Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane

We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of $u_\infty$. Furthermore a spacial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the directino of the flow as \emph{time} direction. The analysis is done in framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modeled by elliptic equations

Asymptotic expansion of the solution of the steady Stokes equation with variable viscosity in a two-dimensional tube structure

The Stokes equation with the varying viscosity is considered in a thin tube structure, i.e. in a connected union of thin rectangles with heights of order $\varepsilon<<1$ and with bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed: it contains some Poiseuille type flows in the channels (rectangles) with some boundary layers correctors in the neighborhoods of the bifurcations of the channels. The estimates for the difference of the exact solution and its asymptotic approximation are proved.Comment: 22 pages, 20 figure

Oscillation dynamics of embolic microspheres in flows with red blood cell suspensions

Dynamic nature of particle motion in blood flow is an important determinant of embolization based cancer therapy. Yet, the manner in which the presence of high volume fraction of red blood cells influences the particle dynamics remains unknown. Here, by investigating the motions of embolic microspheres in pressure-driven flows of red blood cell suspensions through capillaries, we illustrate unique oscillatory trends in particle trajectories, which are not observable in Newtonian fluid flows. Our investigation reveals that such oscillatory behavior essentially manifests when three simultaneous conditions, namely, the Reynolds number beyond a threshold limit, degree of confinement beyond a critical limit, and high hematocrit level, are fulfilled simultaneously. Given that these conditions are extremely relevant to fluid dynamics of blood or polymer flow, the observations reported here bear significant implications on embolization based cancer treatment as well as for complex multiphase fluidics involving particle

Liouville theorems in unbounded domains for the time-dependent Stokes system

In this paper, We characterize bounded ancient solutions to the time-dependent Stokes system with zero boundary value in various domains, including the half space.Comment: 11 pages; final versio

Evaluation of fiber-optic phase-gradient meta-tips for sensing applications

Recently, within the emerging framework of "lab-on-fiber" technologies, we successfully demonstrated the integration of phase-gradient plasmonic metasurfaces on the tip of an optical fiber. The res..

Mode Confinement in Photonic Quasi-Crystal Point-Defect Cavities for Particle Accelerators

In this Letter, we present a study of the confinement properties of point-defect resonators in finite-size photonic-bandgap structures composed of aperiodic arrangements of dielectric rods, with special emphasis on their use for the design of cavities for particle accelerators. Specifically, for representative geometries, we study the properties of the fundamental mode (as a function of the filling fraction, structure size, and losses) via 2-D and 3-D full-wave numerical simulations, as well as microwave measurements at room temperature. Results indicate that, for reduced-size structures, aperiodic geometries exhibit superior confinement properties by comparison with periodic ones.Comment: 4 pages, 4 figures, accepted for publication in Applied Physics Letter

Multiple double-exchange mechanism by Mn2+^{2+}-doping in manganite compounds

Double-exchange mechanisms in RE$_{1-x}$AE$_{x}$MnO$_{3}$ manganites (where RE is a trivalent rare-earth ion and AE is a divalent alkali-earth ion) relies on the strong exchange interaction between two Mn$^{3+}$ and Mn$^{4+}$ ions through interfiling oxygen 2p states. Nevertheless, the role of RE and AE ions has ever been considered "silent" with respect to the DE conducting mechanisms. Here we show that a new path for DE-mechanism is indeed possible by partially replacing the RE-AE elements by Mn$^{2+}$-ions, in La-deficient La$_{x}$MnO$_{3-\delta}$ thin films. X-ray absorption spectroscopy demonstrated the relevant presence of Mn$^{2+}$ ions, which is unambiguously proved to be substituted at La-site by Resonant Inelastic X-ray Scattering. Mn$^{2+}$ is proved to be directly correlated to the enhanced magneto-transport properties because of an additional hopping mechanism trough interfiling Mn$^{2+}$-ions, theoretically confirmed by calculations within the effective single band model. The very idea to use Mn$^{2+}$ both as a doping element and an ions electronically involved in the conduction mechanism, has never been foreseen, revealing a new phenomena in transport properties of manganites. More important, such a strategy might be also pursed in other strongly correlated materials.Comment: 6 pages, 5 figure

Evolution of magnetic phases and orbital occupation in (SrMnO3)n/(LaMnO3)2n superlattices

The magnetic and electronic modifications induced at the interfaces in (SrMnO$_{3}$)$_{n}$/(LaMnO$_{3}$)$_{2n}$ superlattices have been investigated by linear and circular magnetic dichroism in the Mn L$_{2,3}$ x-ray absorption spectra. Together with theoretical calculations, our data demonstrate that the charge redistribution across interfaces favors in-plane ferromagnetic (FM) order and $e_{g}(x^{2}-y^{2})$ orbital occupation, in agreement with the average strain. Far from interfaces, inside LaMnO$_3$, electron localization and local strain favor antiferromagnetism (AFM) and $e_{g}(3z^{2}-r^{2})$ orbital occupation. For $n=1$ the high density of interfacial planes ultimately leads to dominant FM order forcing the residual AFM phase to be in-plane too, while for $n \geq 5$ the FM layers are separated by AFM regions having out-of-plane spin orientation.Comment: accepted for publication as a Rapid Communication in Physical Review