Electrical models elements

Winter heating items fitted within room air-conditioners may be electric resistance elements, hot water or steam coils, or reverse cycle (heat pump). One model of water-cooled unit operates with a condenser water temperature high enough to be used also in the heating coil. 

Purely electrical models of the heart are only a start. Combined electromechanical finite-element models of the heart take into account the close relationship that exists between the electrical and mechanical properties of individual heart cells. The mechanical operation of the heart is also influenced by the fluid-structure interactions between the blood and the blood vessels, heart walls, and valves. All of these interactions would need to be included in a complete description of heart contraction. 

Figure 11. Experimental and predicted differential conductance plots of the double-island device of Figure 10(b). (a) Differential conductance measured at 4.2 K four peaks are found per gate period. Above the threshold for the Coulomb blockade, the current can be described as linear with small oscillations superposed, which give the peaks in dljdVj s- The linear component corresponds to a resistance of 20 GQ. (b) Electrical modeling of the device. The silicon substrate acts as a common gate electrode for both islands, (c) Monte Carlo simulation of a stability plot for the double-island device at 4.2 K with capacitance values obtained from finite-element modeling Cq = 0.84aF (island-gate capacitance). Cm = 3.7aF (inter-island capacitance). Cl = 4.9 aF (lead-island capacitance) the left, middle and right tunnel junction resistances were, respectively, set to 0.1, 10 and 10 GQ to reproduce the experimental data. (Reprinted with permission from Ref [28], 2006, American Institute of Physics.)...

Coggon, J. Z., 1971, Electromagnetic and electrical modeling by the finite-element method Geophysics, 36, 132-155. 

The other two models, proposed by Haim et alP and Koper and Sluyters, become reduced to electrical models in the spatially homogeneous case. Hence the double-layer potential is a dependent variable, and the models contain elements that are also included in the model by Hatgen and Krischer. In this respect, these two models can be viewed as predecessors of the one presented above. However, each of them contains physically unreasonable assumptions that lead to results contradictory to those obtained with the above-discussed model. 

A similar equation hut containing the function coth was used hy Inzelt and L ng to descrihe the diffusional impedance of conducting polymers under reflective conditions [see Section III.6(ii) and Eq. (99)]. An electrical model containing this element accounted well for the impedance spectra, with a minimum number of free parameters. 

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. 

The problem when trying to make an electrical model of the physical or chemical processes in tissue is often that it is not possible to mimic the electrical behavior with ordinary lumped, physically realisable components such as resistors (R), capacitors (C), inductors, semiconductor components, and batteries. Let us mention three examples 1) The constant phase element (CPE), not realizable with a finite number of ideal resistors and capacitors. 2) The double layer in the electrolyte in contact with a metal surface. Such a layer has capacitive properties, but perhaps with a capacitance that is voltage or frequency dependent. 3) Diffusion-controlled processes (see Section 2.4). Distributed components such as a CPE can be considered composed of an infinite number of lumped components, even if the mathematical expression for a CPE is simple. 

Technique using an approximate and simplified representation of complex phenomena as a combination of elements, each of which are individually simple to represent and solve. Many models employ electrical circuit elements to form such representations. 

The next chapter will show a shift in emphasis, too from the practical success of chemistry to the theoretical questions that remained. Of these theoretical questions the most significant was chemical affinity. Starting with Berzelius, chemical affinity had been explained in terms of simple electrical attraction, but this model worked well only in a limited number of cases. It explained nothing about the bonding between like elements. Valence theories of Kekule and Werner addressed attractions between electrically neutral elements, but they were empirical observations with no fundamental theoretical basis. But after World War I this changed. The postwar world saw the birth of the bond. 

One of the first successful electrical models for the biological tissues was introduced by Fricke and Morse (Fricke 1932, Fricke and Morse 1925). It consists of a resistive element R... 

Finally, a module simulation including electrical models of the SMDs, embedded components, wiring, and the module interface (e.g., solder bumps) helps to find out possible problems due to parasitic cross-coupling effects [63]. The internal elements can be modified to compensate these effects. It might be even necessary to increase the distance between components or to change their physical dimension. Process or material tolerances are used to assess repeatability and manufacturability (Figure 9.68). 

RUDY I have a question about the finite element electrical model of the heart. Do you plan on incorporating the actual conduction system as part of it Or how would you establish isochrones and the sequence of activation ... 

Coupling of the model elements can be achieved either in series or in parallel, this being analogous to capacitors in an electrical circuit (Figure 2.11). 

Figure 2.11 Electrical equivalent circuits for arranging rheological model elements, (a) Capacities in series (b) Capacities in parallel.

An example of a real impedance spectrum obtained for a new, fully-charged Graphite-NCA coil element with 10 Ah is shown in Figure 2.22 in accordance with the Nyquist representation. This figure is identical to Figure 2.9 but with the addition of the components of the electrical model. 

