Titlebook: Mathematics as a Laboratory Tool; Dynamics, Delays and John Milton,Toru Ohira Textbook 2021Latest edition Springer Nature Switzerland AG 20

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John Milton,Toru Ohiraing an external energy for steady diamond growth at low pressures. During activated diamond growth from the vapor phase at low pressure the external energy was carried into the system in the form of superequilibrium atomic hydrogen (SAH), which was atomic hydrogen in high concentration and hence wit

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The Mathematics of Change,e it was recognized that the values of variables do not in and of themselves provide insight into mechanisms. A key insight was that it is the change in the magnitude of a variable as a function of time that is of importance. Surprisingly, the changes that variables undergo can often be described in

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Fixed Points: Creation and Destruction,dings, the fixed point can be either an equilibrium or a steady state. In the last chapter, we saw that the responses of the system following a perturbation away from the fixed point can be used to assess the stability of the fixed point, namely its resistance to change. Stability depends on the val

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Transient Dynamics,stems (e.g., the black box shown in Figure?.). Since in the laboratory, we most often investigate dynamical systems that are stable (at least in some sense), we expect the observed responses to an input to contain two components: a transient component on short time scales that describes the immediat

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Frequency Domain I: Bode Plots and Transfer Functions,ever, for certain types of problems, it is often more convenient to analyze dynamics in the .. For example, we typically describe the heartbeat in terms of frequency, namely, the number of beats per minute, rather than in terms of its period, i.e., the time between successive beats. In this chapter,

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Frequency Domain II: Fourier Analysis and Power Spectra,ular, it is extremely difficult to obtain the Laplace integral transform for measured signals, and even if the transform is known, obtaining the inverse transform can be problematic. At the root of these problems is the lack of efficient numerical methods to calculate the Laplace transform and its i

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Time delays, somewhat surprising that it is only in the last 20–30 years that the study of delay differential equations has begun to attract attention in biology. One of the main reasons that DDEs have become so successful as models of biological control stems from the fact that many of the details of the mecha

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