876 research outputs found
Statistical models of mixtures with a biaxial nematic phase
We consider a simple Maier-Saupe statistical model with the inclusion of
disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like
and disc-like molecules. A quenched distribution of shapes leads to the
existence of a stable biaxial nematic phase, in qualitative agreement with
experimental findings for some ternary lyotropic liquid mixtures. An annealed
distribution, however, which is more adequate to liquid mixtures, precludes the
stability of this biaxial phase. We then use a two-temperature formalism, and
assume a separation of relaxation times, to show that a partial degree of
annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure
Aharonov-Bohm-like effect for light propagating in nematics with disclinations
Using a geometric approach for the propagation of light in anisotropic media,
we investigate what effect the director field of disclinations may have on the
polarization state of light. Parallel transport around the defect, of the
spinor describing the polarization, indicates the acquisition of a topological
phase, in analogy with the Aharonov-Bohm effect.Comment: 6 pages, to appear in Europhysics Letter
Primera cita de Cloudina carinata Cortijo et al., 2010 en Sudamérica, Formación de Tamengo, Grupo de Corumbá, Brasil Brazil
It is herein presented the unprecedented occurrence of Cloudina carinata Cortijo et al., 2010 in the American continent. This new occurrence expanded the geographic distribution of this species, until now reported from sections in Spain and Siberia. The assembled biomineralizing metazoans Cloudina carinata, Cloudina lucianoi (Beurlen & Sommer, 1957) and Corumbella werneri Hahn et al., 1982 are presented for the first time from the Tamengo Formation, Corumbá Group, Porto Figueiras section, Corumbá Municipality, Mato Grosso do Sul State, Brazil. This new occurrence could be employed as an additional biostratigraphic tool for international correlation of the terminal Ediacaran, as well as for palaeobiogeographic and palaeoecologic reconstructions.Se documenta en este resumen la primera aparición de Cloudina carinata Cortijo et al., 2010 en el continente americano. Esta nueva aparición extiende la distribución geográfica de esta especie, hasta ahora restringida a España y Siberia. Se presenta por primera vez en la Formación de Tamengo (Corumbá, Estado de Mato Grosso do Sul, Brasil) la asociación de metazoos mineralizados compuesta por Cloudina carinata, Cloudina lucianoi (Beurlen & Sommer, 1957) y Corumbella werneri Hahn et al., 1982. Esta asociación podría ser útil como marcador bioestratigráfico en las correlaciones internacionales del Ediacárico terminal, así como para futuras reconstrucciones paleobiogeográficas y paleoecológicas
Soliton surfaces associated with symmetries of ODEs written in Lax representation
The main aim of this paper is to discuss recent results on the adaptation of
the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras,
which was originally derived for PDEs [Grundland, Post 2011], to the case of
integrable ODEs admitting Lax representations. We give explicit forms of the
\g-valued immersion functions based on conformal symmetries involving the
spectral parameter, a gauge transformation of the wave function and generalized
symmetries of the linear spectral problem. The procedure is applied to a
symmetry reduction of the static -field equations leading to the
Jacobian elliptic equation. As examples, we obtain diverse types of surfaces
for different choices of Jacobian elliptic functions for a range of values of
parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu
Caracterización quimioestratigráfica y facies carbonatadas de una plataforma ediacárica, Formación de Tamengo, Grupo de Corumbá: resultados preliminares
This study presents updates and upgrades concerning the stable isotopic register of the Tamengo Formation, upper part of the Corumbá Group, which crops out in the meridional portion of the Paraguay Belt. This work includes detailed stratigraphic sections paired with high-resolution δ13C and δ18O geochemistry from two mining sites near Corumbá (Mato Grosso do Sul, Brazil).Este estudio presenta una actualización del registro isotópico de la Formación de Tamengo, parte superior del Grupo Corumbá, que se encuentra en la parte meridional del Cinturón Paraguayo. Este trabajo incluye cortes estratigráficos detallados enlazados con la geoquímica de alta resolución δ13C y δ18O de dos yacimientos mineros cercanos a Corumbá (Mato Grosso do Sul, Brasil)
Interface mediated interactions between particles -- a geometrical approach
Particles bound to an interface interact because they deform its shape. The
stresses that result are fully encoded in the geometry and described by a
divergence-free surface stress tensor. This stress tensor can be used to
express the force on a particle as a line integral along any conveniently
chosen closed contour that surrounds the particle. The resulting expression is
exact (i.e., free of any "smallness" assumptions) and independent of the chosen
surface parametrization. Additional surface degrees of freedom, such as vector
fields describing lipid tilt, are readily included in this formalism. As an
illustration, we derive the exact force for several important surface
Hamiltonians in various symmetric two-particle configurations in terms of the
midplane geometry; its sign is evident in certain interesting limits.
