1,519 research outputs found
Exhaustive families of representations of -algebras associated to -body Hamiltonians with asymptotically homogeneous interactions
We continue the analysis of algebras introduced by Georgescu, Nistor and
their coauthors, in order to study -body type Hamiltonians with
interactions. More precisely, let be a linear subspace of a finite
dimensional Euclidean space , and be a continuous function on
that has uniform homogeneous radial limits at infinity. We consider, in this
paper, Hamiltonians of the form , where the
subspaces belong to some given family S of subspaces. We prove results on
the spectral theory of the Hamiltonian when is any family of subspaces and
extend those results to other operators affiliated to a larger algebra of
pseudo-differential operators associated to the action of introduced by
Connes. In addition, we exhibit Fredholm conditions for such elliptic
operators. We also note that the algebras we consider answer a question of
Melrose and Singer.Comment: 5 page
Waves and instabilities in rotating free surface flows
The stability properties of the rotating free surface flow in a cylindrical container is studied using a global stability approach, considering succesively three models. For the case of solid body rotation (Newton’s bucket), all eigenmodes are found to be stable, and are classified into three families : gravity waves, singular inertial modes, and Rossby waves. For the case of a potential flow, an instability is found. The mechanism is explained as a resonance between gravity waves and centrifugal waves, and is thought to be at the origin of the ”rotating polygon instability” observed in experiments where the flow is driven by rotation of the bottom plate (see [9]). Finally, we give some preliminary results concerning a third model : the Rankine vortex
Synchronized flutter of two slender flags
The interactions and synchronization of two parallel and slender flags in a
uniform axial flow are studied in the present paper by generalizing Lighthill's
Elongated Body Theory (EBT) and Lighthill's Large Amplitude Elongated Body
Theory (LAEBT) to account for the hydrodynamic coupling between flags. The
proposed method consists in two successive steps, namely the reconstruction of
the flow created by a flapping flag within the LAEBT framework and the
computation of the fluid force generated by this nonuniform flow on the second
flag. In the limit of slender flags in close proximity, we show that the effect
of the wakes have little influence on the long time coupled-dynamics and can be
neglected in the modeling. This provides a simplified framework extending LAEBT
to the coupled dynamics of two flags. Using this simplified model, both linear
and large amplitude results are reported to explore the selection of the
flapping regime as well as the dynamical properties of two side-by-side slender
flags. Hydrodynamic coupling of the two flags is observed to destabilize the
flags for most parameters, and to induce a long-term synchronization of the
flags, either in-phase or out-of-phase.Comment: 14 pages, 10 figures, to appear in J. Fluid Mec
Rotating Polygon Instability of a Swirling Free Surface Flow
We explain the rotating polygon instability on a swirling fluid surface [G. H. Vatistas, J. Fluid Mech. 217, 241 (1990) and Jansson et al., Phys. Rev. Lett. 96, 174502 (2006)] in terms of resonant interactions between gravity waves on the outer part of the surface and centrifugal waves on the inner part. Our model is based on potential flow theory, linearized around a potential vortex flow with a free surface for which we show that unstable resonant states appear. Limiting our attention to the lowest order mode of each type of wave and their interaction, we obtain an analytically soluble model, which, together with estimates of the circulation based on angular momentum balance, reproduces the main features of the experimental phase diagram. The generality of our arguments implies that the instability should not be limited to flows with a rotating bottom (implying singular behavior near the corners), and indeed we show that we can obtain the polygons transiently by violently stirring liquid nitrogen in a hot container
The Anatomy of a Scientific Rumor
The announcement of the discovery of a Higgs boson-like particle at CERN will
be remembered as one of the milestones of the scientific endeavor of the 21st
century. In this paper we present a study of information spreading processes on
Twitter before, during and after the announcement of the discovery of a new
particle with the features of the elusive Higgs boson on 4th July 2012. We
report evidence for non-trivial spatio-temporal patterns in user activities at
individual and global level, such as tweeting, re-tweeting and replying to
existing tweets. We provide a possible explanation for the observed
time-varying dynamics of user activities during the spreading of this
scientific "rumor". We model the information spreading in the corresponding
network of individuals who posted a tweet related to the Higgs boson discovery.
Finally, we show that we are able to reproduce the global behavior of about
500,000 individuals with remarkable accuracy.Comment: 11 pages, 8 figure
Generation of three-dimensional patterns through wave interaction in a model of free surface swirling flow
The free surface flow in a cylindrical tank over a rotating bottom is known to support spectacular three-dimensional patterns, including deformation of the inner free surface into the shape of rotating polygons, and sloshing behavior of the upper free surface (e.g. Iga et al., FDR 2014, same issue). Through a stability analysis of a simplified model of this flow, we show that such patterns can be explained as a resonance mechanism involving different families of waves. The approach extends a previous work (Tophoj et al., PRL 2013) which explained the rotating polygons as an interaction between gravity waves and centrifugal waves, under the assumption that the base flow can be modeled as a potential vortex. We show that this previous model is justified for strong rotation rates (Dry-Potential case), and that for weaker rotations it can be improved by introducing an inner vortex core in solid-body rotation, which either extends to the center of the plate (Wet case) or surrounds a dry central region (Dry-Composite case). The study of this improved model predicts two new kind of instabilities. The first occurs at low rotations (Wet case) and results from an interaction between gravity waves and the Kelvin-Kirchhoff wave (namely, oscillation of the boundary of the vortex core). This instability is proposed to be at the origin of the sloshing phenomenon. The second new instability occurs, for moderate rotations, (Dry-Composite case) as an interaction between gravity waves and a "Kelvin-Centrifugal" wave characterized by deformation of the inner surface and the vortex core boundary in opposite directions. This instability exists for all azimuthal wave numbers starting from m = 1, this case corresponding to a "monogon" pattern
Séquence didactique à partir de Un hivernage dans les glaces de J. Verne
International audienceLes auteurs proposent une séquence didactique associant exploration du lexique, étude morphosyntaxique (grammaire, conjugaison), et analyse thématique de passages textuels.L'attention se porte sur les corrélations entre l'emploi du mode subjonctif et la dramatisation du récit ; on quitte ainsi la localité des phrases pour la globalité textuelle
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