Simple electric network models

Instead we want to emphasize that simple electric network models of LPS may include three different elemental systems capacitors, resistances, and inductances [6.12]. The basic physical relations, admittance functions, elements of the representation theorem (6.55) and corresponding static and optical permittivity are collected in Table 6.1 below. These elements can be combined by series or parallel connections in may different ways. For the admittance functions of the electric network generated in this way, the simple rules hold that... 

Abstract. Electrical measurements of heterogeneous media composed of solid polyelectrolytes and dilute aqueous solutions (or pure water) are interpreted in terms of a simple electrical network. It is demonstrated that this model network represents an extension of Maxwell s equation for the conductance of dilute suspensions of spheres to condensed systems. Discussing past work on cation exchange resinsolution systems, it is shown that the three empirical geometrical parameters of the model explain quantitatively the change of the low-frequency 1000 Hz) conductivity of the heterogeneous mixture... 

Past work on electrical measurements of columns consisting of spheres of ion-exchange resins and electrolyte solutions, and on the interpretation of the results by the simple equivalent-network model described above is then reviewed. The experimental results covered are conductivity measurements at low frequencies (60 and 1000 Hz), electrical potential differences between two different NaCl solutions separated by such columns, and the variation of the dielectric constant and conductivity of the columns above 20 MHz, all over a range of sulution concentrations. It will be shown that not only does the proposed network describe the variation of the measured parameters with solution concentration and/or frequency, but that the geometrical parameters of the model are roughly the same for all these measurements. 

The Maxwell and Voigt models of the last two sections have been investigated in all sorts of combinations. For our purposes, it is sufficient that they provide us with a way of thinking about relaxation and creep experiments. Probably one of the reasons that the various combinations of springs and dash-pots have been so popular as a way of representing viscoelastic phenomena is the fact that simple and direct comparison is possible between mechanical and electrical networks, as shown in Table 3.3. In this parallel, the compliance of a spring is equivalent to the capacitance of a condenser and the viscosity of a dashpot is equivalent to the resistance of a resistor. The analogy is complete... 

As mentioned in Section 2.4, in the ionic model the chemical bond is an electrical capacitor. It is therefore possible to replace the bond network by an equivalent electric circuit consisting of links which contain capacitors as shown in Fig. 2.6. The appropriate Kirchhoff equations for this electrical network are eqns (2.7) and (2.11). It is thus possible in principle to determine the bond fluxes for a bond network in exactly the same way as one solves for the charges on the capacitors of an electrical network. While solving these equations is simple in principle providing the capacitances are known, the calculation itself can be... 

It is generally accepted that the stratum comeum represents the primary electrical barrier in skin. Though impedance results vary from subject to subject and from site to site on the same individual, the electrical response of skin can be modeled as a simple RC network. Nonideal behavior is associated with environmental conditions, the hydration of the skin, and the integrity of the stratum comeum. 

To model the microstructure and evaluate the thermoelectric properties, we used following simple equivalent electric circuit model shown in Figure 2. We considered the two phase composite as a cluster pararrel network circuit. Setting for each cluster the characteristic single phase physical property, and settle the material composition to the cluster number ratio, we can simulate the total thermopower of the system by Millman s theorem of d.c. circuit. 

Consider the simple linear electrical network depicted in Fig. 4.19. It can be viewed as an electrical analogue of the coupled hydraulic tank system considered in Section 4.4.1. A bond graph of the direct model with the two inputs I(t) and E(t) and the two outputs e and /2 appears in Fig. 4.20. There is one set of two disjoint input-output causal paths... 

Electrical network finite-difference models for study of various phenomena occurring in solid-state devices, circuits, and systems have been widely reported in Hterature (Ellison 1987 Fukuoka and Ishizuka, 1984 Riemer, 1990). One of the advantages of such a technique is a simple physical interpretation of the phenomena in question in terms of electrical signals and parameters existing in the network/circuit model (see Fig. 11.45). For all but very simple cases, the equivalent circuits are sufficiently complex that computer solution is required. It is important to note, however, that once the equivalent circuit is established the analysis can readily be accompHshed by existing network analysis programs, such as SPICE (SPICE2G User s Manual). 

With these rules and Table 6.1 in mind, it is very simple to write down the admittance functions of simple 2-pole electrical network considered as models for the permittivity of sorption systems [6.12]. 

While the word mode I is frequently used for a device that is the same as the protot5q)e in all regards but size, such a restricted defrnition is not to be inferred here. An engineering model may differ from a simple scale model only in that air is substituted for water as the fluid. On the other hand, a model may bear no outward resemblance to its prototype. In this latter situation, the model is usually called an analog. An example of an analog model is an electrical network that is used to study the flow of fluid in a system by utilizing the fact that the flow of current and fluid are governed by similar equations. 

The first extension of the percolation theory to address the problem of electrical transport in composite materials was conducted by Kirkpatrick rrsing a random resistor network model. Random resistor networks are created by assigning each node in the network with a random resistivity value and calculating the arrrent flow through the entire network at a fixed external voltage by solving Kirchoff s law at every node. Kirkpatrick s random resistor model provides a simple and convenient discrete model for the conductivity of a continuorrs medium if the spatial distribution of particles is known. As a... 

Grunow et al. (2006) present a model developed for supply network design in electrical components manufacturing. The model focuses on product relocation and capacity expansion decisions and does not consider setup of new plants or closure of existing ones. Additionally, simple assembly plants supplied with complete kits from a major production site are modeled. To account for production-development synergies in early life-cycle... 

The experimental data for a were compared with theoretical values calculated by means of analogy considerations to electric flow (Ohm s law) [112]. Simple circuit models based on a network of resistors were applied to simulate the cross-type configuration chosen. It could be shown that the calculated values for amin and am3X were in excellent agreement with the experimental data. 

Many researchers take the view that the transfer function for a given system should be derived from the equations governing the kinetics of the electrochemical reactions involved. This will be demonstrated for a simple charge-transfer reaction in Sect. 2.6.3. A second method for modeling electrochemical processes involves the use of networks of electrical circuit elements, so-called equivalent circuits, which can be selected on the basis of an intuitive understanding of the electrochemical system. It has been shown many times that for simple systems, equivalent circuits can be used to derive useful information from impedance spectra as long as they are based on the physical and chemical properties of the system and do not contain arbitrarily chosen circuit elements. 

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