Instability twist

The degree of twist in a modem rifle is generally just about the minimum that will produce stability in a bullet passing thru an atmosphere of a density corresponding to a temperature of zero degrees centigrade. This is to ensure that entry into a denser medium — i.e. the target — will produce complete instability, which is a desired criterion for wound baLlistics... 

Pang JH, ClarkNA (1994) Observation of a chiral-symmetry-braking twist-bend instability in achiral freely suspended liquid-crystal films. Phys Rev Lett 73 2332-2335... 

Consider the shear flow geometry in Fig. 1, with three different anchoring conditions on the top and bottom planes. The initial condition is a uniform n field consistent with the wall anchoring. Cases (a) and (b) are similar in which n lies initially in the y-z plane. In both cases, the LE theory predicts an in-plane tumbling instability and an out-of-plane twist instability. ... 

Experiments demonstrate that at even higher Er, the rolls become unstable and irregular. Ultimately, defect lines called disclinations form in the flow direction. As the linear analysis concerns the behavior of infinitesimal disturbances, the growth of the instability and further bifurcations are inaccessible to such analyses. This motivated Feng, Tao, and Leal to carry out a direct numerical simulation of a sheared nematic. Using the LE theory, with the one-constant approximation, they predicted a cascade of instabilities illustrated in Fig. 3. Steady state rolls first appear at Er = 2368. The director twists toward the flow (z) direction at the center of the cells. With increasing Er, the secondary flow and the director twisting intensify. 

More recently, Marks and coworkers developed a totally different approach for obtaining very high fi values. Their strategy does not focus on extensive planar 7r-conjugation, which is prone to chemical, thermal, and photochemical instabilities [58], but on twisted 7r-electron system chromophores. These unconventional twisted % zwitterionic structures (TM and TMC) exhibit unprecedented hyperpolarizabilities as large as 15 times greater than those reported previously (fj.fi as high as -488,000 x 10 48 esu) [59,60],... 

For a poly(parabanic acid) resin as substrate, a6T as semiconductor, and cyanoethylpullulan, a highly flexible device could be obtained which shows no changes in the transistor characteristic after bending and twisting. However, the metallic gate and source electrodes sometimes disconnect. A really pure all-organic FET with a graphite-based polymer ink used to prepare the source and drain contacts does not even show this instability [305],... 

The twisted alkene present in acetoxydithiocin (176 R = Ac) was suggested to be a possible cause of its relative unreactivity as a diene in Diels-Alder cycloaddition reactions. No reaction is seen with maleic anhydride, tetracyanoethylene, or hexafluoro-2-butyne at 45 °C higher temperatures were precluded by the thermal instability of (176 R = Ac) <78T363i>. iV-Phenyltriazolinedione reacted with (176 R = Ac), but afforded no identifiable products. 

Fig. 3.11.1. The mechanism for homogeneous instability the flow is along y and the velocity gradient along z. (a) An angular fluctuation 0 = n > 0 results in a viscous torque T, > 0 such that a small twist (j> = n >Q is produced, (b) a deformation > 0 results in a torque < 0 such that tne initial deformation 0 is...

Electric field effects are more complicated because of conduction. The Carr-Helfrich instability, which occurs in nematics of negative dielectric anisotropy (see 3.10.2), may be expected to take place in this case too, only the bend and twist distortions are now coupled. Moreover, the fluid motion along z can occur only by the process of permeation ( 4.5.1). 

N.V. Madhusudana, J.F. Palierne, Ph. Martinot-Lagarde and G. Durand, Twist instability of a flexoelectric nematic domain in an external field, Phys. Rev. A 30, 2153R-2154R, (1984). doi 10.1103/PhysRevA.30.2153... 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Secondary effects can introduce small errors in this method of measuring twist. Dust and surface scatches can, of course, seriously affect local alignment. More subtle are perturbations apparently produced by variations in the flow pattern (hydrodynamic domains) of neutral molecules. In the cells used here hydrodynamic instabilities become quite pronounced at field frequencies around 5 Hz at 17v and resemble the patterns described by Sussman.9 They were not visible at 0.3 Hz and 17v but Fig. 11 shows evidence of their presence. In this case, the 0 orientation of the cell was fixed and the cell was translated relative to the beam while applying 17v at 0.3 Hz. A slow variation in polarity modulation amplitude is expected because of the effects discussed in connection with Fig. 3. Superimposed are local oscillations of modulation amplitude possibly attributable to hydrodynamic domains. It may be surprising that neutral molecule flow would not exhibit a more pronounced effect however, the flow adjacent to the cell walls must be parallel to the walls and exert a minor orienting force on the thin layer of molecules with significant homogeneous component at 17v. 

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