Sensitivity exponential

The resulting expression, Eq. 8.6-2, has a weak temperature-dependent preexponential term, and a temperature sensitive exponential term. The latter contains the surface tension to the third power and the superheat to the second power. With increasing temperature the surface tension drops, and superheat increases, giving rise to an increase of orders of magnitude in J over a very narrow temperature range. 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

As already mentioned, the motion of a chaotic flow is sensitive to initial conditions [H] points which initially he close together on the attractor follow paths that separate exponentially fast. This behaviour is shown in figure C3.6.3 for the WR chaotic attractor at /c 2=0.072. The instantaneous rate of separation depends on the position on the attractor. However, a chaotic orbit visits any region of the attractor in a recurrent way so that an infinite time average of this exponential separation taken along any trajectory in the attractor is an invariant quantity that characterizes the attractor. If y(t) is a trajectory for the rate law fc3.6.2] then we can linearize the motion in the neighbourhood of y to get... 

Nonradiative energy transfer is induced by an interaction between the state of the system, in which the sensitizer is in the excited state and the activator in the ground state, and the state in which the activator is in the excited and the sensitizer in the ground state. In the presence of radiative decay, nonradiative decay, and energy transfer the emission of radiation from a single sensitizer ion decays exponentially with time, /. 

Ideal Performance and Cooling Requirements. Eree carriers can be excited by the thermal motion of the crystal lattice (phonons) as well as by photon absorption. These thermally excited carriers determine the magnitude of the dark current,/ and constitute a source of noise that defines the limit of the minimum radiation flux that can be detected. The dark carrier concentration is temperature dependent and decreases exponentially with reciprocal temperature at a rate that is determined by the magnitude of or E for intrinsic or extrinsic material, respectively. Therefore, usually it is necessary to operate infrared photon detectors at reduced temperatures to achieve high sensitivity. The smaller the value of E or E, the lower the temperature must be. 

Growth rate is very sensitive to liquid content for narrow initial-size distributions, with increases in liquid content for fine powders leading to an approximate exponential increase in granule size. For low-viscosity hquids, granulation occurs when very Hose to the saturation of the granule. This leads to the following equation to estimate moisture requirements [Capes, Pai ticle Size Enlargement, Elsevier (1980)] ... 

ZnO instead of T1O2 because ZnO provides a 220 times higher mobility for photoinjected electrons, which would allow reduction of the exciting laser intensity. The slow PMC decay of TiOrbased nanostructured sensitization solar cells (the Ru complex as sensitizer), which cannot be matched by a single exponential curve and is influenced by a bias illumination, is strongly affected by the concentration of iodide in the electrolyte (Fig. 38). On the basis of PMC transients and their dependence on the iodide concentration, a kinetic mechanism for the reaction of photoinjected electrons could be elaborated.40... 

A note on good practice Exponential functions (inverse logarithms, e ) are very sensitive to the value of x, so carry out all the arithmetic in one step to avoid rounding errors. 

A note on good practice Note that, because exponential functions ex are so sensitive to the value of x, we avoid rounding errors by leaving the numerical calculation to a single final step. 

If the signal decay is a single-exponential curve, equations 16 and 17 result in values for X that are in agreement with each other. Dissimilar values indicate multiexponential decay, which usually means that the sample contains more than one fluorophore. Multiexponential decay can be resolved by using a phase fluorometer with phase sensitive detection. A time-independent, direct-current signal is produced that is proportional to the cosine of the difference between the phase angle of the detector ( D) and the phase angle of the fluorescence ( ) ... 

In conclusion, one remark. It Is evident Chat Che calculations describing the ideal case are rather far from reality. Further, it should be noticed, that it is absolutely incorrect, to take as a measure of surface concentration the AES signals (eventually normalized) Chat is to put N] = 1. Even for Che signals most sensitive for the surface, N] - 0.5 It is equally incorrect to say (what is very popular in the literature) that the AES signals characterize the average concentration over the free pathlength X of the electrons monitored the contribution of the deeper layer decreases exponentially and not linearly with the distances from the surface (8). 

Water-sensitive papers are readily available in most countries and provide a convenient system for visually assessing spray drift performance. These papers are coated with bromoethyl blue, which turns from yellow to blue when contacted with water. " However, since any water can cause this change in color, care needs to be taken to prevent accidental exposure to sources of water other than the pesticide. Such cards do not work well under humid conditions, and are not appropriate for sampling droplets with diameter below 15 qm. Quantitative estimates of droplet size distributions must take account of the exponential increase in droplet volume as the droplet diameter increases. As droplets strike the paper, the liquid spreads over the surface and leaves a stain with a size that is dependent on the volume of the droplet. The apparent droplet size will be greater for large droplets than for small droplets, and the size determination must be corrected to avoid bias. 

---