Reciprocity behavior

Leal W. S. (1996) Chemical communication in scarab beetles reciprocal behavioral agonist-antagonist activities of chiral pheromones. Proc. Natl. Acad. Sci. USA 93, 12112-12115. 

Piezoelectric crystals are transducers that generate an oscillating electrical polarization when subjected to an external oscillating mechanical stress, and vice versa. The brothers Paul-Jacques and Pierre Curie discovered the piezoelectric effect in 1880 when they compressed certain crystals along certain axes (Curie and Curie, 1880). The reciprocal behavior was deduced from thermodynamic principles a year later by Gabriel Lippman... 

Resist Behavior in Excimer Laser Irradiation 3.4.5.1 Reciprocity Behavior... 

A remarkable reciprocity failure was observed in the inorganic resist described in Section 3.4.2 (210). The effect of dose rate on the total dose required for response is shown in Figure 3.71, where the number of pulses required for exposure is plotted as a function of pulse energy density. As a pulse energy is increased, a drastic reduction in the required dose is observed. The reciprocity failure was attributed to a locally induced temperature rise. Further investigations are needed to clarify the reciprocity behavior of resist systems under excimer laser radiation. Multiphoton mechanistic studies are clearly warranted. 

Plotted in terms of ellipticities in Figure 17, there is a reciprocal behavior of the bands as the band at I,- gets more negative, the band at 2 gets more positive. This has been termed reciprocal relations in optical rotation [30,31] and represents the specific way in which the electric transitions adhere to the sum rule in optical rotation [28,32], i.e. 

K. Jain, C.G. WiUson, and B.J. Lin, Ultrafast deep UV lithography with excimer lasers, IEEE Electron Device Lett. EDL-3, 53 (1982) S. Rice and K. Jain, Reciprocity behavior of photoresists in excimer laser lithography, IEEE Trans. Electron Dev. ED-31, 1 (1984). 

Figure 3. Reciprocity behavior of the microcolumn imaging system.

The magnitude of the atomic weight determines the properties of an element. Therefore, in the study of compounds, not just the quantities, properties of the elements and their reciprocally behavior should be considered, but also the atomic weight of elements. Therefore, the compounds of Sand Te, Cl andJ, have enough similarities, but also significant differences. 

Supramolecular systems offer distinct advantages as biomaterials over chemically cross-linked gels. First, because of their noncovalent nature, supramolecular systems are inherently responsive to stimuli such as variations in temperature and pH. Second, the noncovalent bonding allows a unique mix-and-match principle to be used for tuning properties. Third, supramolecular materials biodegrade faster than chemically cross-linked gels as a result of the small molecular precursors that these materials are made of. Furthermore, these supramolecular systems are proposed to be able to display dynamic reciprocal behavior, as found in the natural environment of cells [13]. Supramolecular biomaterials are proposed to be able to spatiotemporally adapt to changes exerted by cells and their natural environment. To fulfill this promise, important features of supramolecular systems are their hierarchical structure/assembly, their dynamic and nonlinear behavior, and then-biochemical properties. 

Figure 4.14 Schematic illustration of the principles underlying design of Pirkle-type chiral stationary phases (CSPs). (a) Illustration of the concept of reciprocity a single enantiomer of a racemate which separates well on the CSP shown on the left, when used to produce a second CSP shown at the right, will usually afford separation of the enantiomers of analytes that are structurally similar to the chiral selector of the first CSP. Reproduced from Pirkle et al, J. Org. Chem. 57 (1992), 3854, Copyright (1992), with permission of the American Chemical Society, (b) Two CSPs that exhibit reciprocal behavior, and (c) enantiomeric recognition model for the more stable diastereomeric complex between (S)-naproxen dimethylamide and the Whelk-0-1 (3R,4R) analog. Note that hydrogen atoms bonded to carbons are omitted for clarity. Reproduced from Wolf and Pirkle (2002), Tetrahedron 58, 3597, copyright (2002), with permission from Elsevier.

In practical emulsions, the sensitivity and reciprocity behavior are usually greatly increased by sensitizers, compounds that are added during emulsion-making and are adsorbed on the surface of the crystals. Chemical sensitization produces a major decrease in the number of absorbed photons needed to make a crystal developable and can greatly decrease low-intensity reciprocity failure. Care must be exercised, however, since too much sensitization can cause the formation of chemical nuclei that can act like LI during development, giving rise to fog (spurious density in nonexposed areas). 

