Surface, size and topological effects for some nematic equilibria on rectangular domains

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, [Formula: see text], which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the [Formula: see text] 0 limit relevant for macroscopic domains and the [Formula: see text] limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the [Formula: see text] limit, whereas we observe fractional point defects in the [Formula: see text] 0 limit. The analytical studies are complemented by some bifurcation diagrams for these reduced equilibria as a function of [Formula: see text] and the rectangular aspect ratio. We also introduce the concept of ‘non-trivial’ topologies and study the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics.

Revisiting the Privacy Paradox on Social Media With an Extended Privacy Calculus Model: The Effect of Privacy Concerns, Privacy Self-Efficacy, and Social Capital on Privacy Management

This study builds on the privacy calculus model to revisit the privacy paradox on social media. A two-wave panel data set from Hong Kong and a cross-sectional data set from the United States are used. This study extends the model by incorporating privacy self-efficacy as another privacy-related factor in addition to privacy concerns (i.e., costs) and examines how these factors interact with social capital (i.e., the expected benefit) in influencing different privacy management strategies, including limiting profile visibility, self-disclosure, and friending. This study proposed and found a two-step privacy management strategy in which privacy concerns and privacy self-efficacy prompt users to limit their profile visibility, which in turn enhances their self-disclosing and friending behaviors in both Hong Kong and the United States. Results from the moderated mediation analyses further demonstrate that social capital strengthens the positive–direct effect of privacy self-efficacy on self-disclosure in both places, and it can mitigate the direct effect of privacy concerns on restricting self-disclosure in Hong Kong (the conditional direct effects). Social capital also enhances the indirect effect of privacy self-efficacy on both self-disclosure and friending through limiting profile visibility in Hong Kong (the conditional indirect effects). Implications of the findings are discussed.

LIMITING PROFILE OF AXISYMMETRIC INDENTER DUE TO THE INITIALLY DISPLACED DUAL-MOTION FRETTING WEAR

Recently the final worn shape of elastic indenters due to fretting wear was analytically solved using the method of dimensionality reduction. In this paper we extend this model to dual-motion fretting wear and take into account that the indenter is initially pressed with constant indentation depth and moved horizontally with constant displacement. Two key parameters, the maximal indentation depth during oscillation and the stick area radius in the final state as well as the liming shape of indenter are analytically calculated. It is shown that the oscillation amplitudes and the initially indented or moved displacements have an influence on the final shaking-down shape.

Solitary waves on a ferrofluid jet

The propagation of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet subjected to a magnetic field is investigated. An azimuthal magnetic field is generated by an electric current flowing along a stationary metal rod which is mounted along the axis of the moving jet. A numerical method is used to compute fully nonlinear travelling solitary waves, and the predictions of elevation waves and depression waves made by Rannacher and Engel (New J. Phys., vol. 8, 2006, pp. 108–123) using a weakly nonlinear theory are confirmed in the appropriate ranges of the magnetic Bond number. New nonlinear branches of solitary wave solutions are identified. As the Bond number is varied, the solitary wave profiles may approach a limiting configuration with a trapped toroidal-shaped bubble, or they may approach a static wave (i.e. one with zero phase speed). For a sufficiently large axial rod, the limiting profile may exhibit a cusp.