The Reasons for Instabilities

Let us take a small volume of a liquid and consider two forces, the gravity force that push that volume down and the buoyancy force that push it up. Such a situation happens when a liquid is heated from below in a shallow pan then, with increasing temperature, warm bottom layers of the liquid tend to rise but the upper cool layers tend to sink, Fig. 11.32a. Evidently, the two vertical forces (both along the z-axis) counteract and we are tempted to conclude that warm liquid would penetrate through the cold one. In reality, however, a nice steady-state periodic pattern of flow is observed in the horizontal plane xy due to up and down vertical streams. 

Such a pattern occurs at a critical value of the vertical temperature gradient and has a form of a two-dimensional hexagonal lattice. This is another example of a break of the symmetry of the system caused by convective hydrodynamic instability, the so-called Benard instability. 

In both the cases considered, an optical contrast of the patterns observed in isotropic liquids is very small. Certainly, the anisotropy of Uquid crystals brings new features in. For instance, the anisotropy of (helectric or diamagnetic susceptibility causes the Fredericks transition in nematics and wave like instabilities in cholesterics (see next Section), and the flexoelectric polarizaticm results in the field-controllable domain patterns. In turn, the anisotropy of electric conductivity is responsible for instability in the form of rolls to be discussed below. All these instabilities are not observed in the isotropic liquids and have an electric field threshold controlled by the corresponding parameters of anisotropy. In addition, due to the optical anisotropy, the contrast of the patterns that are driven by isotropic mechanisms , i.e. only indirectly dependent on anisotropy parameters, increases dramatically. Thanks to this, one can easily study specific features and mechanisms of different instability modes, both isotropic and anisotropic. The characteristic pattern formation is a special branch of physics dealing with a nonlinear response of dissipative media to external fields, and liquid crystals are suitable model objects for investigation of the relevant phenomena [39]. 

Assume that our capacitor is filled by a nematic mixture with 0 well aligned along the x-axis and let the same charge injection mechanism works. Then, in a dc regime, the periodic flow will inevitably interact with the director. The maximum realignment, i.e. the deflection of the director angle 9 in the z-direction, will be 

11 Optics and Electric Field Effects in Nematic and Smectic A Liquid Crystals 

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Usually the presence of a carbonyl group in a sample compound does not give rise to serious difficulties in GC analysis. However, sometimes it can be the reason for instability of the compounds. Owing to its polarity and strong interactions with the support, it can cause peak asymmetry and, in more complex samples, the peaks of carbonyl compounds in the chromatogram can be overlapped by those of interfering components. In these instances the carbonyl group must be converted into an inert derivative. Suitable properties of the derivatives are often utilized also for the preliminary isolation of carbonyl compounds from other components of the sample [98]. 

Study of processes leading to rupture of foam films can serve to establish the reasons for their stability. The nature of the unstable state of thin liquid films is a theoretical problem of major importance (it has been under discussion for the past half a century), since film instability causes the instability of some disperse systems. On the other hand, the rupture of unstable films can be used as a model in the study of various flotation processes. The unstable state of thin liquid films is a topic of contemporary interest and is often considered along with the processes of spreading of thin liquid films on a solid substrate (wetting films). Thermodynamic and kinetic mechanisms of instability should be clearly distinguished so that the reasons for instability of thin liquid films could be found. Instability of bilayer films requires a special treatment, presented in Section 3.4.4. 

If instability of a drug product leads to these unwelcome effects on patients, it could also lead to expensive costs to manufacturers as they attempt to discover the reasons for instability and methods of minimizing them. An unstable product would highlight an uncontrolled process, and could require a substantial product and process investigation with possible product recalls. FDA has authority to issue cGMP violations with follow-up warning letters and possible consent decrees and criminal prosecutions. 

It should be noted that it is impossible to determine the main reason for gas sensor instabilities in a general sense the task is too complicated. In addition, the reasons for instability could depend on the constructive and/or technological features of the sensor fabrication or on temperature effects at the point of use. Therefore, at present there are a great number of approaches, aU of which—in the author s opinion—can be effective in resolving instability problems in gas sensors. According to Korotcenkov and Cho (2011), to attain maximum gas sensor operational stability, it is necessary to stick to the following recommendations. 

The polymer-nanocomposites possess some attractive features. In contrast to thin metal films and cermets they are three-dimensional objects containing nano-size particles. The polymer matrix ixevents the oxidation of particles and coalescence, which is one of the reasons for instability and aging effects of free nanoparticle systems. 

