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Epifanio G. Virga

Publications and source records attributed to Epifanio G. Virga.

50 records · Page 3Linked to original sources
arXiv2018

Lifting map for ordered surfaces

When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is described on the curved, physical surface where it belongs, or it is described on a flat surface that is unrolled as pre-image of the physical surface under a suitable height function. This paper proposes a general method that pursues the latter avenue by lifting whatever order tensor is deemed appropriate from a flat to a curved surface. To produce a specific application, we specialize this method to nematic shells, for which it also provides a simple, but convincing interpretation of the outcomes of some molecular-dynamics experiments on ellipsoidal shells.

cond-mat.soft↗
arXiv2017

On a paradox in the impact dynamics of smooth rigid bodies

Paradoxes in the impact dynamics of rigid bodies are known to arise in the presence of friction. We show here that, on specificc occasions, in the absence of friction, the conservation laws of classical mechanics are also incompatible with the collisions of smooth, strictly convex rigid bodies. Under the assumption that the impact impulse is along the normal direction to the surface at the contact point, two convex rigid bodies which are well separated can come into contact, and then interpenetrate each other. This paradox can be constructed in both 2D and 3D when the collisions are tangential, in which case no momentum or energy transfer between the two bodies is possible. The postcollisional interpenetration can be realized through the contact points or through neighboring points only. The penetration distance is shown to be O(t^3). The conclusion is that rigid body dynamics is not compatible with the conservation laws of classical mechanics.

physics.class-ph↗
arXiv2017

Onsager's missing steps retraced

Onsager's paper on phase transition and phase coexistence in anisotropic colloidal systems is a landmark in the theory of lyotropic liquid crystals. However, an uncompromising scrutiny of Onsager's original derivation reveals that it would be rigorously valid only for ludicrous values of the system's number density (of the order of the reciprocal of the number of particles) Based on Penrose's tree identity and an appropriate variant of the mean-field approach for purely repulsive, hard-core interactions, our theory shows that Onsager's theory is indeed valid for a reasonable range of densities.

cond-mat.soft↗
arXiv2017

Density functional theory for dense nematics with steric interactions

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it fails to provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature: it vanishes on a nonzero measure set in orientational space.

cond-mat.soft↗
arXiv2017

Bistable curvature potential at hyperbolic points of nematic shells

Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature potential for the molecular torque. At hyperbolic points on the colloid's surface, and only there, the alignment preferred by the curvature potential may fail to be a direction of principal curvature. There the fossil energy becomes bistable.

cond-mat.soft↗
arXiv2017

Octupolar Tensors for Liquid Crystals

A third-order three-dimensional symmetric traceless tensor, called the \emph{octupolar} tensor, has been introduced to study tetrahedratic nematic phases in liquid crystals. The octupolar \emph{potential}, a scalar-valued function generated on the unit sphere by that tensor, should ideally have four maxima capturing the most probable molecular orientations (on the vertices of a tetrahedron), but it was recently found to possess an equally generic variant with \emph{three} maxima instead of four. It was also shown that the irreducible admissible region for the octupolar tensor in a three-dimensional parameter space is bounded by a dome-shaped surface, beneath which is a \emph{separatrix} surface connecting the two generic octupolar states. The latter surface, which was obtained through numerical continuation, may be physically interpreted as marking a possible \emph{intra-octupolar} transition. In this paper, by using the resultant theory of algebraic geometry and the E-characteristic polynomial of spectral theory of tensors, we give a closed-form, algebraic expression for both the dome-shaped surface and the separatrix surface. This turns the envisaged intra-octupolar transition into a quantitative, possibly observable prediction. Some other properties of octupolar tensors are also studied.

