706 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
Homogenization results for chemical reactive flows through porous media
This paper deals with the homogenization of a nonlinear problem mod-elllng chemica! reactive flows through periodically perforated domains. The chemical reactions take place on the walls of the porous médium. The effective behavior of these reactive flows is described by a new elliptic boundary-value problem contalning an extra zero-order term which captures the effect of the chemical reactions
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
On the Castelnuovo-Mumford regularity of subspace arrangements
Let be the union of generic linear subspaces of codimension in
. Improving an earlier bound due to Derksen and Sidman, we prove
that the Castelnuovo-Mumford regularity of satisfies .Comment: 21 page
Perceived Risk Reduction In E-commerce Environments
During the past three decades, the growth of e-commerce has presented marketers with many new arenas for research and application. Certainly e-commerce has become a significant portion of the world economy and in particular the consumer sector. As previous literature has consistently considered perceived risk as a major factor consumer purchase decisions, this research identifies several major components of consumer perceived risk (PR) and their normative implications in the e-commerce environmen
Asymptotics for models of non-stationary diffusion in domains with a surface distribution of obstacles
We consider a time-dependent model for the diffusion of a substance through an incompressible fluid in a perforated domain ??, urn:x-wiley:mma:media:mma5323:mma5323-math-0001 with n?=?3,4. The fluid flows in a domain containing a periodical set of ?obstacles? (?\??) placed along an inner (n???1)?dimensional manifold urn:x-wiley:mma:media:mma5323:mma5323-math-0002. The size of the obstacles is much smaller than the size of the characteristic period ?. An advection term appears in the partial differential equation linking the fluid velocity with the concentration, while we assume a nonlinear adsorption law on the boundary of the obstacles. This law involves a monotone nonlinear function ? of the concentration and a large adsorption parameter. The ?critical adsorption parameter? depends on the size of the obstacles , and, for different sizes, we derive the time?dependent homogenized models. These models contain a ?strange term? in the transmission conditions on ?, which is a nonlinear function and inherits the properties of ?. The case in which the fluid velocity and the concentration do not interact is also considered for n???3.The authors would like to thank the anonymous referees for their
careful reading of the manupscript and useful comments. The work has been partially
supported by MINECO, MTM2013-44883-P
Bloch Approximation in Homogenization and Applications
The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions of boundary value problems associated with such operators when the period of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as towards the homogenized solution was furnished using Bloch wave decomposition.
Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution . We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to capture the oscillations of the solution in a sharper way. The present approach sheds new light and offers an alternative for viewing classical results
On the symbolic powers of binomial edge ideals
We show that under some conditions, if the initial ideal in of an
ideal in a polynomial ring has the property that its symbolic and ordinary
powers coincide, then the ideal shares the same property. We apply this
result to prove the equality between symbolic and ordinary powers for binomial
edge ideals with quadratic Gr\"obner basis
A Model of Learning for Research in Information Systems Education
Educational researchers have long studied the role of the student in educational settings with the goal of improving learning outcomes. In this paper, we review constructs commonly employed in studies reported in the education literature undertaken to better understand how and why people learn. We then incorporate these constructs into a model of learning that we hope can be utilized as a starting point in further research in information systems education
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