Bulk and surface biaxiality in nematic liquid crystals

Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces. In this paper we show that any spatially-varying director pattern may be a source of biaxiality. We prove that biaxiality arises naturally whenever the symmetric tensor \Sb=(\grad \nn)(\grad \nn)^T possesses two distinct nonzero eigenvalues. The eigenvalue difference may be used as a measure of the expected biaxiality. Furthermore, the corresponding eigenvectors indicate the directions in which the order tensor \QQ is induced to break the uniaxial symmetry about the director \nn. We apply our general considerations to some examples. In particular we show that, when we enforce homeotropic anchoring on a curved surface, the order tensor become biaxial along the principal directions of the surface. The effect is triggered by the difference in surface principal curvatures

Impermeability effects in three-dimensional vesicles

We analyse the effects that the impermeability constraint induces on the equilibrium shapes of a three-dimensional vesicle hosting a rigid inclusion. A given alteration of the inclusion and/or vesicle parameters leads to shape modifications of different orders of magnitude, when applied to permeable or impermeable vesicles. Moreover, the enclosed-volume constraint wrecks the uniqueness of stationary equilibrium shapes, and gives rise to pear-shaped or stomatocyte-like vesicles.Comment: 16 pages, 7 figure

Replica Symmetry Breaking in the Random Replicant Model

We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica symmetry breaking and we compare our findings with accurate numerical simulations.Comment: 12 pages, TeX, 5 postscript figures are avalaible upon request, submitted to Journal of Physics A: Mathematical and Genera

Telephone-cord instabilities in thin smectic capillaries

Telephone-cord patterns have been recently observed in smectic liquid crystal capillaries. In this paper we analyse the effects that may induce them. As long as the capillary keeps its linear shape, we show that a nonzero chiral cholesteric pitch favors the SmA*-SmC* transition. However, neither the cholesteric pitch nor the presence of an intrinsic bending stress are able to give rise to a curved capillary shape. The key ingredient for the telephone-cord instability is spontaneous polarization. The free energy minimizer of a spontaneously polarized SmA* is attained on a planar capillary, characterized by a nonzero curvature. More interestingly, in the SmC* phase the combined effect of the molecular tilt and the spontaneous polarization pushes towards a helicoidal capillary shape, with nonzero curvature and torsion.Comment: Submitte

Special solutions in a generalized theory of nematics

Abstract: Using a model of a nematic liquid crystal which extends Ericksen’s and allows for biaxiality, we solve two simple problems for a slab of a nematic with strong anchoring conditions on the boundary planes. We show that, as the anchoring angle changes, a first-order transition between two solution types would be predicted on the basis of the Frank’s and Ericksen’s models, whereas, when biaxiality is allowed, the transition predicted is second-order, but with a non-smooth transition mode of the chevron type

Interface-mediated interactions: Entropic forces of curved membranes

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.Comment: 11 pages, 5 figures; final version, as appeared in Phys. Rev.

Fast Vertical Beam Instability in the CTF3 Combiner Ring

The CLIC Test Facility CTF3 is being built at CERN by an international collaboration, in order to demonstrate the main feasibility issues of the CLIC two-beam technology by 2010. The facility includes an 84 m combiner ring, which was installed and put into operation in 2007. High-current operation has shown a vertical beam break-up instability, leading to high beam losses over the four turns required for nominal operation of the CTF3 ring. Such instability is most likely due to the vertically polarized transverse mode in the RF deflectors used for beam injection and combination. In this paper we report the experimental data and compare them with simulations. Possible methods to eliminate the instability are also outlined

Experimental Studies on Drive Beam Generation in CTF3

The objective of the CLIC Test Facility CTF3, built at CERN by an international collaboration, is to demonstrate the main feasibility issues of the CLIC two-beam technology by 2010. CTF3 consists of a 150 MeV electron linac followed by a 42 m long delay loop, an 84 m combiner ring and a two-beam test area. One keyissue studied in CTF3 is the efficient generation of a very high current drive beam, used in CLIC as the power source for the acceleration of the main beam to multi-TeV energies. The beam current is first doubled in the delay loop and then multiplied again by a factor four in the combiner ring by interleaving bunches using transverse deflecting RF cavities. The combiner ring and the connecting transfer line have been installed and put into operation in 2007. In this paper we give the status of the commissioning, illustrate the beam optics measurements, discuss the main issues and present the results of the combination tests

Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random, Gaussian interactions of order p >= 2, and deterministic self-interactions u <= 0. We show that for nonzero u the effect of increasing the order of the interactions is to make the system more cooperative, in the sense that the fraction of extinct species is greatly reduced. Furthermore, we find that for p > 2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.Comment: 7 pages, 4 Postscript figure

Two-population replicator dynamics and number of Nash equilibria in random matrix games

We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed points of the dynamics and the Nash equilibria. Except for the special case of zero-sum games one finds a transition as a function of the so-called co-operation pressure between a phase in which there is a unique stable fixed point of the dynamics coinciding with a unique Nash equilibrium, and an unstable phase in which there are exponentially many Nash equilibria with statistical properties different from the stationary state of the replicator equations. Our analytical results are confirmed by numerical simulations of the replicator dynamics, and by explicit enumeration of Nash equilibria.Comment: 9 pages, 2x2 figure