Orientational transitions in a nematic confined by competing surfaces

The effect of confinement on the orientational structure of a nematic liquid crystal model has been investigated by using a version of density-functional theory (DFT). We have focused on the case of a nematic confined by opposing flat surfaces, in slab geometry (slit pore), which favor planar molecular alignment (parallel to the surface) and homeotropic alignment (perpendicular to the surface), respectively. The spatial dependence of the tilt angle of the director with respect to the surface normal has been studied, as well as the tensorial order parameter describing the molecular order around the director. For a pore of given width, we find that, for weak surface fields, the alignment of the nematic director is perpendicular to the surface in a region next to the surface favoring homeotropic alignment, and parallel along the rest of the pore, with a interface separating these regions (S phase). For strong surface fields, the director is distorted uniformly, the tilt angle exhibiting a linear dependence with the distance normal to the surface (L phase). Our calculations reveal the existence of a first-order transition between the two director configurations, which is driven by changes in the surface field strength, and also by changes in the pore width. In the latter case the transition occurs, for a given surface field, between the S phase for narrow pores and the L phase for wider pores. A link between the L-S transition and the anchoring transition observed for the semi-infinite case is proposed. We also provide calculations with a phenomenological approach that yields the same main result that DFT in the scale length where this is valid.Comment: submitted to PR

Judgment Aggregation with Abstentions under Voters' Hierarchy

International audienceSimilar to Arrow’s impossibility theorem for preference aggregation, judgment aggregation has also an intrinsic impossibility for generating consistent group judgment from individual judgments. Removing some of the pre-assumed conditions would mitigate the problem but may still lead to too restrictive solutions. It was proved that if completeness is removed but other plausible conditions are kept, the only possible aggregation functions are oligarchic, which means that the group judgment is purely determined by a certain subset of participating judges. Instead of further challenging the other conditions, this paper investigates how the judgment from each individual judge affects the group judgment in an oligarchic environment. We explore a set of intuitively demanded conditions under abstentions and design a feasible judgment aggregation rule based on the agents’ hierarchy. We show this proposed aggregation rule satisfies the desirable conditions. More importantly, this rule is oligarchic with respect to a subset of agenda instead of the whole agenda due to its literal-based characteristics

Topological Defects and Interactions in Nematic Emulsions

Inverse nematic emulsions in which surfactant-coated water droplets are dispersed in a nematic host fluid have distinctive properties that set them apart from dispersions of two isotropic fluids or of nematic droplets in an isotropic fluid. We present a comprehensive theoretical study of the distortions produced in the nematic host by the dispersed droplets and of solvent mediated dipolar interactions between droplets that lead to their experimentally observed chaining. A single droplet in a nematic host acts like a macroscopic hedgehog defect. Global boundary conditions force the nucleation of compensating topological defects in the nematic host. Using variational techniques, we show that in the lowest energy configuration, a single water droplet draws a single hedgehog out of the nematic host to form a tightly bound dipole. Configurations in which the water droplet is encircled by a disclination ring have higher energy. The droplet-dipole induces distortions in the nematic host that lead to an effective dipole-dipole interaction between droplets and hence to chaining.Comment: 17 double column pages prepared by RevTex, 15 eps figures included in text, 2 gif figures for Fig. 1

A High Statistics Measurement of the Lambdac+ Lifetime

A high statistics measurement of the Lambdac+ lifetime from the Fermilab fixed-target FOCUS photoproduction experiment is presented. We describe the analysis technique with particular attention to the determination of the systematic uncertainty. The measured value of 204.6 +/- 3.4 (stat.) +/- 2.5 (syst.) fs from 8034 +/- 122 Lambdac -> pKpi decays represents a significant improvement over the present world average.Comment: Submitted to Physical Review Letter

