526 research outputs found
On the 3D steady flow of a second grade fluid past an obstacle
We study steady flow of a second grade fluid past an obstacle in three space
dimensions. We prove existence of solution in weighted Lebesgue spaces with
anisotropic weights and thus existence of the wake region behind the obstacle.
We use properties of the fundamental Oseen tensor together with results
achieved in \cite{Koch} and properties of solutions to steady transport
equation to get up to arbitrarily small \ep the same decay as the Oseen
fundamental solution
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
at infinity. The main result shows the existence of unique solutions for
arbitrary force, provided sufficient largeness of . 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
Rejection Properties of Stochastic-Resonance-Based Detectors of Weak Harmonic Signals
In (V. Galdi et al., Phys. Rev. E57, 6470, 1998) a thorough characterization
in terms of receiver operating characteristics (ROCs) of stochastic-resonance
(SR) detectors of weak harmonic signals of known frequency in additive gaussian
noise was given. It was shown that strobed sign-counting based strategies can
be used to achieve a nice trade-off between performance and cost, by comparison
with non-coherent correlators. Here we discuss the more realistic case where
besides the sought signal (whose frequency is assumed known) further unwanted
spectrally nearby signals with comparable amplitude are present. Rejection
properties are discussed in terms of suitably defined false-alarm and
false-dismissal probabilities for various values of interfering signal(s)
strength and spectral separation.Comment: 4 pages, 5 figures. Misprints corrected. PACS numbers added. RevTeX
Very weak solutions and large uniqueness classes of stationary NavierâStokes equations in bounded domains of R2
AbstractExtending the notion of very weak solutions, developed recently in the three-dimensional case, to bounded domains ΩâR2 we obtain a new class of unique solutions u in Lq(Ω), q>2, to the stationary NavierâStokes system âÎu+uâ
âu+âp=f, divu=k, u|âΩ=g with data f,k,g of low regularity. As a main consequence we obtain a new uniqueness class also for classical weak or strong solutions. Indeed, such a solution is unique if its Lq-norm is sufficiently small or the data satisfy the uniqueness condition of a very weak solution
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
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
Microwave apparatus for gravitational waves observation
In this report the theoretical and experimental activities for the
development of superconducting microwave cavities for the detection of
gravitational waves are presented.Comment: 42 pages, 28 figure
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
A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions
Stents are medical devices designed to modify blood flow in aneurysm sacs, in
order to prevent their rupture. Some of them can be considered as a locally
periodic rough boundary. In order to approximate blood flow in arteries and
vessels of the cardio-vascular system containing stents, we use multi-scale
techniques to construct boundary layers and wall laws. Simplifying the flow we
turn to consider a 2-dimensional Poisson problem that conserves essential
features related to the rough boundary. Then, we investigate convergence of
boundary layer approximations and the corresponding wall laws in the case of
Neumann type boundary conditions at the inlet and outlet parts of the domain.
The difficulty comes from the fact that correctors, for the boundary layers
near the rough surface, may introduce error terms on the other portions of the
boundary. In order to correct these spurious oscillations, we introduce a
vertical boundary layer. Trough a careful study of its behavior, we prove
rigorously decay estimates. We then construct complete boundary layers that
respect the macroscopic boundary conditions. We also derive error estimates in
terms of the roughness size epsilon either for the full boundary layer
approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda
Multiple double-exchange mechanism by Mn-doping in manganite compounds
Double-exchange mechanisms in REAEMnO 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 and Mn 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-ions, in La-deficient
LaMnO thin films. X-ray absorption spectroscopy demonstrated
the relevant presence of Mn ions, which is unambiguously proved to be
substituted at La-site by Resonant Inelastic X-ray Scattering. Mn is
proved to be directly correlated to the enhanced magneto-transport properties
because of an additional hopping mechanism trough interfiling Mn-ions,
theoretically confirmed by calculations within the effective single band model.
The very idea to use Mn 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
Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals
The equations for the three-dimensional incompressible flow of liquid
crystals are considered in a smooth bounded domain. The existence and
uniqueness of the global strong solution with small initial data are
established. It is also proved that when the strong solution exists, all the
global weak solutions constructed in [16] must be equal to the unique strong
solution
- âŠ