Critical field strength

Applying resonance overlap criterion to this Hamiltonian we get the following estimate for the critical field strength ... 

Table I. The values of the critical field strength for various quarkonia.

The critical ac field strength depends on d, but the minimum critical field strength, which corresponds to (5 = 0 is given by = 0.908. Thus, a particle can be stably levitated provided that p < P = 0.908 or, in terms of the ac voltage and frequency, stable trapping occurs provided that... 

FIGURE 10.5 The variation of the critical field strength, He, for lead. Note that He is zero when the temperature, T, equals the critical temperature, Tc. 

Of much interest are the electroluminescence properties of conjugated polymers that allow the development of electrically switched light-emitting devices [8.257]. Electric field activated bistable molecules are expected to switch at a critical field strength [8.258]. 

The behavior of type II superconductors in an applied field is more complicated. This behavior is illustrated in Figure 13.16b. Below a certain field strength 2 c, i, the magnetic field lines are repelled, and the material is superconducting. From 2 c, i to a second critical field strength magnetic field lines are able to penetrate the type II material in its superconducting state... 

For comparison, in iron(III) crossover systems the critical field strength is conceivably higher in energy than in iron(II) complexes. As an example, Tsipis et al.39)... 

In the solid state, II, III, and IV show 1 Ai ST2 spin equilibrium, while I is low-spin. In solution, II and III retain the spin equilibrium property, whereas IV is fully high-spin and I is low-spin over a temperature range of approximately 200 degrees. From the electronic spectra the critical field strength (crossover point) has been estimated to lie near 11700 cm-1. No solvent dependence has been observed. 

In most cases these chemical waves involve ionic species and hence two interesting possibilities arise (l) these waves can be affected by applied electric fields and (2) the strong tendency towards charge neutrality and the possible presence of membranes may lead to strong electrical disturbances in association with the propagating compositional disturbance. In this section we review some recent work on the response of reaction-transport waves (10-14) and find strong variations of wave velocity and profile with applied field, induction of new types of waves not found in the field free medium (.11), annihilation of waves beyond critical field strengths (11-14) and new two dimensional wave forms with free ends (15). 

At time zero (top) the circular wave is subject to a plane parallel electric (ohmic) field. The part of the circle propagating towards the negative electrode is annihilated beyond a critical field strength and a crescent wave is observed to propagate (bottom). Note the free ends which are stabilized by the applied field and which become Winfree spirals when the field is turned off. (See Ref. 13 for details.)... 

Without the external field, two stable oscillations with frequencies 0). and anstable oscillations are shown in Figure 1. By external means and by parameter variations the sys tem can be driven from one stable oscillation to the other one, exhibiting a threshold and excitability. Furthermore, the external field can lead to a complete collapse of the small amplitude oscillation. The closer the external frequency X is to the internal one, Wj, the smaller is the critical field strength F, which is necessary for the breakdown of the small oscillation and the subsequent transition to the other one. For F >F, the system can only exist in the large amplitude state. Tfiis°state is stable with respect to F, but there exists a region, where partial quenching of the oscillation can occur. 

The critical strength F, which is necessary for the LC to collapse and to create a response signal, is given by the external as well as by the internal parameters. Predominant are the dielectric ones(c, d ), since these parameters determine the frequency and amplitude of the internal oscillation. We have been able to show that pulsed and modulated external fields can only shift the instability point towards smaller or higher values of the critical field strength per cycle. Qualitative changes in the overall behaviour of the driven LC system are impossible. 

The central idea of the overlap criterion is to focus on the most important resonances in the phase space and to calculate their widths as a function of the strength of the apphed field. In a classical picture the critical field strength is reached when the resonances overlap. 

It follows that there exist a critical field strength, E, below which no gas amplification takes place. From (A.4) it follows that... 

The minimum value of the field strength required to bring about this change is called the critical field strength (Hc) its value depending on the material and on the temperature. 

Studies of the electron mobilities as a function of field strength and temperature on liquid M(CH3)4 compounds with M = Si, Ge, and Sn revealed rather high values ( 50 cm - s ) in comparison to unbranched hydrocarbons like butane and pentane however above a critical field strength the electron mobility decreases with increasing field strength [40]. 

Hoburg and Melcher [6] demonstrated electrohydrodynamic instabilities in macroscale systems at an oil-oil interface with a discrete conductivity change at the interface under the influence of an applied electric field. In the presence of an applied electric field, charge accumulates at the fluid-fluid interface, and the electrical force on the interface is balanced by the fluid interfacial stress tensor. At a critical field strength, the electrical force exceeds the... 

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