In actual practice, a weight W is obtained, which is less than the ideal value W. The reason for this becomes evident when the process of drop formation is observed closely. What actually happens is illustrated in Fig. 11-10. The small drops arise from the mechanical instability of the thin cylindrical neck that develops (see Section II-3) in any event, it is clear that only a portion of the drop that has reached the point of instability actually falls—as much as 40% of the liquid may remain attached to the tip. 

Hydrogen as it occurs in nature is predominantly composed of atoms in which the nucleus is a single proton. In addition, terrestrial hydrogen contains about 0.0156% of deuterium atoms in which the nucleus also contains a neutron, and this is the reason for its variable atomic weight (p. 17). Addition of a second neutron induces instability and tritium is radioactive, emitting low-energy particles with a half-life of 12.33 y. Some characteristic properties of these 3 atoms are given in Table 3.1, and their implications for stable isotope studies, radioactive tracer studies, and nmr spectroscopy are obvious. 

The reason for this instability is that the blowers are incorrectly sized for the application and are mnning well outside their performance curve. In effect, the blowers have no back-pressure and are operating in a mn-out condition. The result of operating in this condition is that the design load intended to stabilized the rotor is no longer present. This causes the shaft to deflect or flex, generating the high amplitudes observed in the horizontal mode plot. 

At the beginning of sliding, the system is accelerated because the driven force must excess the resistance from lubricating film. For this reason, the system actually jumps from A to the point B, instead of B, to gain a shear stress lower than the critical value This phenomenon, so called velocity-weakening has been regarded widely in the literatures as the cause for instability and stick-slip motion in lubricated systems. 

There are five fundamental t T)es of nuclear decay process, as listed in Table 22-3. Figure 22-5 on the next page diagrams how nuclear decays affect N and Z. As the figure suggests, the decay process of any particular unstable nuclide depends on the reason for its instability. 

Most substances which appear in the examples of this chapter are analysed In Part Two and their enthalpy of decomposition determined experimentally. This is because most of them are considered hardly stable. This is one of the reasons for assigning no Tow risk in the suggested classifications. But it is also indisputable that criterion Cf overestimates the instability risk. It is the case for all aromatic compounds that are generally very stable. In the examples above, N-methylaniline, dichlorobenzene... 

Although poly(vinyl chloride) (PVC) is one of the most important commercial polymers, its outdoor use has been restricted by its photochemical instability. The reasons for this instability are incompletely understood, but some progress has been made recently on this problem, and the present paper attempts to summarize the current status of fundamental knowledge in this field. This survey is not intended to be comprehensive it is concerned primarily with work published since the early 1970 s and with basic chemical principles rather than technological developments. The photodegradation of PVC has been discussed in other recent reviews (1,2, 3 4) ... 

What are the reasons for clock instability High-frequency noise is always generated at turn-on and turnoff in any switcher. This noise can infiltrate into the IC via various pins. It can be very hard to filter out and control. You may need to ultimately simply avoid turning the Fet OFF too dramatically. In most switchers, the turn-on transition is traditionally delayed (or slowed) just a little, so as to allow the output/catch diodes to recover... 

The occurrence of necking in the spin line indicates the instability of deformation and the system therefore restabilizes. Similar behavior to that shown with temperature can be observed in the presence of plasticizers. The fracture is promoted by increased stress in the case of plastic deformation. Cracks or notches at the surfaces of fibers and films are also the reason for disturbed deformation due to the more rapidly increased stress at the tips of these defect sites. 

It is desirable to examine in greater detail the reasons for the thermodynamic instability (small dissociation energy) of the alkyl carbon-transition metal a bond, which appears to be so much less than the carbon-metal a bond of the nontransition metals. The reasons for the instability are (a) the very small covalent energy of the metal-carbon bond and (6) the relatively small difference in electronegativities between the trairsition metal and the carbon atom, which accounts for the small ionic resonance energy contribution to the total energy of the bond. 

The nitrate ion in potassium nitrate contains the highly electronegative atoms nitrogen and oxygen which are covalently bonded. When such atoms form a bond there is less stability than when bonds involve atoms of differing electronegativities. Intense competition for the electron pair in the N-0 bond is thought to be the reason for some of this instability. 

All nitrosomethanides represent resonance-stabilized anions, which are stable at ambient temperatures. However, their alkali and silver salts are energetic materials and hence most of them are explosive. The reason for this thermodynamic instability lies in the smaller CN and NO bond energies compared to those of N2 and CO (in CO2). 

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