165 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
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
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
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.
Antibacterial Broad-Spectrum Dendritic/Gellan Gum Hybrid Hydrogels with Rapid Shape-Forming and Self-Healing for Wound Healing Application
Treating wound infections is a difficult task ever since pathogenic bacteria started to develop resistance to common antibiotics. The present study develops hybrid hydrogels based on the formation of a polyelectrolyte complex between the anionic charges of dopamine-functionalized Gellan Gum (GG-DA) and the cationic moieties of the TMP-G2-alanine dendrimer. The hydrogels thus obtained can be doubly crosslinked with CaCl2, obtaining solid hydrogels. Or, by oxidizing dopamine to GG-DA, possibly causing further interactions such as Schiff Base and Michael addition to take place, hydrogels called injectables can be obtained. The latter have shear-thinning and self-healing properties (efficiency up to 100%). Human dermal fibroblasts (HDF), human epidermal keratinocytes (HaCaT), and mouse monocyte cells (RAW 264.7), after incubation with hydrogels, in most cases show cell viability up to 100%. Hydrogels exhibit adhesive behavior on various substrates, including porcine skin. At the same time, the dendrimer serves to crosslink the hydrogels and endows them with excellent broad-spectrum microbial eradication activity within four hours, evaluated using Staphylococcus aureus 2569 and Escherichia coli 178. Using the same GG-DA/TMP-G2-alanine ratios hybrid hydrogels with tunable properties and potential for wound dressing applications can be produced
Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
In this work we analyse the Parisi's infinity-replica symmetry breaking
solution of the Sherrington - Kirkpatrick model without external field using
high order perturbative expansions. The predictions are compared with those
obtained from the numerical solution of the infinity-replica symmetry breaking
equations which are solved using a new pseudo-spectral code which allows for
very accurate results. With this methods we are able to get more insight into
the analytical properties of the solutions. We are also able to determine
numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T
--> 0} x_{max}(T) > 0.5.Comment: 15 pages, 11 figures, RevTeX 4.
Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional -Vector Model for
We have computed the four-loop contribution to the beta-function and to the
anomalous dimension of the field for the two-dimensional lattice -vector
model. This allows the determination of the second perturbative correction to
various long-distance quantities like the correlation lengths and the
susceptibilities. We compare these predictions with new Monte Carlo data for . From these data we also extract the values of various universal
nonperturbative constants, which we compare with the predictions of the
expansion.Comment: 68456 bytes uuencoded gzip'ed (expands to 155611 bytes Postscript); 4
pages including all figures; contribution to Lattice '9
Random replicators with asymmetric couplings
Systems of interacting random replicators are studied using generating
functional techniques. While replica analyses of such models are limited to
systems with symmetric couplings, dynamical approaches as presented here allow
specifically to address cases with asymmetric interactions where there is no
Lyapunov function governing the dynamics. We here focus on replicator models
with Gaussian couplings of general symmetry between p>=2 species, and discuss
how an effective description of the dynamics can be derived in terms of a
single-species process. Upon making a fixed point ansatz persistent order
parameters in the ergodic stationary states can be extracted from this process,
and different types of phase transitions can be identified and related to each
other. We discuss the effects of asymmetry in the couplings on the order
parameters and the phase behaviour for p=2 and p=3. Numerical simulations
verify our theory. For the case of cubic interactions numerical experiments
indicate regimes in which only a finite number of species survives, even when
the thermodynamic limit is considered.Comment: revised version, removed some mathematical parts, discussion of
negatively correlated couplings added, figures adde
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