178 research outputs found
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
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
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
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
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