Search for CP Violation in the decays D+ -> K_S pi+ and D+ -> K_S K+

A high statistics sample of photo-produced charm from the FOCUS(E831) experiment at Fermilab has been used to search for direct CP violation in the decays D+->K_S pi+ and D+ -> K_S K+. We have measured the following asymmetry parameters relative to D+->K-pi+pi+: A_CP(K_S pi+) = (-1.6 +/- 1.5 +/- 0.9)%, A_CP(K_S K+) = (+6.9 +/- 6.0 +/- 1.5)% and A_CP(K_S K+) = (+7.1 +/- 6.1 +/- 1.2)% relative to D+->K_S pi+. The first errors quoted are statistical and the second are systematic. We also measure the relative branching ratios: \Gamma(D+->\bar{K0}pi+)/\Gamma(D+->K-pi+pi+) = (30.60 +/- 0.46 +/- 0.32)%, \Gamma(D+->\bar{K0}K+)/\Gamma(D+->K-pi+pi+) = (6.04 +/- 0.35 +/- 0.30)% and \Gamma(D+->\bar{K0}K+)/\Gamma(D+->\bar{K0}pi+) = (19.96 +/- 1.19 +/- 0.96)%.Comment: 4 pages, 3 figure

A measurement of branching ratios of D+D^+ and Ds+D^+_s hadronic decays to four-body final states containing a KSK_S

We have studied hadronic four-body decays of $D^+$ and $D^+_s$ mesons with a $K_S$ in the final state using data recorded during the 1996-1997 fixed-target run at Fermilab high energy photoproduction experiment FOCUS. We report a new branching ratio measurement of $\Gamma(D^+\to K_S K^-\pi^+\pi^+)/\Gamma(D^+\to K_S \pi^+\pi^+\pi^-)=0.0768\pm0.0041\pm0.0032$. We make the first observation of three new decay modes with branching ratios $\Gamma(D^+\to K_S K^+\pi^+\pi^-)/\Gamma(D^+\to K_S \pi^+\pi^+\pi^-)=0.0562\pm0.0039\pm0.0040$, \Gamma(D^+\to\K_S K^+ K^-\pi^+)/\Gamma(D^+\to K_S \pi^+\pi^+\pi^-)=0.0077\pm0.0015\pm0.0009, and $\Gamma(D^+_s\to K_S K^+\pi^+\pi^-)/\Gamma(D^+_s\to K_S K^-\pi^+\pi^+)=0.586\pm0.052\pm0.043$, where in each case the first error is statistical and the second error is systematic.Comment: 4 pages, 1 table, 2 figures, submitted to Physical Review Letter

A Measurement of the Ds+ Lifetime

A high statistics measurement of the Ds+ lifetime from the Fermilab fixed-target FOCUS photoproduction experiment is presented. We describe the analysis of the two decay modes, Ds+ -> phi(1020)pi+ and Ds+ -> \bar{K}*(892)0K+, used for the measurement. The measured lifetime is 507.4 +/- 5.5 (stat.) +/- 5.1 (syst.) fs using 8961 +/- 105 Ds+ -> phi(1020)pi+ and 4680 +/- 90 Ds+ -> \bar{K}*(892)0K+ decays. This is a significant improvement over the present world average.Comment: 5 pages, 3 figures, 2 tables, submitted to PR

New FOCUS results on charm mixing and CP violation

We present a summary of recent results on CP violation and mixing in the charm quark sector based on a high statistics sample collected by photoproduction experiment FOCUS (E831 at Fermilab). We have measured the difference in lifetimes for the $D^0$ decays: $D^0 \to K^-\pi^+$ and $D^0 \to K^-K^+$. This translates into a measurement of the $y_{CP}$ mixing parameter in the \d0d0 system, under the assumptions that $K^-K^+$ is an equal mixture of CP odd and CP even eigenstates, and CP violation is negligible in the neutral charm meson system. We verified the latter assumption by searching for a CP violating asymmetry in the Cabibbo suppressed decay modes $D^+ \to K^-K^+\pi^+$, $D^0 \to K^-K^+$ and $D^0 \to \pi^-\pi^+$. We show preliminary results on a measurement of the branching ratio $\Gamma(D^{*+}\to \pi^+ (K^+\pi^-))/\Gamma(D^{*+}\to \pi^+ (K^-\pi^+))$.Comment: 9 pages, 6 figures, requires espcrc2.sty. Presented by S.Bianco at CPConf2000, September 2000, Ferrara (Italy). In this revision, fixed several stylistic flaws, add two significant references, fixed a typo in Tab.