9,072 research outputs found
Coherent Presentations of Monoidal Categories
Presentations of categories are a well-known algebraic tool to provide
descriptions of categories by means of generators, for objects and morphisms,
and relations on morphisms. We generalize here this notion, in order to
consider situations where the objects are considered modulo an equivalence
relation, which is described by equational generators. When those form a
convergent (abstract) rewriting system on objects, there are three very natural
constructions that can be used to define the category which is described by the
presentation: one consists in turning equational generators into identities
(i.e. considering a quotient category), one consists in formally adding
inverses to equational generators (i.e. localizing the category), and one
consists in restricting to objects which are normal forms. We show that, under
suitable coherence conditions on the presentation, the three constructions
coincide, thus generalizing celebrated results on presentations of groups, and
we extend those conditions to presentations of monoidal categories
Structure, stability and evolution of 3D Rossby vortices in protoplanetary disks
Large-scale persistent vortices are known to form easily in 2D disks via the
Rossby wave or the baroclinic instability. In 3D, however, their formation and
stability is a complex issue and still a matter of debate. We study the
formation of vortices by the Rossby wave instability in a stratified inviscid
disk and describe their three dimensional structure, stability and long term
evolution. Numerical simulations are performed using a fully compressible
hydrodynamical code based on a second order finite volume method. We assume a
perfect gas law and a non-homentropic adiabatic flow.The Rossby wave
instability is found to proceed in 3D in a similar way as in 2D. Vortices
produced by the instability look like columns of vorticity in the whole disk
thickness; the small vertical motions are related to a weak inclination of the
vortex axis appearing during the development of the RWI. Vortices with aspect
ratios larger than 6 are unaffected by the elliptical instability. They relax
to a quasi-steady columnar structure which survives hundred of rotations while
slowly migrating inward toward the star at a rate that reduces with the vortex
aspect ratio. Vortices with a smaller aspect ratio are by contrast affected by
the elliptic instability. Short aspect ratio vortices are completely destroyed
in a few orbital periods. Vortices with an intermediate aspect ratio are
partially destroyed by the elliptical instability in a region away from the
mid-plane where the disk stratification is sufficiently large. Elongated Rossby
vortices can survive a large number of orbital periods in protoplanetary disks
in the form of vorticity columns. They could play a significant role in the
evolution of the gas and the gathering of the solid particles to form
planetesimals or planetary cores, a possibility that receives a renewed
interest with the recent discovery of a particle trap in the disk of Oph IRS48.Comment: 12 pages, 15 figures, Accepted for publication in A&
A large time-step and well-balanced Lagrange-Projection type scheme for the shallow-water equations
This work focuses on the numerical approximation of the Shallow Water
Equations (SWE) using a Lagrange-Projection type approach. We propose to extend
to this context recent implicit-explicit schemes developed in the framework of
compressibleflows, with or without stiff source terms. These methods enable the
use of time steps that are no longer constrained by the sound velocity thanks
to an implicit treatment of the acoustic waves, and maintain accuracy in the
subsonic regime thanks to an explicit treatment of the material waves. In the
present setting, a particular attention will be also given to the
discretization of the non-conservative terms in SWE and more specifically to
the well-known well-balanced property. We prove that the proposed numerical
strategy enjoys important non linear stability properties and we illustrate its
behaviour past several relevant test cases
A knowledge-based system with learning for computer communication network design
Computer communication network design is well-known as complex and hard. For that reason, the most effective methods used to solve it are heuristic. Weaknesses of these techniques are listed and a new approach based on artificial intelligence for solving this problem is presented. This approach is particularly recommended for large packet switched communication networks, in the sense that it permits a high degree of reliability and offers a very flexible environment dealing with many relevant design parameters such as link cost, link capacity, and message delay
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