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

Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological non-equilibrium thermodynamics for a general non-isothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analysed.Comment: Submitted to Physics of Fluid

Charge density waves enhance the electronic noise of manganites

The transport and noise properties of Pr_{0.7}Ca_{0.3}MnO_{3} epitaxial thin films in the temperature range from room temperature to 160 K are reported. It is shown that both the broadband 1/f noise properties and the dependence of resistance on electric field are consistent with the idea of a collective electrical transport, as in the classical model of sliding charge density waves. On the other hand, the observations cannot be reconciled with standard models of charge ordering and charge melting. Methodologically, it is proposed to consider noise-spectra analysis as a unique tool for the identification of the transport mechanism in such highly correlated systems. On the basis of the results, the electrical transport is envisaged as one of the most effective ways to understand the nature of the insulating, charge-modulated ground states in manganites.Comment: 6 two-column pages, 5 figure

Analytical Study of Sub-Wavelength Imaging by Uniaxial Epsilon-Near-Zero Metamaterial Slabs

We discuss the imaging properties of uniaxial epsilon-near-zero metamaterial slabs with possibly tilted optical axis, analyzing their sub-wavelength focusing properties as a function of the design parameters. We derive in closed analytical form the associated two-dimensional Green's function in terms of special cylindrical functions. For the near-field parameter ranges of interest, we are also able to derive a small-argument approximation in terms of simpler analytical functions. Our results, validated and calibrated against a full-wave reference solution, expand the analytical tools available for computationally-efficient and physically-incisive modeling and design of metamaterial-based sub-wavelength imaging systems.Comment: 25 pages, 9 figures (modifications in the text; two figures and several references added

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

Share option awards: SFAS 123 revised

Different kinds of awards have been developed to stimulate employers to focus on the maximization of the fi rm value. To reach this target, entities use share-based payment in exchange for the employee services they receive. However, the utilization of these instruments results in controversial questions for Accounting. Should equity awards be recognized as expenses? Is a share option award (issued to pay for employee services) a liability or an equity instrument? What method should be used to measure the value of this instrument? What period of time should be considered to account for this kind of transaction? In order to establish accounting standards for transactions in which an entity exchanges its equity instruments for services, the FASB recently released SFAS 123 revised. This paper discusses share-based payment issues, concentrating on employee share options, and aims to review and analyze the conceptual framework of SFAS 123 revised. It presents the historical evolution of controversial regulations about this theme, discusses the main concepts issued by SFAS 123 revised and addresses FASB's argumentation about the theoretical background of this standard.Diferentes mecanismos de remuneração têm sido desenvolvidos com o intuito de estimular os empregados a agir com foco na maximização do valor da firma. Uma das maneiras utilizadas pelas empresas na busca desse objetivo é a remuneração vinculada à entrega de ações ou opções de ações da empresa para os empregados (chamada genericamente de remuneração baseada em ações) em troca de seus serviços. Contudo, a utilização desse instrumento acarreta algumas questões controversas para a Contabilidade. Esse tipo de remuneração deve ser reconhecido como despesa? Opções de compra lançadas pela empresa para a remuneração de seus funcionários representam um passivo ou um item do patrimônio líquido? Por qual valor deve ser mensurado esse tipo de remuneração? E qual o período que deve ser considerado para a contabilização? No intuito de regulamentar o assunto, o FASB emitiu o SFAS 123 revisado. Este trabalho aborda os temas relacionados com a remuneração baseada em ações, concentrando-se na remuneração com opções de ações, e objetiva expor e analisar o arcabouço conceitual do SFAS 123 revisado. Para isso apresenta a evolução histórica da controversa normatização do tema, discorre sobre os principais conceitos emanados do SFAS 123 revisado e aborda a argumentação utilizada pelo FASB para o embasamento teórico da norma

Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in half-plane

We investigate the Navier-Stokes initial boundary value problem in the half-plane $R^2_+$ with initial data $u_0 \in L^\infty(R^2_+)\cap J_0^2(R^2_+)$ or with non decaying initial data $u_0\in L^\infty(R^2_+) \cap J_0^p(R^2_+), p > 2$ . We introduce a technique that allows to solve the two-dimesional problem, further, but not least, it can be also employed to obtain weak solutions, as regards the non decaying initial data, to the three-dimensional Navier-Stokes IBVP. This last result is the first of its kind

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

Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy

Homogenization of oxygen transport in biological tissues

In this paper, we extend previous work on the mathematical modeling of oxygen transport in biological tissues (Matzavinos et al., 2009). Specifically, we include in the modeling process the arterial and venous microstructure within the tissue by means of homogenization techniques. We focus on the two-layer tissue architecture investigated in (Matzavinos et al., 2009) in the context of abdominal tissue flaps that are commonly used for reconstructive surgery. We apply two-scale convergence methods and unfolding operator techniques to homogenize the developed microscopic model, which involves different unit-cell geometries in the two distinct tissue layers (skin layer and fat tissue) to account for different arterial branching patterns