290 research outputs found
Detection of a Moving Rigid Solid in a Perfect Fluid
In this paper, we consider a moving rigid solid immersed in a potential
fluid. The fluid-solid system fills the whole two dimensional space and the
fluid is assumed to be at rest at infinity. Our aim is to study the inverse
problem, initially introduced in [3], that consists in recovering the position
and the velocity of the solid assuming that the potential function is known at
a given time. We show that this problem is in general ill-posed by providing
counterexamples for which the same potential corresponds to different positions
and velocities of a same solid. However, it is also possible to find solids
having a specific shape, like ellipses for instance, for which the problem of
detection admits a unique solution. Using complex analysis, we prove that the
well-posedness of the inverse problem is equivalent to the solvability of an
infinite set of nonlinear equations. This result allows us to show that when
the solid enjoys some symmetry properties, it can be partially detected.
Besides, for any solid, the velocity can always be recovered when both the
potential function and the position are supposed to be known. Finally, we prove
that by performing continuous measurements of the fluid potential over a time
interval, we can always track the position of the solid.Comment: 19 pages, 14 figure
Linear resolutions of powers and products
The goal of this paper is to present examples of families of homogeneous
ideals in the polynomial ring over a field that satisfy the following
condition: every product of ideals of the family has a linear free resolution.
As we will see, this condition is strongly correlated to good primary
decompositions of the products and good homological and arithmetical properties
of the associated multi-Rees algebras. The following families will be discussed
in detail: polymatroidal ideals, ideals generated by linear forms and Borel
fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi
deformation
Absolutely Koszul algebras and the Backelin-Roos property
We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos
property and their behavior under standard algebraic operations. In particular,
we identify some Veronese subrings of polynomial rings that have the
Backelin-Roos property and conjecture that the list is indeed complete. Among
other things, we prove that every universally Koszul ring defined by monomials
has the Backelin-Roos property
Epitaxial Co2Cr0.6Fe0.4Al thin films and magnetic tunneling junctions
Epitaxial thin films of the theoretically predicted half metal
Co2Cr0.6Fe0.4Al were deposited by dc magnetron sputtering on different
substrates and buffer layers. The samples were characterized by x-ray and
electron beam diffraction (RHEED) demonstrating the B2 order of the Heusler
compound with only a small partition of disorder on the Co sites. Magnetic
tunneling junctions with Co2Cr0.6Fe0.4Al electrode, AlOx barrier and Co counter
electrode were prepared. From the Julliere model a spin polarisation of
Co2Cr0.6Fe0.4Al of 54% at T=4K is deduced. The relation between the annealing
temperature of the Heusler electrodes and the magnitude of the tunneling
magnetoresistance effect was investigated and the results are discussed in the
framework of morphology and surface order based of in situ STM and RHEED
investigations.Comment: accepted by J. Phys. D: Appl. Phy
Effective pressure interface law for transport phenomena between an unconfined fluid and a porous medium using homogenization
We present modeling of the incompressible viscous flows in the domain
containing an unconfined fluid and a porous medium. For such setting a rigorous
derivation of the Beavers-Joseph-Saffman interface condition was undertaken by
J\"ager and Mikeli\'c [SIAM J. Appl. Math. \rm 60 (2000), p. 1111-1127] using
the homogenization method. So far the interface law for the pressure was
conceived and confirmed only numerically. In this article we justify rigorously
the pressure jump condition using the corresponding boundary layer
Powers of componentwise linear ideals
We give criteria for graded ideals to have the property that all their powers
are componentwise linear. Typical examples to which our criteria can be applied
include the vertex cover ideals of certain finite graphs
Deterministically Computing Reduction Numbers of Polynomial Ideals
We discuss the problem of determining reduction number of a polynomial ideal
I in n variables. We present two algorithms based on parametric computations.
The first one determines the absolute reduction number of I and requires
computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I)
variables. The second one computes via a Grobner system the set of all
reduction numbers of the ideal I and thus in particular also its big reduction
number. However,it requires computations in a ring with n.dim(I) parameters and
n variables.Comment: This new version replaces the earlier version arXiv:1404.1721 and it
has been accepted for publication in the proceedings of CASC 2014, Warsaw,
Polna
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Optimized patient transfer using an innovative multidisciplinary assessment in the Kanton Aargau (OPTIMA I): an observational survey in lower respiratory tract infections
BACKGROUND: Current medical scores have limited efficiency and safety profiles to enable assignment to the most appropriate treatment site in patients with lower respiratory tract infections (LRTIs). We describe our current triage practice and assess the potential of a combination of CURB65 with proadrenomedullin (ProADM) levels for triage decisions. METHODS: Consecutive patients with LRTIs presenting to our emergency department were prospectively followed and retrospectively classified according to CURB65 and ProADM levels (CURB65-A). Low medical risk patients were further subgrouped according to biopsychosocial and functional risks. We compared the proportion of patients virtually allocated to triage sites with actual triage decisions and assessed the added impact of ProADM in a subgroup. RESULTS: Overall, 93% of 146 patients were hospitalised. Among the 138 patients with available CURB65-A, 17.4% had a low medical risk indicating possible treatment in an outpatient or non-acute medical setting; 34.1% had an intermediate medical risk (short-hospitalisation); and 48.6% had a high medical risk (hospitalisation). Fewer patients were in a low CURB65-A class (I) than a low CURB65 class (0,1) (17.4% vs. 46.3%, p >0.001). Mean length of hospitalisation was 9.8 days including 3.6 days after reaching medical stability. In 60.3% of patients, hospitalisation was prolonged after medical stability mainly for medical reasons. CONCLUSIONS: Current rates of hospitalisation are high in patients with LRTI and length of stay frequently extended beyond time of medical stabilization. The lower proportion of patients reclassified as low risk by adding ProADM to the CURB65 score might improve confidence in the triage algorithm
A Kato type Theorem for the inviscid limit of the Navier-Stokes equations with a moving rigid body
The issue of the inviscid limit for the incompressible Navier-Stokes
equations when a no-slip condition is prescribed on the boundary is a famous
open problem. A result by Tosio Kato says that convergence to the Euler
equations holds true in the energy space if and only if the energy dissipation
rate of the viscous flow in a boundary layer of width proportional to the
viscosity vanishes. Of course, if one considers the motion of a solid body in
an incompressible fluid, with a no-slip condition at the interface, the issue
of the inviscid limit is as least as difficult. However it is not clear if the
additional difficulties linked to the body's dynamic make this issue more
difficult or not. In this paper we consider the motion of a rigid body in an
incompressible fluid occupying the complementary set in the space and we prove
that a Kato type condition implies the convergence of the fluid velocity and of
the body velocity as well, what seems to indicate that an answer in the case of
a fixed boundary could also bring an answer to the case where there is a moving
body in the fluid
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