2,796 research outputs found
Decay of semilinear damped wave equations:cases without geometric control condition
We consider the semilinear damped wave equation . In
this article, we obtain the first results concerning the stabilization of this
semilinear equation in cases where does not satisfy the geometric
control condition. When some of the geodesic rays are trapped, the
stabilization of the linear semigroup is semi-uniform in the sense that
for some function with when
. We provide general tools to deal with the semilinear
stabilization problem in the case where has a sufficiently fast decay
Balancing clusters to reduce response time variability in large scale image search
Many algorithms for approximate nearest neighbor search in high-dimensional
spaces partition the data into clusters. At query time, in order to avoid
exhaustive search, an index selects the few (or a single) clusters nearest to
the query point. Clusters are often produced by the well-known -means
approach since it has several desirable properties. On the downside, it tends
to produce clusters having quite different cardinalities. Imbalanced clusters
negatively impact both the variance and the expectation of query response
times. This paper proposes to modify -means centroids to produce clusters
with more comparable sizes without sacrificing the desirable properties.
Experiments with a large scale collection of image descriptors show that our
algorithm significantly reduces the variance of response times without
seriously impacting the search quality
Large-Eddy Simulation of combustion instabilities in a variable-length combustor.
This article presents a simulation of a model rocket combustor with continuously variable acoustic properties thanks to a variable-length injector tube. Fully compressible Large-Eddy Simulations are conducted using the AVBP code. An original flame stabilization mechanism is uncovered where the recirculation of hot gases in the corner recirculation zone creates a triple flame structure. An unstable operating point is then chosen to investigate the mech- anism of the instability. The simulations are compared to experimental results in terms of frequency and mode structure. Two-dimensional axi-symmetric computations are com- pared to full 3D simulations in order to assess the validity of the axi-symmetry assumption for the prediction of mean and unsteady features of this flow. Despite the inaccuracies in- herent to the 2D description of a turbulent flow, for this configuration and the particular operating point investigated, the axi-symmetric simulation qualitatively reproduces some features of the instability
Coupling and robustness of intra-cortical vascular territories
Vascular domains have been described as being coupled to neuronal functional units enabling dynamic blood supply to the cerebral cyto-architecture. Recent experiments have shown that penetrating arterioles of the grey matter are the building blocks for such units. Nevertheless, vascular territories are still poorly known, as the collection and analysis of large three-dimensional micro-vascular networks are difficult. By using an exhaustive reconstruction of the micro-vascular network in an 18 mm 3 volume of marmoset cerebral cortex, we numerically computed the blood flow in each blood vessel. We thus defined arterial and venular territories and examined their overlap. A large part of the intracortical vascular network was found to be supplied by several arteries and drained by several venules. We quantified this multiple potential to compensate for deficiencies by introducing a new robustness parameter. Robustness proved to be positively correlated with cortical depth and a systematic investigation of coupling maps indicated local patterns of overlap between neighbouring arteries and neighbouring venules. However, arterio-venular coupling did not have a spatial pattern of overlap but showed locally preferential functional coupling, especially of one artery with two venules, supporting the notion of vascular units. We concluded that intra-cortical perfusion in the primate was characterised by both very narrow functional beds and a large capacity for compensatory redistribution, far beyond the nearest neighbour collaterals
Modelling the kinetics of transesterification reaction of sunflower oil with ethanol in microreactors
Transesterification reaction of vegetable oil with ethanol leads to ethyl esters, used to date for applications principally in food and cosmetic industry. To open the application field to biofuels (to substitute current fuels resulting from fossil resources), the process efficiency has to be developed to be economically profitable. In this work, the sunflower oil ethanolysis was performed in a micro-scaled continuous device, inducing better control for heat and mass transfer in comparison with batch processes. Moreover, this device ensures kinetic data acquisition at the first seconds of the reaction, which was not feasible in a conventional batch process. These data were used to model occurring phenomena and to determine kinetic constants and mass transfer coefficients. A single set of these parameters is able to represent the evolution of the reaction media composition function of time for five ethanol to oil molar ratios (6.0, 9.0, 16.2, 22.7 and 45.4). The model was validated in reaction and diffusion mode. Finally, it was subsequently used to simulate reactions with other operational conditions and to propose other process implementation
Breakdown of scale invariance in a quasi-two-dimensional Bose gas due to the presence of the third dimension
In this Rapid Communication, we describe how the presence of the third
dimension may break the scale invariance in a two-dimensional Bose gas in a
pancake-shaped trap. From the two-dimensional perspective, the possibility of a
weak spilling of the atomic density beyond the ground-state of the confinement
alters the two-dimensional chemical potential; in turn, this correction no
longer supports scale invariance. We compare experimental data with numerical
and analytic perturbative results and find a good agreement.Comment: 4 pages, 1 figure, published in PRA Rapid Com
Constructing Attractors of Nonlinear Dynamical Systems
In a previous work, we have shown how to generate attractor sets of affine hybrid systems using a method of state space decomposition. We show here how to adapt the method to polynomial dynamics systems by approximating them as switched affine systems. We show the practical
interest of the method on standard examples of the literature
Parametric Schedulability Analysis of Fixed Priority Real-Time Distributed Systems
Parametric analysis is a powerful tool for designing modern embedded systems,
because it permits to explore the space of design parameters, and to check the
robustness of the system with respect to variations of some uncontrollable
variable. In this paper, we address the problem of parametric schedulability
analysis of distributed real-time systems scheduled by fixed priority. In
particular, we propose two different approaches to parametric analysis: the
first one is a novel technique based on classical schedulability analysis,
whereas the second approach is based on model checking of Parametric Timed
Automata (PTA).
The proposed analytic method extends existing sensitivity analysis for single
processors to the case of a distributed system, supporting preemptive and
non-preemptive scheduling, jitters and unconstrained deadlines. Parametric
Timed Automata are used to model all possible behaviours of a distributed
system, and therefore it is a necessary and sufficient analysis. Both
techniques have been implemented in two software tools, and they have been
compared with classical holistic analysis on two meaningful test cases. The
results show that the analytic method provides results similar to classical
holistic analysis in a very efficient way, whereas the PTA approach is slower
but covers the entire space of solutions.Comment: Submitted to ECRTS 2013 (http://ecrts.eit.uni-kl.de/ecrts13
Stabilization for the semilinear wave equation with geometric control condition
In this article, we prove the exponential stabilization of the semilinear
wave equation with a damping effective in a zone satisfying the geometric
control condition only. The nonlinearity is assumed to be subcritical,
defocusing and analytic. The main novelty compared to previous results, is the
proof of a unique continuation result in large time for some undamped equation.
The idea is to use an asymptotic smoothing effect proved by Hale and Raugel in
the context of dynamical systems. Then, once the analyticity in time is proved,
we apply a unique continuation result with partial analyticity due to Robbiano,
Zuily, Tataru and H\"ormander. Some other consequences are also given for the
controllability and the existence of a compact attractor
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