Times inverse characteristic

Droplet size, particularly at high velocities, is controlled primarily by the relative velocity between liquid and air and in part by fuel viscosity and density (7). Surface tension has a minor effect. Minimum droplet size is achieved when the nozzle is designed to provide maximum physical contact between air and fuel. Hence primary air is introduced within the nozzle to provide both swid and shearing forces. Vaporization time is characteristically related to the square of droplet diameter and is inversely proportional to pressure drop across the atomizer (7). 

The experiments discussed above were all carried out with total pressures below 10-4 Torr. However, Hori and Schmidt (187) have also reported non-stationary state experiments for total pressures of approximately 1 Torr in which the temperature of a Pt wire immersed in a CO—02 mixture was suddenly increased to a new value within a second. The rate of C02 production relaxed to a steady-state value characteristic of the higher temperature with three different characteristic relaxation times that are temperature dependent and vary between 3 and 100 seconds between 600 and 1500 K. The extremely long relaxation time compared with the inverse gas phase collision rate rule out an explanation based on changes within the chemisorption layer since this would require unreasonably small sticking coefficients or reaction probabilities of less than 10-6. The authors attribute the relaxation times to characteristic changes of surface multilayers composed of Pt, CO, and O. The effects are due to phases that are only formed at high pressures and, therefore, cannot be compared to the other experiments described here. 

Assume that a noninteracting nanosystem is coupled weakly to a thermal bath (in addition to the leads). The effect of the thermal bath is to break phase coherence of the electron inside the system during some time Tph, called decoherence or phase-breaking time. rph is an important time-scale in the theory, it should be compared with the so-called tunneling time - the characteristic time for the electron to go from the nanosystem to the lead, which can be estimated as an inverse level-width function / 1. So that the criteria of sequential tunneling is... 

Capillary forces in mixed fluid phase conditions are inversely proportional to the curvature of the interface. Therefore, menisci introduce elasticity to the mixed fluid, and mixtures of two Newtonian fluids exhibit global Maxwellian response. For more details see Alvarellos [1], his behavior is experimentally demonstrated with a capillary tube partially filled with a water droplet. The tube is tilted at an angle (3 smaller than the critical angle that causes unstable displacement. Then, a harmonic excitation is applied to the tube in the axial direction. For each frequency, the amplitude of the vibration is increased until the water droplet becomes unstable and flows in the capillary. Data in Figure 3 show a minimum required tube velocity between 40 and 50 Hz. This behavior indicates resonance of the visco-elastic system. The ratio of the relaxation time and characteristic time for pure viscous effect is larger than 11.64. 

At the present time, two types of LiTa03 single crystals are widely known one is stoichiometric LiTa03 (slt) [20] and the other is congruent LiTa03 (clt). It is reported that domain inversion characteristics of these crystals are distinctly different each other [21-23], slt has... 

Note that assumptions (2) and (3) are about timescales. Denoting by x, and tlz the characteristic times (inverse rates) of the electron transfer reaction, the solvent relaxation, and the Landau-Zener transition, respectively, (the latter is the duration of a single curve-crossing event) we are assuming that the inequalities Tr A Ts tlz hold. The validity of this assumption has to be addressed, but for now let us consider its consequences. When assumptions (1)—(3) are satisfied we can invoke the extended transition-state theory of Section 14.3.5 that leads to an expression for the electron transfer rate coefficient of the form (cf. Eq. 14.32)... 

The elasticity of pure surfactant solutions also exhibits a maximum, but at higher concentrations, close to CMC (Figure 6). Below this maximum, the monolayer behaves as if it were insoluble, because the frequency of compression is much larger that the inverse characteristic adsorption/desorption time which is here diffusion controlled. The elasticity is then the Gibbs elasticity , given by ... 

Before electronic relays were developed the standard inverse characteristic was taken as the reference e.g. in BS142 for UK practice. A point on the characteristic was chosen for the comparison with others, e.g. extremely inverse. The reference point was 10 times the nominal relay current and an operating time of 3 seconds. 

A time-delayed overcurrent (51) relay would normally be nsed for a static load. The choice of the characteristic would depend to some extent on the natme of the load. A standard inverse characteristic would normally be adequate. Its pick-up current wonld be set at between 105% and 115% of the rated current of the load. 

Another method that uses the random phases, but has no complete control over the spectral characteristics, is called the random complex spectrum method. Its synthesis procedure is as follows. A Gaussian distributed white noise complex spectrum, with a standard deviation of 1, is first generated and then filtered using the amplitude spectrum derived from the target spectral density. Subsequent inverse Fourier transform results in a time series of desired record length. Unlike the previous method, the waves produced by this technique will not match exactly the desired spectral density. Obviously, this method does not also exercise control on the time domain characteristics. However, both these synthesis methods based on random phases have their own proponents. Funke and Mansard describe the rationale associated with each of these methods. 

The next term reflects the existence of fluctuations in the system (a is the fluctuation strength, hj (x) are elements of the Nxn diffusion matrix). The third term uses a coalescence-dispersion mechanism (for details, see [1,4]) to model turbulent mixing (23 is the inverse characteristic mixing time). The last term describes the flow of reactants into and out of the CSTR (a is the inverse residence time p (2c,t) is the probability density for input reactant stream concentrations). 

Table 1.8 shows the time response of the frequency-dependent characteristic impedance given in Table 1.3. The time-dependent characteristic impedance increases as time increases. This is quite reasonable because of the inverse relation of time and frequency.

Note that assumptions (2) and (3) are about timescales. Denoting by Xx, Xg, and xiz the characteristic times (inverse rates) of the electron transfer reaction, the solvent relaxation, and the Landau-Zener transition, respectively, (the latter is the duration of a single curve-crossing event) we are assuming that the inequalities... 

Since the operation of the eutectic alloy relays depends upon the magnitude of heating, which is a function of current and time, these relays also give an inverse current-time characteristics. 

This is obvious for the simplest case of nondeformable anisotropic particles. Even if such particles do not change the form, i.e. they are rigid, a new in principle effect in comparison to spherical particles, is their turn upon the flow of dispersion. For suspensions of anisodiametrical particles we can introduce a new characteristic time parameter Dr-1, equal to an inverse value of the coefficient of rotational diffusion and, correspondingly, a dimensionless parameter C = yDr 1. The value of Dr is expressed via the ratio of semiaxes of ellipsoid to the viscosity of a dispersion medium. 

In the hrst case, the degree of self coherence depends on the spectral characteristics of the source. The coherence time Tc represents the time scale over which a held remains correlated this hme is inversely proportional to the spectral bandwidth Au) of the detected light. A more quantitative dehnition of quasi-monochromatic conditions is based on the coherence time all relevant delays within the interferometer should be much shorter than the coherence length CTc. A practical way to measure temporal coherence is to use a Michel-son interferometer. As we shall see, in the second case the spatial coherence depends on the apparent extent of a source. 

The corresponding formulae have been listed in previous work . They will not be reproduced here because we think that the most characteristics of the result can be discussed on the spectrum of inverse relaxation times given in Table 3. 

For Reynolds numbers higher than 5,000 (usually the case in practice), the blend number (t99.A0 is only slightly dependent on the Reynolds number. In this region the blend time becomes inversely proportional to the speed of rotation. It is also dependent on the geometric characteristics of both the tank and the stirrer as shown below ... 

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