In the same section, we also see that the source of the appropriate analytic behavior of the wave function is outside its defining equation (the Schibdinger equation), and is in general the consequence of either some very basic consideration or of the way that experiments are conducted. The analytic behavior in question can be in the frequency or in the time domain and leads in either case to a Kramers-Kronig type of reciprocal relations. We propose that behind these relations there may be an equation of restriction, but while in the former case (where the variable is the frequency) the equation of resh iction expresses causality (no effect before cause), for the latter case (when the variable is the time), the restriction is in several instances the basic requirement of lower boundedness of energies in (no-relativistic) spectra [39,40]. In a previous work, it has been shown that analyticity plays further roles in these reciprocal relations, in that it ensures that time causality is not violated in the conjugate relations and that (ordinary) gauge invariance is observed [40]. 

Reciprocating Compressors. Prior to 1895, when Linde developed his air Hquefaction apparatus, none of the chemical processes used industrially required pressures much in excess of I MPa (145 psi) and the need for a continuous supply of air at 20 MPa provided the impetus for the development of reciprocating compressors. The introduction of ammonia, methanol, and urea processes in the early part of the twentieth century, and the need to take advantage of the economy of scale in ammonia plants, led to a threefold increase in the power required for compression from 1920 to 1940. The development of reciprocating compressors was not easy Htfle was known about the effects of cycles of fluctuating pressure on the behavior of the... 

Many users consider rotaiy compressors, such as the Rootes -type blower, as turbomachines because their behavior in terms of the rotor dynamics is very close to centrifugal and axial flow machineiy. Unhke the reciprocating machines, the rotary machines do not have a veiy high vibration problem but, like the reciprocating machines, they are positive displacement machines. 

This equation successfully describes the kinetic behavior of a surprisingly large number of reac tions of different enzymes. Taking reciprocals of both sides gives ... 

The JKR model predicts that the contact radius varies with the reciprocal of the cube root of the Young s modulus. As previously discussed, the 2/3 and — 1/3 power-law dependencies of the zero-load contact radius on particle radius and Young s modulus are characteristics of adhesion theories that assume elastic behavior. 

For intermediate drift rates (4 < BN < 8), when chain conformations are already distorted, deviates from linear behavior and goes through a maximum at some critical value Bf. of the field, confirming earlier findings by Pandey et al. [103,104]. This critical bias B at which the velocity starts to decrease depends rather weakly on the density Cobs, turns out to be reciprocal to chain length A, implying that only when the total force, /c = B,N 9, acting upon the whole driven molecule, exceeds a certain threshold, which does not depend on the size of the macromolecule, the chains start to get stuck in the medium. 

An overview of the superplastic behavior of aluminum alloys to demonstrate the grain-size effect is depicted in Fig. 1, in which the quantitative relation between the logarithm of the optimum strain rate for superplastic flow and the grain size (plotted as the logarithm of reciprocal grain size) is clearly shown [4]. The slope of the curve in Fig. 1 is noted to be about 3. 

This section describes machinery that exhibits reciprocating and/or linear motion(s) and discusses typical vibration behavior for these types of machines. 

The behavior of the failure rate as a function of time can be gaged from a hazard plot. If data are plotted on exponential hazard paper, the derivative of the cumulative hazard function at some time is the instantaneous failure rate at that time. Since time to failure is plotted as a function of the cumulative hazard, the instantaneous failure rate is actually the reciprocal of the slope of the plotted data, and the slope of the plotted data corresponds to the instantaneous mean time to failure. For the data that are plotted on one of the other hazard papers and that give a curved plot, one can determine from examining the changing slope of the plot whether the tme failure rate is increasing or decreasing relative to the failure rate of the theoretical distribution for the paper. Such information on the behavior of the failure rate cannot be obtained from probability plots. 

The time required to produce a 50% reduction in properties is selected as an arbitrary failure point. These times can be gathered and used to make a linear Arrhenius plot of log time versus the reciprocal of the absolute exposure temperature. An Arrhenius relationship is a rate equation followed by many chemical reactions. A linear Arrhenius plot is extrapolated from this equation to predict the temperature at which failure is to be expected at an arbitrary time that depends on the plastic s heat-aging behavior, which... 

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