592 research outputs found
Nonlinear Effects in the TGB_A Phase
We study the nonlinear interactions in the TGB_A phase by using a
rotationally invariant elastic free energy. By deforming a single grain
boundary so that the smectic layers undergo their rotation within a finite
interval, we construct a consistent three-dimensional structure. With this
structure we study the energetics and predict the ratio between the intragrain
and intergrain defect spacing, and compare our results with those from linear
elasticity and experiment.Comment: 4 pages, RevTeX, 2 included eps figure
Optimal antiviral treatment strategies and the effects of resistance
Recent pandemic planning has highlighted the importance of understanding the effect that widespread antiviral use will have on the emergence and spread of resistance. A number of recent studies have determined that if resistance to antiviral medication can evolve, then deploying treatment at a less than maximum rate often minimizes the outbreak size. This finding, however, involves the assumption that treatment levels remain constant during the entire outbreak. Using optimal control theory, we address the question of optimal antiviral use by considering a large class of time-varying treatment strategies. We prove that, contrary to previous results, it is always optimal to treat at the maximum rate provided that this treatment occurs at the right time. In general the optimal strategy is to wait some fixed amount of time and then to deploy treatment at the maximum rate for the remainder of the outbreak. We derive analytical conditions that characterize this optimal amount of delay. Our results show that it is optimal to start treatment immediately when one of the following conditions holds: (i) immediate treatment can prevent an outbreak, (ii) the initial pool of susceptibles is small, or (iii) when the maximum possible rate of treatment is low, such that there is little de novo emergence of resistant strains. Finally, we use numerical simulations to verify that the results also hold under more general conditions
Boundary Effects in Chiral Polymer Hexatics
Boundary effects in liquid-crystalline phases can be large due to long-ranged
orientational correlations. We show that the chiral hexatic phase can be locked
into an apparent three-dimensional N+6 phase via such effects. Simple numerical
estimates suggest that the recently discovered "polymer hexatic" may actually
be this locked phase.Comment: 4 pages, RevTex, 3 included eps figure
Topological defects and shape of aromatic self-assembled vesicles
We show that the stacking of flat aromatic molecules on a curved surface
results in topological defects. We consider, as an example, spherical vesicles,
self-assembled from molecules with 5- and 6-thiophene cores. We predict that
the symmetry of the molecules influences the number of topological defects and
the resulting equilibrium shape.Comment: accepted as a Letter in the J. Phys. Chem.
A generalized Tullock contest
We construct a generalized Tullock contest under complete information where contingent upon winning or losing, the payoff of a player is a linear function of prizes, own effort, and the effort of the rival. This structure nests a number of existing contests in the literature and can be used to analyze new types of contests. We characterize the unique symmetric equilibrium and show that small parameter modifications may lead to substantially different types of contests and hence different equilibrium effort levels
Order and Frustration in Chiral Liquid Crystals
This paper reviews the complex ordered structures induced by chirality in
liquid crystals. In general, chirality favors a twist in the orientation of
liquid-crystal molecules. In some cases, as in the cholesteric phase, this
favored twist can be achieved without any defects. More often, the favored
twist competes with applied electric or magnetic fields or with geometric
constraints, leading to frustration. In response to this frustration, the
system develops ordered structures with periodic arrays of defects. The
simplest example of such a structure is the lattice of domains and domain walls
in a cholesteric phase under a magnetic field. More complex examples include
defect structures formed in two-dimensional films of chiral liquid crystals.
The same considerations of chirality and defects apply to three-dimensional
structures, such as the twist-grain-boundary and moire phases.Comment: 39 pages, RevTeX, 14 included eps figure
Structures and orientational transitions in thin films of tilted hexatic smectics
We present detailed systematic studies of structural transformations in thin
liquid crystal films with the smectic-C to hexatic phase transition. For the
first time all possible structures reported in the literature are observed for
one material (5 O.6) at the variation of temperature and thickness. In unusual
modulated structures the equilibrium period of stripes is twice with respect to
the domain size. We interpret these patterns in the frame work of
phenomenological Landau type theory, as equilibrium phenomena produced by a
natural geometric frustration in a system having spontaneous splay distortion.Comment: 7 pages, 6 figure
- …