Specializing to the linear regime, where the shape can be analytically
determined, these general expressions yield force-distance relations, several
of which have originally been derived by using an energy based approach.Comment: 18 pages, 7 figures, REVTeX4 style; final version, as appeared in
Phys. Rev. E. Compared to v2 several minor mistakes, as well as one important
minus sign in Eqn. (18a) have been cured. Compared to v1, this version is
significantly extended: Lipid tilt degrees of freedom for membranes are
included in the stress framework, more technical details are given, estimates
for the magnitude of forces are mad
GEOMETRICAL OPTIMIZATION OF MIXED CONVECTIVE FLOWS OVER TRIANGULAR ARRANGEMENT OF CYLINDERS
The present study consists on the numerical evaluation of a triangular arrangement of circular cylinders submitted to transient, two-dimensional, incompressible, laminar and mixed convective flows. The geometrical evaluation is performed by means of Constructal Design. For all simulations it is considered Reynolds and Prandtl numbers of ReD = 100 and Pr = 0.71. Moreover, three different values of Richardson number are investigated: Ri = 0.1 (which represents flows dominated by forced convective), 1.0 (which represents an equilibrium between forced and natural driven forces) and 10.0 (which represents flows with dominance of natural convective). The conservation equations of mass, momentum and energy are solved with the use of Finite Volume Method (FVM). The buoyancy forces are tackled with the Boussinesq approximation. The area occupied by the triangular arrangement of cylinders is a geometric constraint of the problem and the cylinders have the same diameter. The main purpose is to evaluate the effect of Richardson number over the drag coefficient (CD) and Nusselt number (NuD) between the cylinders and the surrounding flow, as well as, over the optimal ratio ST/D (ratio between transversal pitch and the cylinder) for two different values of the ratio SL/D = 1.5 and 2.5 (ratio between longitudinal pitch and the cylinders diameter). Results showed that the effect of ST/D over drag coefficient and Nusselt number is strongly affected by the magnitude of Richardson number. Concerning the Nusselt number, for Ri = 0.1 the optimal geometry which maximizes the NuD is reached for the highest magnitude of ST/D, while for Ri = 10.0 an intermediate optimal ratio of ST/D maximizes the NuD. The Richardson magnitudes also have large influence over the fluid dynamic and thermal behavior of fluid flow for all evaluated geometries. An increase in the ratio SL/D improved the heat exchange of the flow, but decreased the fluid dynamic performance
The compensation of Gaussian curvature in developable cones is local
In this paper we use the angular deficit scheme [V. Borrelli, F. Cazals, and
J.-M. Morvan, {\sl Computer Aided Geometric Design} {\bf 20}, 319 (2003)] to
determine the distribution of Gaussian curvature in developable cones (d-cones)
[E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, {\sl Nature} {\bf 401}, 46
(1999)] numerically. These d-cones are formed by pushing a thin elastic sheet
into a circular container. Negative Gaussian curvatures are identified at the
rim where the sheet touches the container. Around the rim there are two narrow
bands with positive Gaussian curvatures. The integral of the (negative)
Gaussian curvature near the rim is almost completely compensated by that of the
two adjacent bands. This suggests that the Gauss-Bonnet theorem which
constrains the integral of Gaussian curvature globally does not explain the
spontaneous curvature cancellation phenomenon [T. Liang and T. A. Witten, {\sl
Phys. Rev. E} {\bf 73}, 046604 (2006)]. The locality of the compensation seems
to increase for decreasing d-cone thickness. The angular deficit scheme also
provides a new way to confirm the curvature cancellation phenomenon.Comment: 12 pages; 5 figure
Geometric Mechanics of Curved Crease Origami
Folding a sheet of paper along a curve can lead to structures seen in
decorative art and utilitarian packing boxes. Here we present a theory for the
simplest such structure: an annular circular strip that is folded along a
central circular curve to form a three-dimensional buckled structure driven by
geometrical frustration. We quantify this shape in terms of the radius of the
circle, the dihedral angle of the fold and the mechanical properties of the
sheet of paper and the fold itself. When the sheet is isometrically deformed
everywhere except along the fold itself, stiff folds result in creases with
constant curvature and oscillatory torsion. However, relatively softer folds
inherit the broken symmetry of the buckled shape with oscillatory curvature and
torsion. Our asymptotic analysis of the isometrically deformed state is
corroborated by numerical simulations which allow us to generalize our analysis
to study multiply folded structures
Second variation of the Helfrich-Canham Hamiltonian and reparametrization invariance
A covariant approach towards a theory of deformations is developed to examine
both the first and second variation of the Helfrich-Canham Hamiltonian --
quadratic in the extrinsic curvature -- which describes fluid vesicles at
mesoscopic scales. Deformations are decomposed into tangential and normal
components; At first order, tangential deformations may always be identified
with a reparametrization; at second order, they differ. The relationship
between tangential deformations and reparametrizations, as well as the coupling
between tangential and normal deformations, is examined at this order for both
the metric and the extrinsic curvature tensors. Expressions for the expansion
to second order in deformations of geometrical invariants constructed with
these tensors are obtained; in particular, the expansion of the Hamiltonian to
this order about an equilibrium is considered. Our approach applies as well to
any geometrical model for membranes.Comment: 20 page
- …