154 research outputs found
Standard and Embedded Solitons in Nematic Optical Fibers
A model for a non-Kerr cylindrical nematic fiber is presented. We use the
multiple scales method to show the possibility of constructing different kinds
of wavepackets of transverse magnetic (TM) modes propagating through the fiber.
This procedure allows us to generate different hierarchies of nonlinear partial
differential equations (PDEs) which describe the propagation of optical pulses
along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium
and derive an extended Nonlinear Schrodinger equation (eNLS) with a third order
derivative nonlinearity, governing the dynamics for the amplitude of the
wavepacket. In this derivation the dispersion, self-focussing and diffraction
in the nematic are taken into account. Although the resulting nonlinear
may be reduced to the modified Korteweg de Vries equation (mKdV), it also has
additional complex solutions which include two-parameter families of bright and
dark complex solitons. We show analytically that under certain conditions, the
bright solitons are actually double embedded solitons. We explain why these
solitons do not radiate at all, even though their wavenumbers are contained in
the linear spectrum of the system. Finally, we close the paper by making
comments on the advantages as well as the limitations of our approach, and on
further generalizations of the model and method presented.Comment: "Physical Review E, in press
Defects in nematic membranes can buckle into pseudospheres
A nematic membrane is a sheet with embedded orientational order, which can
occur in biological cells, liquid crystal films, manufactured materials, and
other soft matter systems. By formulating the free energy of nematic films
using tensor contractions from differential geometry, we elucidate the elastic
terms allowed by symmetry, and indicate differences from hexatic membranes. We
find that topological defects in the orientation field can cause the membrane
to buckle over a size set by the competition between surface tension and
in-plane elasticity. In the absence of bending rigidity the resulting shape is
universal, known as a parabolic pseudosphere or a revolved tractrix. Bending
costs oppose such buckling and modify the shape in a predictable manner. In
particular, the anisotropic rigidities of nematic membranes lead to different
shapes for aster and vortex defects, in principle enabling measurement of
couplings specific to nematic membranes.Comment: 9 pages, 3 figure
'An Apotheosis of Well-Being': Durkheim on austerity and double-dip recessions
This article is an attempt to contribute a view on the economic crisis from classical sociology, a voice often missing from the sociological response to the crisis. The work of Émile Durkheim provides a unique perspective here centred on morality and inequality produced in a historical context akin to our neoliberal times. It is argued there are four key points to take from Durkheim’s work. Firstly, that the initial credit crunch can be more fully understood with reference to the economic anomie which Durkheim sees as ‘chronic’ in a time of marketization. Secondly, that this creates an antagonistic relationship between a supposedly self-dependent rich and lazy poor. Thirdly, this conception of self-dependency and individual initiative makes any attempt to regulate the economy akin to sacrilege. Finally, the state is unwilling to intervene due to the emergence of ‘pseudo-democracies’. Therefore, Durkheim’s theory accounts for the initial crisis, austerity and double-dip recessions in a sociological framework. The article concludes by returning to the centrality of morality to the crisis for Durkheim and highlighting the omission of this in contemporary debates
Formation of disclination lines near a free nematic interface
We have studied the nucleation and the physical properties of a -1/2 wedge
disclination line near the free surface of a confined nematic liquid crystal.
The position of the disclination line has been related to the material
parameters (elastic constants, anchoring energy and favored anchoring angle of
the molecules at the free surface). The use of a planar model for the structure
of the director field (whose predictions have been contrasted to those of a
fully three-dimensional model) has allowed us to relate the experimentally
observed position of the disclination line to the relevant properties of the
liquid crystals. In particular, we have been able to observe the collapse of
the disclination line due to a temperature-induced anchoring angle transition,
which has allowed us to rule out the presence of a real disclination line near
the nematic/isotropic front in directional growth experiments.
61.30.Jf,61.30.G
Disclinations, dislocations and continuous defects: a reappraisal
Disclinations, first observed in mesomorphic phases, are relevant to a number
of ill-ordered condensed matter media, with continuous symmetries or frustrated
order. They also appear in polycrystals at the edges of grain boundaries. They
are of limited interest in solid single crystals, where, owing to their large
elastic stresses, they mostly appear in close pairs of opposite signs. The
relaxation mechanisms associated with a disclination in its creation, motion,
change of shape, involve an interplay with continuous or quantized dislocations
and/or continuous disclinations. These are attached to the disclinations or are
akin to Nye's dislocation densities, well suited here. The notion of 'extended
Volterra process' takes these relaxation processes into account and covers
different situations where this interplay takes place. These concepts are
illustrated by applications in amorphous solids, mesomorphic phases and
frustrated media in their curved habit space. The powerful topological theory
of line defects only considers defects stable against relaxation processes
compatible with the structure considered. It can be seen as a simplified case
of the approach considered here, well suited for media of high plasticity
or/and complex structures. Topological stability cannot guarantee energetic
stability and sometimes cannot distinguish finer details of structure of
defects.Comment: 72 pages, 36 figure
Propagation of excitations induced by shear flow in nematic liquid crystals
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Communitarian perspectives on social enterprise
Concepts of social enterprise have been debated repeatedly, and continue to cause confusion. In this paper, a meta-theoretical framework is developed through discussion of individualist and communitarian philosophy. Philosophers from both traditions build social theories that emphasise either consensus (a unitarist outlook) or diversity (a pluralist outlook). The various discourses in corporate governance reflect these assumptions and create four distinct approaches that impact on the relationship between capital and labour. In rejecting the traditional discourse of private enterprise, social enterprises have adopted other approaches to tackle social exclusion, each derived from different underlying beliefs about the purpose of enterprise and the nature of governance. The theoretical framework offers a way to understand the diversity found within the sector, including the newly constituted Community Interest Company (CIC).</p
Legal origin and social solidarity: the continued relevance of Durkheim to comparative institutional analysis
By using the classic works of Durkheim as a theoretical platform, this research explores the relationship between legal systems and social solidarity. We found that certain types of civil law system, most notably those of Scandinavia, are associated with higher levels of social capital and better welfare state provision. However, we found the relationship between legal system and societal outcomes is considerably more complex than suggested by currently fashionable economistic legal origin approaches, and more in line with the later writings of Durkheim, and, indeed, the literature on comparative capitalisms. Relative communitarianism was strongly affected by relative development, reflecting the complex relationship between institutions, state capabilities and informal social ties and networks
Nucleon charge exchange on the deuteron: A critical review
The existing experimental data on the d(n,p)nn and d(p,n)pp cross sections in
the forward direction are reviewed in terms of the Dean sum rule. It is shown
that the measurement of the ratio of the charge exchange on the deuteron to
that on the proton might, if taken together with other experimental data, allow
a direct construction of the np -> np scattering amplitude in the backward
direction with few ambiguities.Comment: 7 pages with 3 figure
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