ABSTRACT
We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.
ABSTRACT
Background: A growing evidence base supports the value of peer recovery support specialists (PRSS), particularly due to shared lived experience with participants (recipients of PRSS services). However, little research has examined whether congruence on certain aspects of "peerness" (e.g., demographics, experiences) matters for PRSS-participant relationships. Methods: Through a pilot study under the NIDA-funded Initiative for Justice and Emerging Adult Populations (JEAP), adults who had recently received PRSS services (N=100) were interviewed. Participants completed a modified version of the Scales for Participant Alliance with Recovery Coach (SPARC), a measure of PRSS-participant relationship quality, and rated themselves as different/similar to their PRSS in several domains using a six-point scale. Results: Participants had met with their PRSS for a median of 10 sessions over two months. SPARC scores were unrelated to participant demographics or lived experiences. However, better-quality relationships were reported by participants who believed their PRSS was similar to them in relationships with family (p=.004), spirituality/religion (p=.001), age (p<.001), and overall recovery pathway (p<.001). Total SPARC scores were not significantly correlated with perceived PRSS-participant similarities on gender, race/ethnicity, substances of choice, and history of incarceration or substance use treatment. Discussion: Results from this pilot study suggest that PRSS-participant alignment on past experiences (e.g., prior incarceration, choice of drugs) may not be needed to establish good-quality working relationships. However, similarities on factors related to current life stage (e.g., age, family relationships) and/or recovery process (e.g., overall pathway, spirituality) may be more important. Future research should employ mixed-methods approaches to elucidate these unique findings.