593 research outputs found
Destruction of the family of steady states in the planar problem of Darcy convection
The natural convection of incompressible fluid in a porous medium causes for
some boundary conditions a strong non-uniqueness in the form of a continuous
family of steady states. We are interested in the situation when these boundary
conditions are violated. The resulting destruction of the family of steady
states is studied via computer experiments based on a mimetic finite-difference
approach. Convection in a rectangular enclosure is considered under different
perturbations of boundary conditions (heat sources, infiltration). Two scenario
of the family of equilibria are found: the transformation to a limit cycle and
the formation of isolated convective patterns.Comment: 12 pages, 6 figure
Staggered grids discretization in three-dimensional Darcy convection
We consider three-dimensional convection of an incompressible fluid saturated
in a parallelepiped with a porous medium. A mimetic finite-difference scheme
for the Darcy convection problem in the primitive variables is developed. It
consists of staggered nonuniform grids with five types of nodes, differencing
and averaging operators on a two-nodes stencil. The nonlinear terms are
approximated using special schemes. Two problems with different boundary
conditions are considered to study scenarios of instability of the state of
rest. Branching off of a continuous family of steady states was detected for
the problem with zero heat fluxes on two opposite lateral planes.Comment: 20 pages, 9 figure
Qualitative versus quantitative data tools for sustainable package design at Eastman Kodak company
Due to the increased sustainability trends in the packaging industry during the last decade and a push from major retailers, in conjunction with the dire economic climate and internal reorganizations within the company, a need for an official design tool was born; a tool that would simplify, unify and improve the design process within the company. Following the creation of the original tool, the Packaging Development and Optimization Tool (PDOT), a critique arose that suggested an addition of LCA data, creating a more quantitatively based tool. A modified design process followed, the Sustainable Packaging Design Tool (SPDT), which utilized LCA data in addition to all other package specifications to recommend a design option with a minimal impact. This study compares the two different packaging design tools. It assumes that a quantitatively based design tool is superior to a qualitatively based tool. It suggests that a quantitative tool can reduce decision-making time, improve satisfaction with design decision and create consistency of results. The research was based on the study and survey of packaging engineers in the company
Properties of Gas Mixtures and Liquid Solutions from Infinite Dilution Studies
Chemical Engineerin
On the flow map for 2D Euler equations with unbounded vorticity
In Part I, we construct a class of examples of initial velocities for which
the unique solution to the Euler equations in the plane has an associated flow
map that lies in no Holder space of positive exponent for any positive time. In
Part II, we explore inverse problems that arise in attempting to construct an
example of an initial velocity producing an arbitrarily poor modulus of
continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio
The Vortex-Wave equation with a single vortex as the limit of the Euler equation
In this article we consider the physical justification of the Vortex-Wave
equation introduced by Marchioro and Pulvirenti in the case of a single point
vortex moving in an ambient vorticity. We consider a sequence of solutions for
the Euler equation in the plane corresponding to initial data consisting of an
ambient vorticity in and a sequence of concentrated blobs
which approach the Dirac distribution. We introduce a notion of a weak solution
of the Vortex-Wave equation in terms of velocity (or primitive variables) and
then show, for a subsequence of the blobs, the solutions of the Euler equation
converge in velocity to a weak solution of the Vortex-Wave equation.Comment: 24 pages, to appea
Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions
The paper is concerned with the vanishing viscosity limit of the
two-dimensional degenerate viscous lake equations when the Navier slip
conditions are prescribed on the impermeable boundary of a simply connected
bounded regular domain. When the initial vorticity is in the Lebesgue space
with , we show the degenerate viscous lake equations
possess a unique global solution and the solution converges to a corresponding
weak solution of the inviscid lake equations. In the special case when the
vorticity is in , an explicit convergence rate is obtained
Moser functions and fractional Moser-Trudinger type inequalities
We improve the sharpness of some fractional Moser-Trudinger type
inequalities, particularly those studied by Lam-Lu and Martinazzi. As an
application, improving upon works of Adimurthi and Lakkis, we prove the
existence of weak solutions to the problem with Dirichlet
boundary condition, for any domain in with finite
measure. Here is the first eigenvalue of on
On the 2D Isentropic Euler System with Unbounded Initial vorticity
37 pagesThis paper is devoted to the study of the low Mach number limit for the 2D isentropic Euler system associated to ill-prepared initial data with slow blow up rate on . We prove in particular the strong convergence to the solution of the incompressible Euler system when the vorticity belongs to some weighted spaces allowing unbounded functions. The proof is based on the extension of the result of \cite{B-K} to a compressible transport model
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