4,425 research outputs found
The 2D/3D dynamics of wall-bounded low-Rm magnetohydrodynamic (MHD) turbulence
No full textWith this experimental study, we give evidence that the dynamics of low-Rm MHD turbulence depends on the diffusion length l_z, which corresponds to the distance over which the Lorentz force is able to diffuse momentum before it is balanced by inertia
On the structure and classification of Bernstein algebras
No full textWe prove that any Bernstein algebra is isomorphic to a
semidirect product associated to a
commutative algebra such that , for all and
an idempotent endomorphism of
satisfying two compatibility conditions. The set of types of -dimensional Bernstein algebras is parametrized by an explicitely
constructed (using linear algebra tools) classified object. The automorphisms
group of any Bernstein algebra is described as a subgroup of the canonical
semidirect product of groups .Comment: The final version will appear in Journal of Algebra and its
Application
Approximation properties for modified -Bernstein-Durrmeyer operators
No full textsummary:We introduce modified -Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators and compute the rate of convergence for the function belonging to the class
Spectroscopie photoassociative des états moléculaires à longue distance de Rb. Analyse Lu-Fano et amélioration de la formule de Le Roy-Bernstein
No full textNous avons étudié la photoassociation de Rb sous la
limite 5S (D), par spectroscopie de
pertes d'atomes froids. Les spectres montrent les progressions
vibrationnelles des trois séries d'états moléculaires
attractifs , et
convergents vers la limite .
L'analyse de nos données utilise l'approche de Lu-Fano
associé au modèle de LeRoy-Bernstein. Pour la série
, cette approche met en évidence un écart au
modèle. Une amélioration de la formule de LeRoy-Bernstein
permet de rendre compte des mesures expérimentales. Pour la
série avec la même
méthode, on montre le couplage avec la série
An estimate for F-jumping numbers via the roots of the Bernstein-Sato polynomial
No full textGiven a smooth complex algebraic variety and a nonzero regular function
on , we give an effective estimate for the difference between the
jumping numbers of and the -jumping numbers of a reduction of
to characteristic , in terms of the roots of the Bernstein-Sato
polynomial of . As an application, we show that if has no roots
of the form , with a positive integer, then the -pure
threshold of is equal to the log canonical threshold of for
with .Comment: 10 pages; v.2: using a bound for the roots of the Bernstein-Sato
polynomial, we deduce a uniform estimate only involving the dimension of the
ambient variety and explain how this extends to possibly non-principal
ideals. V.3: revised version, to appear in Proceedings of the AM
Brian\c{c}on-Skoda exponents and the maximal root of reduced Bernstein-Sato polynomials
No full textFor a holomorphic function on a complex manifold , the
Brian\c{c}on-Skoda exponent is the smallest integer with
(replacing with a neighborhood of ), where
denotes the Jacobian ideal of . It is shown that by Brian\c con-Skoda. We prove that with the
maximal root of the reduced Bernstein-Sato polynomial , assuming
the latter exists (shrinking if necessary). This implies for instance that
in the case has only rational
singularities, that is, if .Comment: 10 page
Triangular Constellations in Flows
No full textParticles advected on the surface of a fluid can exhibit fractal clustering. The local structure of a fractal set is described by its dimension , which is the exponent of a power-law relating the mass in a ball to its radius : . It is desirable to characterise the {\em shapes} of constellations of points sampling a fractal measure, as well as their masses. The simplest example is the distribution of shapes of triangles formed by triplets of points, which we investigate for fractals generated by chaotic dynamical systems. The most significant parameter describing the triangle shape is the ratio of its area to the radius of gyration squared. We show that the probability density of has a phase transition: is independent of and approximately uniform below a critical flow compressibility , which we estimate. For the distribution appears to be described by two power laws: when , and when
Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field
No full textWe investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: for very strong applied magnetic field, is the flow mostly two-dimensional, with remaining weak three-dimensional fluctuations, or does it become exactly 2D, with no dependence along the vertical? We restrict attention to low-magnetic-Reynolds number (Rm) flow. Because liquid metals have low magnetic Prandtl number, such low- flows can have a kinetic Reynolds number as large as one million and therefore be strongly turbulent. We first focus on the quasi-static approximation, i.e. the asymptotic limit of vanishing magnetic Reynolds number Rm << 1: we prove that the flow becomes exactly 2D asymptotically in time, regardless of the initial condition and provided the interaction parameter N is larger than a threshold value. We call this property absolute two-dimensionalization: the attractor of the system is necessarily a (possibly turbulent) 2D flow. We then consider the full-magnetohydrodynamic equations and we prove that, for low enough Rm and large enough N, the flow becomes exactly two-dimensional in the long-time limit provided the initial vertically-dependent perturbations are infinitesimal. We call this phenomenon linear two-dimensionalization: the (possibly turbulent) 2D flow is an attractor of the dynamics, but it is not necessarily the only attractor of the system. Some 3D attractors may also exist and be attained for strong enough initial 3D perturbations. These results shed some light on the existence of a dissipative anomaly for magnetohydrodynamic flows subject to a strong external magnetic field
The Decay of Wall Bounded MHD Turbulence at Low RM
No full textWe have developed a new spectral method to simulate flows with very fine boundary layers present. We apply it to calculate the evolution of freely decaying MHD turbulence between isolating walls. By comparison them with results obtained in fully periodic domain we quantify the influence of the channel walls on the character of freely decaying MHD turbulence
Bernstein-Sato polynomials for projective hypersurfaces with weighted homogeneous isolated singularities
No full textWe present an efficient method to calculate the roots of the Bernstein-Sato
polynomial for a defining polynomial of a projective hypersurface
of degree having only weighted homogeneous isolated
singularities. The computation of roots can be reduced to that of the Hilbert
series of the Jacobian ring of except some special case. For this we prove
the -degeneration of the pole order spectral sequence. Combined with the
self-duality of the Koszul complex and also a theorem of Dimca and Popescu on
the weak Lefschetz property of the "torsion part" of the Jacobian ring (with
respect to a general linear function), it implies in the case the
discrete connectivity of the absolute values of the roots of supported
at 0 modulo the roots coming from the singularities of , except some special
case which does not contain any essential indecomposable central hyperplane
arrangements in ; more precisely, we have , where are the roots of Bernstein-Sato
polynomials of up to sign, and with the maximal degree of the "torsion part" of the Jacobian ring
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