Linear Passive System

The Newton-Fourier Law (2.41) seems to be adequate for the heat transfer process from the sensor gas to the thermostat as long as there is no turbulent convection within the gas, i. e. for Grashof numbers Gr < 10 , [2.30, 2.31]. For situations with Gr > 10 it has to be generalized taking aftereffects, i. e. the history of the sensor gas temperature [T(s), 0 < s < t into account. This can be done by using the theory of Linear Passive Systems (LPS), cp. Chap. 6 and the literature cited there. Details will be published in a forthcoming paper [2.32]. 

Let us consider again a sorption system consisting on a sorbent-sorbate phase and a sorptive gas located between the plates or cylinders of a capacitor, Fig. 6.8. This system is an electric network which for small applied voltages (U(t)) can be interpreted as a Linear Passive System (LPS). That is a stimulus (U(t)) applied to the system creates a response, the electric current I(t), which is linearly related to U(t). However it may exhibit a phase shift and also lead to energy dissipation, i. e. Ohmian heat which, as a consequence of the Second Law of Thermodynamics at finite ambient temperature, never can completely be reverted again to electric energy. Linear Passive Systems can be found quite frequently in Physics. A mathematical theory of such systems has been developed by H. Kdnig and J. Meixner in the 1960 s, [6.27] and later on extended and applied to various stochastic processes, i. e. statistical physics by J. U. Keller, [6.28]. 

The third approach is called the thermodynamic theory of passive systems. It is based on the following postulates (1) The introduction of the notion of entropy is avoided for nonequilibrium states and the principle of local state is not assumed, (2) The inequality is replaced by an inequality expressing the fundamental property of passivity. This inequality follows from the second law of thermodynamics and the condition of thermodynamic stability. Further the inequality is known to have sense only for states of equilibrium, (3) The temperature is assumed to exist for non-equilibrium states, (4) As a consequence of the fundamental inequality the class of processes under consideration is limited to processes in which deviations from the equilibrium conditions are small. This enables full linearization of the constitutive equations. An important feature of this approach is the clear physical interpretation of all the quantities introduced. 

IZI=J(Z )2+(Z ), and phase angle shift,, vs. f). The electrochemical system is then simulated with an electrical circuit that gives the same impedance response. Ideally this electrical circuit is composed of linear passive elements, e.g. resistors and capacitors, each of which represents individual physicochemical steps in the electrochemical reaction. ... 

In Section 8.1, the conditions for black box theory are found. To be valid the network must be linear, passive, and causal. A nonlinear system is a system that does not obey the superposition theorem, the output of a nonlinear system is not proportional to the input. 

Tissue Properties. The properties of human tissues when the body is considered a linear, passive mechanical system are summarized in Table 10.1 (von Gierke et al., 2002 Goldstein et al., 1993). The values shown for soft tissues are typical of muscle tissue, while those for bone depend on the structure of the specific bone. Cortical bone is the dominant constituent of the long bones (e.g., femiu, tibia), while trabecular bone, which is more elastic and energy absorbent, is the dominant constituent of the vertebrae. The shear viscosity and bulk elasticity of soft tissue are from a model for the response in vivo of a human thigh to the vibration of a small-diameter piston (von Gierke et al., 1952)... 

Frasca, R., Camlibel, M. K., Goknar, 1. C., lannelU, 1., Vasca, F. (2010). Linear passive networks vrith ideal switches Consistent initial conditions and state discontinuities. IEEE Transactions on Circuits and Systems, 57(12), 3138-3151. 

Linear polarization resistance can be applied to corrosion systems with electrochemical activation control, such as carbon steels and some stainless steels in low concentrations of sulfuric acid. For corrosion systems with a mass transport control or passivating systems, such as carbon steels in water with a pH between 5 and 10, the hnear polarization equation is not valid. Additionally, the normal fluctuation of corrosion potential during the measurements can significantly affect the accuracy of the measurements. Under most circumstances, a larger polarization than 10 mV may be used to increase the signal/noise ratio. However, it may put the system out of the linear region, introducing some additional errors in the measurements. 

Although important contributions in the use of electrical measurements in testing have been made by numerous workers it is appropriate here to refer to the work of Stern and his co-workerswho have developed the important concept of linear polarisation, which led to a rapid electrochemical method for determining corrosion rates, both in the laboratory and in plant. Pourbaix and his co-workers on the basis of a purely thermodynamic approach to corrosion constructed potential-pH diagrams for the majority of metal-HjO systems, and by means of a combined thermodynamic and kinetic approach developed a method of predicting the conditions under which a metal will (a) corrode uniformly, (b) pit, (c) passivate or (d) remain immune. Laboratory tests for crevice corrosion and pitting, in which electrochemical measurements are used, are discussed later. 

The term passive interception is used to describe recovery systems that rely upon natural groundwater flow to deliver free-phase NAPLs to the collection facility without the addition of external energy (such as pumping). These systems often include linear interception-type systems such as trenches (or French drains), subsurface dams ( funnel-and-gate structures), combined hydraulic underflow with skimming, and density skimming units. 

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