math-ph↗
arXiv2016

Interfacial and morphological features of a twist-bend nematic drop

In this experimental and theoretical study, we examine the equilibrium shapes of quasitwo-dimensional twist-bend nematic (Ntb) drops formed within a planarly aligned nematic layer of the liquid crystal CB7CB. Initially, at the setting point of the Ntb phase, the drops assume a nonequilibrium cusped elliptical geometry with the major axis orthogonal to the director of the surrounding nematic fluid; this growth is governed principally by anisotropic heat diffusion. The drops attain equilibrium through thermally driven dynamical evolutions close to their melting temperature. They are associated with a characteristic twin-striped morphology that transforms into the familiar focal conic texture as the temperature is lowered. At equilibrium, large millimetric drops are tactoidlike, elongated along the director of the surrounding nematic fluid. This geometry is explained by a mathematical model that features two dimensionless parameters, of which one is the structural cone angle of the Ntb phase and the other, the relative strength of mismatch elastic energy at the drop's interface. Both parameters are extracted from the observations by measuring the aspect ratio of the equilibrium shapes and the inner corner angle of the cusps.

cond-mat.soft↗
arXiv2015

Explicit excluded volume of cylindrically symmetric convex bodies

We represent explicitly the excluded volume Ve{B1,B2} of two generic cylindrically symmetric, convex rigid bodies, B1 and B2, in terms of a family of shape functionals evaluated separately on B1 and B2. We show that Ve{B1,B2} fails systematically to feature a dipolar component, thus making illusory the assignment of any shape dipole to a tapered body in this class. The method proposed here is applied to cones and validated by a shape-reconstruction algorithm. It is further applied to spheroids (ellipsoids of revolution), for which it shows how some analytic estimates already regarded as classics should indeed be emended.

cond-mat.soft↗
arXiv2015

Octupolar order in two dimensions

Octupolar order is described in two space dimensions in terms of the maxima (and conjugated minima) of the probability density associated with a third-rank, fully symmetric and traceless tensor. Such a representation is shown to be equivalent to diagonalizing the relevant third-rank tensor, an equivalence which however is only valid in the two-dimensional case.

cond-mat.soft↗
arXiv2014

Chain Paradoxes

For nearly two centuries the dynamics of chains have offered examples of paradoxical theoretical predictions. Here we propose a theory for the dissipative dynamics of one-dimensional continua with singularities which provides a unified treatment for chain problems that have suffered from paradoxical solutions. These problems are duly solved within the present theory and their paradoxes removed---we hope.

physics.class-ph↗
arXiv2014

Dissipative Shocks behind Bacteria Gliding

Gliding is a means of locomotion on rigid substrates utilized by a number of bacteria includingmyxobacteria and cyanobacteria. One of the hypotheses advanced to explain this motility mechanism hinges on the role played by the slime filaments continuously extruded from gliding bacteria. This paper solves in full a non-linear mechanical theory that treats as dissipative shocks both the point where the extruded slime filament comes in contact with the substrate, called the filament's foot, and the pore on the bacterium outer surface from where the filament is ejected. We prove that kinematic compatibility for shock propagation requires that the bacterium uniform gliding velocity (relative to the substrate) and the slime ejecting velocity (relative to the bacterium) must be equal, a coincidence that seems to have already been observed.

physics.bio-ph↗
arXiv2014

Dissipative shocks in a chain fountain

The fascinating and anomalous behaviour of a chain that instead of falling straight down under gravity, first rises and then falls, acquiring a steady shape in space that resembles a fountain's sprinkle, has recently attracted both popular and academic interest. The paper presents a complete mathematical solution of this problem, whose distinctive feature is the introduction of a number of dissipative shocks which can be resolved exactly.

math-ph↗
arXiv2014

Elasticity of Twist-Bend Nematic Phases

The ground state of twist-bend nematic liquid crystals is a heliconical molecular arrangement in which the nematic director precesses uniformly about an axis, making a fixed angle with it. Both precession senses are allowed in the ground state of these phases. When one of the two \emph{helicities} is prescribed, a single helical nematic phase emerges. A quadratic elastic theory is proposed here for each of these phases which features the same elastic constants as the classical theory of the nematic phase, requiring all of them to be positive. To describe the helix axis, it introduces an extra director field which becomes redundant for ordinary nematics. Putting together helical nematics with opposite helicities, we reconstruct a twist-bend nematic, for which the quadratic elastic energies of the two helical variants are combined in a non-convex energy.

cond-mat.soft↗