ABSTRACT State determination of Li-ion cells is often accomplished with Electrochemical Impedance Spectroscopy (EIS). The measurement results are in frequency domain and used to describe the state of a Li-ion cell by parameterizing impedance-based models. Since EIS is a costly measurement method, an alternative method for the parameterization of impedance-based models with time-domain data easier to record is presented in this work. For this purpose the model equations from the impedance-based models are transformed from frequency domain into time domain. As an excitation signal a current step is applied. The resulting voltage step responses are the model equations in time domain. They are presented for lumped and derived for distributed electrical circuit elements, i.e. Warburg impedance, Constant Phase Element and RCPE. A resulting technique is the determination of the inner resistance from an impedance spectrum which is performed on measurement data. 

If the electrical equivalent circuit model is a series connection of model elements, the overall model equation is the vector addition of the single model element equations in time domain and frequency domain, respectively. Time domain correspondences for single model elements to certain excitation signals can be calculated analytically as described in the following sections. In general these transformations can be easily computed for models consisting of lumped elements. For models containing distributed elements, fractional calculus is required. 

An example of a transfer function based on a physical model is the Nemst impedance of a transport controlled electrode reaction. The impedance spectra in Fig. 7-14, which were obtained on a rotating platinum disk electrode at the equilibrium potential of the iron hexacyanoferrate redox system, exhibit the typical shape of a transport-controlled process. The transfer function cannot be described by a limited number of electrical circuit elements but must be derived from the differential equations of Fick s 2nd law and the appropriate boundary conditions. For finite linear diffusion, the so-called Nemst impedance Z can be derived theoretically... 

The conventional electrical model of an electrochemical cell that represents the electrode-electrolyte interface (EEI) includes the association of resistances with capacitance as shown in Fig. 1. The parallel elements are related to the total current through the working electrode that is the sum of distinct contributions from the faradaic process and double-layer charging. The double layer capacitance resembles a pure capacitance, represented in the equivalent circuit by the element C and the faradaic process represented by a resistance, R2. The parameters E and Ri represent the equilibrium potential and the electrolyte resistance, respectively. 

Wallmersperger T, Wittel FK, D Ottavio M, Kroplin B (2008) Multiscale modeling of polymer gels - chemo-electric model versus discrete element model. Mech Adv Mater Struct 15(3-4) 228-234... 

As stated before, electrodes are not standard linear electrical elements. Electrode properties depend on the electrode potential. Especially, in stimulation electrodes, the electrode potential fluctuates over a relatively wide range, thus enhancing the nonlinear characteristics of the electrode-electrolyte interface. However, an approximate electrical model can be helpful in designing the interface circuits to the electrodes, like signal recording or driver circuits. As explained in Chap. 5, impedance spectroscopy is one of the methods to extract the electrode model. In the following this and other methods are explained through practical examples. 

In view of the success of the 3-element model for the quantitative description of the variation of the low-frequency conductivity of resin-solution columns with the solution concentration, it is logical to inquire whether the same model can explain the electrical behavior of these or similar systems at high frequencies, at which the admittance of the system as a whole and/or of the model elements is appreciable. In other words, the question is asked Can the 3-element model describe the change of the complex impedance of these systems with the frequency of the alternating current used to measure the impedance ... 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

In the North American market, water heaters are almost always made with the cold water inlet and hot water outlet lines coming out of the top of the tank. The hot water outlet opens right into the top of the tank and so draws off the hottest water. The hot water has risen to the top of the tank because of its lower density. The cold water on the inlet side is directed to the bottom of the tank by a plastic dip-tube. In some models the dip-tube is curved or bent at the end to increase the turbulence at the bottom of the tank. This is to keep any sediment from settling on the bottom of the tank. As sediment— usually calcium carbonate or lime—precipitated out of the water by the increased temperature builds up, it will increase the thermal stress on the bottom of a gas-fired water heater and increase the likelihood of tank failure. On electric water heaters the sediment builds up on the surface of the elements, especially if the elements are high-density elements. Low-density elements spread the same amount of power over a larger surface of the element so the temperatures are not as high and lime doesn t build up as quickly. If the lower elements get completely buried in the sediment, the element will likely overheat and burn out. 

Figure 2-75. Lumped element models of transmission line electrical characteristics.

Now our nuclear model suffices. We can build up the atoms for all elements. Each atom has a nucleus consisting of protons and neutrons. The protons are responsible for all of the nuclear charge and part of the mass. The neutrons are responsible for the rest of the mass of the nucleus. The neutron plays a role in binding the nucleus together, apparently adding attractive forces which predominate over the electrical repulsions among the protons. ... 

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