized vector. In asynchronous operation of a synchronous two-machine system with two excitation windings on the rotor the current and voltage systems include only harmonics of two frequencies. The mathematical model of synchronous steady-state process of a two-machine system is also provided, and the steady-state regimes with different structures of initial information are considered.

scholarly journals NUMERICAL SIMULATION OF THE DYNAMICS OF A FLEXIBLE ROTOR WITH TWO BALL AUTO-BALANCERS

2020 ◽  
pp. 31-44
Author(s):  
Nikolay Zaytsev ◽  
◽  
Denis Zaytsev ◽  
Andrey Makarov ◽  
Dmitriy Mineev ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Cross Sections ◽  
Experimental Studies ◽  
Element Model ◽  
Rolling Friction ◽  
Published Data ◽  
Flexible Rotor ◽  
Flexible Rotors ◽  
The Mathematical Model

Ball auto-balancing devices can to compensate changes of unbalance "on the move" only for rotors operating at supercritical speeds. For automatic balancing of such rotors, classified as flexible rotors, several auto-balancers located in different cross sections of the shaft are necessary. This makes it necessary to account bending fluctuations on studies of dynamics of the rotor with auto-balancers, that is especially important in the design of the real rotors. In view of the complexity of experimental studies of such rotors in the article the method of direct numerical simulation of the dynamics of the flexible rotor system – supports – auto-balances is considered. The methodological basis of this method is the use of a discrete multi-mass rotor model, which is equivalent in dynamic characteristics to a real rotor, and also the equations of dynamics of the system discrete rotor – supports – auto-balancers, obtained in the direct form of recording. For definition of discrete masses and a matrix of coefficients of influence of stiffness of rotor cross-sections it is supposed to use calculations for finite-element model of a real rotor by existing software complexes of the engineering analysis. The mathematical model of the system dynamics obtained by the Lagrange method takes into account the non-stationarity of the rotor rotation speed, the influence of gravity and the rolling friction of the balls in the auto-balancer cages. Verification of the mathematical model was performed by reproducing the published data using a computational model for a two-support single-disk three-mass rotor with a two-ball auto-balancer. For a four-mass rotor with two two-ball auto-balancers, the results of numerical simulation of dynamics for the modes of acceleration, steady-state rotation and deceleration are presented. It is shown that for the system under consideration, only partial auto-balancing takes place in the steady rotation mode, including after a stepwise increase of the imbalance.

scholarly journals Deterministic chaos in pendulum systems with delay

2019 ◽  
Vol 4 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Aleksandr Shvets ◽  
Alexander Makaseyev
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Differential Equations ◽  
Deterministic Chaos ◽  
Phase Portraits ◽  
Characteristic Exponents ◽  
Systems Of Differential Equations ◽  
Lyapunov Characteristic Exponents ◽  
The Mathematical Model ◽  
Equations With Delay

AbstractDynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".

Numerical Analysis on the Performance of Control Valve in Variable Displacement Wobble Plate Compressor

2005 ◽  
Vol 127 (2) ◽  
pp. 326-333 ◽  
Author(s):  
Chunpeng Dou ◽  
Xinjiang Yang ◽  
Changqing Tian ◽  
Xianting Li
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Dynamic Performance ◽  
Control Point ◽  
Control Valve ◽  
Effective Area ◽  
Suction Pressure ◽  
Study Characteristics ◽  
Variable Displacement ◽  
The Mathematical Model

The performance of control valve is analyzed in this paper in order to study characteristics of the variable displacement wobble plate compressor. The forces acting on the control valve are analyzed and the mathematical model to analyze its performance is developed. A test bench is set up to get the steady and dynamic performance of control valve. The steady-state performances predicted by the mathematical model agree well with the experimental data while the predicted dynamic performances agree with the experimental results qualitatively. With the mathematical model, the steady-state performances of the control valve with four different preset control points and three different effective areas of the evacuated bellows have been analyzed, and the dynamic behavior of one type control valve has been studied. It is shown that: (1) the suction pressure at preset control point is inversely proportional to the discharge pressure; (2) the larger the starting force of spring in control valve or the smaller the effective area of evacuated bellows, the larger the suction pressure at preset control point; and the larger the starting force of spring in control valve and the smaller the maximum opening of ball valve, the more quickly the crankcase pressure changes and the smaller mass flow rate of control valve; the slope ratio of crankcase pressure to suction pressure cannot be influenced by the starting force of spring in control valve but can be influenced by the effective area of evacuated bellows; (3) the transition time of the crankcase pressure is about 1 s and can be neglected when working condition changes.

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