Dissipative systems Ohmic dissipation

The formal structure of (5.77) suggests that the reaction coordinate Q can be combined with the bath coordinates to form a new fictitious bath , so that the Hamiltonian takes the standard form of dissipative TLS (5.55). Suppose that the original spectrum of the bath is ohmic, with friction coefficient q. Then diagonalization of the total system (Q, qj ) gives the new effective spectral density [Garg et al. 1985]... 

To make further progress, it is standard practice to take this definition of the spectral density and replace it by a continuous form based on physical intuition. A form that is often used for the spectral density is a product of ohmic dissipation qco (which corresponds to Markovian dynamics) times an exponential cutoff (which reflects the fact that frequencies of the normal modes of a finite system have an upper cutoff) ... 

In Section IV, we turn to our model system, namely a classical or quantal dissipative free particle. We focus the study on the so-called Ohmic dissipation case, in which the noise is white and the particle equation of motion can be given the form of a classical nonretarded Langevin equation in the high-temperature regime (the Brownian particle then undergoes normal diffusive... 

The Regenesys system stores the combined AG of the two half reactions, and releases the same AG for power delivery, with losses of around 25 % due to overvoltages, ohmic power dissipation and ion diffusion. Electron transfer and sodium ion movement are the agents of the process ... 

Here we apply the LAND-map approach to compute of the time dependent average population difference, A t) = az t)), between the spin states of a spin-boson model. Here az = [ 1)(1 — 2)(2 ]. Within the limits of linear response theory, this model describes the dissipative dynamics of a two level system coupled to an environment [59,63-65]. The environment is represented by an infinite set of harmonic oscillators, linearly coupled to the quantum subsystem. The characteristics of the system-bath coupling are completely described by the spectral density J(w). In the following, we shall restrict ourselves to the case of an Ohmic spectral density... 

This is the simplest model of an electrocatalyst system where the single energy dissipation is caused by the ohmic drop of the electrolyte, with no influence of the charge transfer in the electrochemical reaction. Thus, fast electrochemical reactions occur at current densities that are far from the limiting current density. The partial differential equation governing the potential distribution in the solution can be derived from the Laplace Equation 13.5. This equation also governs the conduction of heat in solids, steady-state diffusion, and electrostatic fields. The electric potential immediately adjacent to the electrocatalyst is modeled as a constant potential surface, and the current density is proportional to its gradient ... 

Loss Ohmic loss in S/N is due to signal dissipation across a resistive load imposed by a component, whereas while nonohmic loss is due to impedance mismatch so that the reflectance coefficient between adjacent components is greater than 0. In a radar system, loss can also occur as a less-than-ideal gain in the signal processing function. 

The Ohmic resistance in the activated carbon and the ionic resistance in the electrolyte form a parallel system which is in series with the other two sonrces of resistance. The data regarding the electrolyte are visible only at low freqnency, in the domain of the millihertz. At higher freqnency, the ions do not have the dynamic necessary to imitate the oscillations of the electrical field. As the ions are immobile, they do not dissipate energy, and therefore the ionic resistance is zero. At very high freqnency, only the electronic part of the resistance can be seen. In the high-freqnency domain, the measmement is skewed by the inductance of the measuring circuit. The series resistance due to the conductors is determined at high frequency -typically 1 kHz. 

At the high-frequency limit of the spectrum the intercept on the resistive axis specifies the serial ohmic component in the measured system, since this element does not introduce a phase shift. Similarly the low-frequency limit approaches the steady-state condition corresponding to the d.c. characteristics of the cell. Each spectral feature detected between these limits represents a dissipation process with the specific time dependence indicated by the inverse of the frequency at which it occurs. It should be noted, therefore that two processes with similar time constants in the anodic system will not be distinguishable by impedance spectroscopy. 

It is evident from the previous discussion that significantly sim-phfied modeling of the current distribution can often be achieved once scaling analysis has identified the controlling dissipative mechanisms in the cell. It has been shown that the current distribution in most common systems can be characterized in terms of three major dissipative processes ohmic (within the electrolyte across the cell), mass transport (across the concentration bmmdary layer), and surface activation (on the electrode). These are designated in terms of the corresponding resistances R q,R q, and R. The Wa number characterizes the cmrent distribution in terms of the relative importance of two of the three resistances the surface (Jfg)and the ohmic (Rq ) resistances.Clearly,more complete characterization of the system requires the comparison of two additional resistance ratios and the formulation of two additional dimensionless parameters. ... 

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