Continuous modelling

About: Continuous modelling is a research topic. Over the lifetime, 1703 publications have been published within this topic receiving 32278 citations.

On dynamics and voltage control of the Modular Multilevel Converter

Abstract: This paper discusses the impact of modulation on stability issues of the Modular Multilevel Converter (M2C) The main idea is to describe the operation of this converter system mathematically, and suggest a control method that offers stable operation in the whole operation range A possible approach is to as­sume a continuous model, where all the modules in each arm are represented by variable voltage sources, and as a result, all pulse width modulation effects are disregarded After simulating this model and test­ing different control methods, useful conclusions on the operation of the M2C have been extracted The control methods are then implemented on a model with discrete half-bridge modules, in order to compare the results and to validate the continuous model approach When assuring that this model functions as expected, the goal of this paper is to conclude into a self-stabilizing voltage controller A controller is proposed, which eliminates circulating currents between the phase legs and balances the arm voltages regardless of the imposed alteranting current

Solution of a process of random genetic drift with a continuous model.

Abstract: 30 See H. C. Urey, Geochim. et cosmochim. acta, 1, 209-277, 1951; see, particularly, pp. 233 ff. This paper was reproduced in The Planets, pp. 124 and 141, particularly. Later G. P. Kuiper published the same idea in Atmospheres of the Earth and Planets (Chicago: University of Chicago Press, 1952), pp. 330, 314 (ref. 18), and 421. 31 See H. Jeffreys, The Earth (4th ed.; Cambridge: At the University Press, 1952), chap iv, p. 159, and papers there cited; H. C. Urey, The Planets, pp. 20 ff. 32 See H. C. Urey, The Planets, p. 124, and Astrophys. J., Suppl., 1, 155, 1954. 33 H. C. Urey, The Planets, pp. 49 ff. 34 See B. Gutenberg, Internal Constitution of the Earth (New York: Dover Publications, Inc., 1951), pp. 150 ff. 36 H. C. Urey, Proc. Roy. Soc. London, A, 219, 281,1953. 36 H. C. Urey, The Planets, p. 176. 37 See H. C. Urey, Phys. Rev., 80, 295,1950; The Planets, pp. 64 ff.

Some discrete-time SI, SIR, and SIS epidemic models

Abstract: Discrete-time models, or difference equations, of some well-known SI, SIR, and SIS epidemic models are considered. The discrete-time SI and SIR models give rise to systems of nonlinear difference equations that are similar in behavior to their continuous analogues under the natural restriction that solutions to the discrete-time models be positive. It is important that the entire system be considered since the difference equation for infectives I in an SI model has a logistic form which can exhibit period-doubling and chaos for certain parameter values. Under the restriction that S and I be positive, these parameter values are excluded. In the case of a discrete SIS model, positivity of solutions is not enough to guarantee asymptotic convergence to an equilibrium value (as in the case of the continuous model). The positive feedback from the infective class to the susceptible class allows for more diverse behavior in the discrete model. Period-doubling and chaotic behavior is possible for some parameter values. In addition, if births and deaths are included in the SI and SIR models (positive feedback due to births) the discrete models exhibit periodicity and chaos for some parameter values. Single-population and multi-population, discrete-time epidemic models are analyzed.