410 research outputs found
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
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
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
Evolution of magnetic phases and orbital occupation in (SrMnO3)n/(LaMnO3)2n superlattices
The magnetic and electronic modifications induced at the interfaces in
(SrMnO)/(LaMnO) superlattices have been investigated
by linear and circular magnetic dichroism in the Mn L x-ray absorption
spectra. Together with theoretical calculations, our data demonstrate that the
charge redistribution across interfaces favors in-plane ferromagnetic (FM)
order and orbital occupation, in agreement with the
average strain. Far from interfaces, inside LaMnO, electron localization
and local strain favor antiferromagnetism (AFM) and
orbital occupation. For the high density of interfacial planes ultimately
leads to dominant FM order forcing the residual AFM phase to be in-plane too,
while for 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
Cancellation of vorticity in steady-state non-isentropic flows of complex fluids
In steady-state non-isentropic flows of perfect fluids there is always
thermodynamic generation of vorticity when the difference between the product
of the temperature with the gradient of the entropy and the gradient of total
enthalpy is different from zero. We note that this property does not hold in
general for complex fluids for which the prominent influence of the material
substructure on the gross motion may cancel the thermodynamic vorticity. We
indicate the explicit condition for this cancellation (topological transition
from vortex sheet to shear flow) for general complex fluids described by
coarse-grained order parameters and extended forms of Ginzburg-Landau energies.
As a prominent sample case we treat first Korteweg's fluid, used commonly as a
model of capillary motion or phase transitions characterized by diffused
interfaces. Then we discuss general complex fluids. We show also that, when the
entropy and the total enthalpy are constant throughout the flow, vorticity may
be generated by the inhomogeneous character of the distribution of material
substructures, and indicate the explicit condition for such a generation. We
discuss also some aspects of unsteady motion and show that in two-dimensional
flows of incompressible perfect complex fluids the vorticity is in general not
conserved, due to a mechanism of transfer of energy between different levels.Comment: 12 page
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
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
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
On the Clark-alpha model of turbulence: global regularity and long--time dynamics
In this paper we study a well-known three--dimensional turbulence model, the
filtered Clark model, or Clark-alpha model. This is Large Eddy Simulation (LES)
tensor-diffusivity model of turbulent flows with an additional spatial filter
of width alpha (). We show the global well-posedness of this model with
constant Navier-Stokes (eddy) viscosity. Moreover, we establish the existence
of a finite dimensional global attractor for this dissipative evolution system,
and we provide an anaytical estimate for its fractal and Hausdorff dimensions.
Our estimate is proportional to , where is the integral spatial
scale and is the viscous dissipation length scale. This explicit bound is
consistent with the physical estimate for the number of degrees of freedom
based on heuristic arguments. Using semi-rigorous physical arguments we show
that the inertial range of the energy spectrum for the Clark- model has
the usual Kolmogorov power law for wave numbers and
decay power law for This is evidence that the
Clark model parameterizes efficiently the large wave numbers within
the inertial range, , so that they contain much less translational
kinetic energy than their counterparts in the Navier-Stokes equations.Comment: 11 pages, no figures, submitted to J of Turbulenc
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