Levitation of non-magnetizable droplet inside ferrofluid

The central theme of this work is that a stable levitation of a denser non-magnetizable liquid droplet, against gravity, inside a relatively lighter ferrofluid -- a system barely considered in ferrohydrodynamics -- is possible, and exhibits unique interfacial features; the stability of the levitation trajectory, however, is subject to an appropriate magnetic field modulation. We explore the shapes and the temporal dynamics of a plane non-magnetizable droplet levitating inside ferrofluid against gravity due to a spatially complex, but systematically generated, magnetic field in two dimensions. The effect of the viscosity ratio, the stability of the levitation path and the possibility of existence of multiple-stable equilibrium states is investigated. We find, for certain conditions on the viscosity ratio, that there can be developments of cusps and singularities at the droplet surface; this phenomenon we also observe experimentally and compared with the simulations. Our simulations closely replicate the singular projection on the surface of the levitating droplet. Finally, we present an dynamical model for the vertical trajectory of the droplet. This model reveals a condition for the onset of levitation and the relation for the equilibrium levitation height. The linearization of the model around the steady state captures that the nature of the equilibrium point goes under a transition from being a spiral to a node depending upon the control parameters, which essentially means that the temporal route to the equilibrium can be either monotonic or undulating. The analytical model for the droplet trajectory is in close agreement with the detailed simulations. (See draft for full abstract).Comment: This article has been published in a revised form in Journal of Fluid Mechanics http://dx.doi.org/10.1017/jfm.2018.733. Copyright: copyright holde

Inner multipliers and Rudin type invariant subspaces

Let $\mathcal{E}$ be a Hilbert space and $H^2_{\mathcal{E}}(\mathbb{D})$ be the $\mathcal{E}$-valued Hardy space over the unit disc $\mathbb{D}$ in $\mathbb{C}$. The well known Beurling-Lax-Halmos theorem states that every shift invariant subspace of $H^2_{\mathcal{E}}(\mathbb{D})$ other than $\{0\}$ has the form $\Theta H^2_{\mathcal{E}_*}(\mathbb{D})$, where $\Theta$ is an operator-valued inner multiplier in $H^\infty_{B(\mathcal{E}_*, \mathcal{E})}(\mathbb{D})$ for some Hilbert space $\mathcal{E}_*$. In this paper we identify $H^2(\mathbb{D}^n)$ with $H^2(\mathbb{D}^{n-1})$-valued Hardy space $H^2_{H^2(\mathbb{D}^{n-1})}(\mathbb{D})$ and classify all such inner multiplier $\Theta \in H^\infty_{\mathcal{B}(H^2(\mathbb{D}^{n-1}))}(\mathbb{D})$ for which $\Theta H^2_{H^2(\mathbb{D}^{n-1})}(\mathbb{D})$ is a Rudin type invariant subspace of $H^2(\mathbb{D}^n)$.Comment: 8 page

Assessment of Personality Traits and Their Changes Over the Undergraduate Medical Course: A Pseudo-longitudinal Analysis among Indian Medical Students

Background: Personality of medical students have been shown to affect both their academic performance as well as their capabilities to develop rapport with patients, with evidence that they change through the medical course. This research aimed to explore the personality traits of undergraduate medical students and assess whether personality parameters changed throughout the medical education course. Methods: A pseudo-longitudinal design was utilized for this study. A total of 346 MBBS students studying in a Medical College of Eastern India were recruited at different stages of their coursework. These participants were similar in their sociodemographic makeup and differed only with respect to their year of MBBS study. The personality characteristics were assessed among these participants using the short-form revised Eysenck personality inventory. Results: The minimum possible score for each subscale was 0, and the maximum was 12. Mean scores of the participants for the extraversion, neuroticism, psychoticism, and lie scales were 6.17±3.09, 7.51±3.16, 3.40±1.61, and 4.98±2.48, respectively. Females scored significantly higher in neuroticism and lie dimensions. There were significant differences of psychoticism scores between rural and urban background participants. Significant negative trend was seen from the first to the final year of study in the extraversion dimension (Kendall’s tau =-0.094, p-value=0.025). Conclusion: Medical students in India scored high on the neuroticism and low on the psychoticism scales of personality with a trend of increasing extraversion over the years of their coursework