By Andre M. Sonnet, Epifanio G. Virga (auth.)
This is a e-book at the dissipative dynamics of ordered fluids,
with a selected concentrate on liquid crystals. It covers a complete
range of other theories, generally curious about nematic liquid
crystals in either their chiral and nonchiral editions. The authors
begin by means of giving an in depth account of the molecular origins of
orientational order in fluids. They then cross directly to strengthen a basic
framework within which continuum theories for ordered fluids may be phrased.
Within this unified surroundings, they disguise either well-established classical theories and new ones with facets that aren't but thoroughly settled. The e-book treats quite a lot of hydrodynamic theories for liquid crystals, from the unique Sixties works by way of Ericksen and Leslie to new, fast-developing principles of liquid crystal technological know-how. the ultimate bankruptcy is dedicated to nematoacoustics and its functions. outdated experiments at the propagation of ultrasound waves in nematic liquid crystals are interpreted and defined
in the sunshine of a brand new idea built in the common theoretical infrastructure proposed within the physique of the booklet.
This publication is meant either for graduate scholars
scholars in arithmetic, physics, and engineering of complex
materials. It can provide a high-quality framework for liquid crystal
hydrodynamics and exhibits the unifying options on the foundation of the
classical theories. It illustrates how those options can be
applied to a large choice of recent subject matters.
Andre M. Sonnet is within the division of arithmetic and records on the college of Strathclyde, Glasgow (Scotland) and Epifanio G.
Virga is within the division of arithmetic on the college of Pavia (Italy). they've got an extended historical past of operating jointly in liquid crystal technological know-how and feature contributed, particularly, to the theories of
defects and biaxial nematics.
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Extra info for Dissipative Ordered Fluids: Theories for Liquid Crystals
E/2 5 1 for all ! / e Á 1, meaning that all molecules are oriented along e. We refer to the molecular alignment in these limiting cases as planar and full, respectively. More generally, a uniaxial state with S < 0 will be called discotic, while a uniaxial state with S > 0 will be called calamitic: planar and full alignments are correspondingly the extreme limiting cases of discotic and calamitic states. 94). 95) These inequalities show that in the limit of planar alignment the biaxial order pa1 1 rameter T ranges in the interval ; , reﬂecting different degrees of anisotropy 2 2 in the molecular distribution.
10) achieves its minimum value (preferred relative orientation) in a completely aligned state ! D ! 3). New types 1 2 1 2 Fig. 3. The admissible region in the parameter space . 72). The dashed parabola represents the singular set D 2 . of uniaxial-to-biaxial transitions were predicted [23, 24, 63, 64, 315], which also unveiled a tricritical point in the phase diagram , whose existence was further conﬁrmed by an alternative theoretical approach  and detected in two independent experiments [219, 232].
X; y/. The intersections between the line y D ˇ1 and the graph of G represent all possible equilibrium uniaxial phases. The isotropic phase, which is at equilibrium for all values of the reduced temperature ˇ1 , is represented by the line x D 0. Solid lines correspond to equilibria locally stable against uniaxial perturbations; dashed lines represent equilibria unstable against the same perturbations. Where the graph of G lies below the graph of F , the uniaxially stable equilibria bear less energy than the isotropic phase.