5,237 research outputs found
Compressive Wave Computation
This paper considers large-scale simulations of wave propagation phenomena.
We argue that it is possible to accurately compute a wavefield by decomposing
it onto a largely incomplete set of eigenfunctions of the Helmholtz operator,
chosen at random, and that this provides a natural way of parallelizing wave
simulations for memory-intensive applications.
This paper shows that L1-Helmholtz recovery makes sense for wave computation,
and identifies a regime in which it is provably effective: the one-dimensional
wave equation with coefficients of small bounded variation. Under suitable
assumptions we show that the number of eigenfunctions needed to evolve a sparse
wavefield defined on N points, accurately with very high probability, is
bounded by C log(N) log(log(N)), where C is related to the desired accuracy and
can be made to grow at a much slower rate than N when the solution is sparse.
The PDE estimates that underlie this result are new to the authors' knowledge
and may be of independent mathematical interest; they include an L1 estimate
for the wave equation, an estimate of extension of eigenfunctions, and a bound
for eigenvalue gaps in Sturm-Liouville problems.
Numerical examples are presented in one spatial dimension and show that as
few as 10 percents of all eigenfunctions can suffice for accurate results.
Finally, we argue that the compressive viewpoint suggests a competitive
parallel algorithm for an adjoint-state inversion method in reflection
seismology.Comment: 45 pages, 4 figure
Brief Announcement: Memory Lower Bounds for Self-Stabilization
In the context of self-stabilization, a silent algorithm guarantees that the communication registers (a.k.a register) of every node do not change once the algorithm has stabilized. At the end of the 90\u27s, Dolev et al. [Acta Inf. \u2799] showed that, for finding the centers of a graph, for electing a leader, or for constructing a spanning tree, every silent deterministic algorithm must use a memory of Omega(log n) bits per register in n-node networks. Similarly, Korman et al. [Dist. Comp. \u2707] proved, using the notion of proof-labeling-scheme, that, for constructing a minimum-weight spanning tree (MST), every silent algorithm must use a memory of Omega(log^2n) bits per register. It follows that requiring the algorithm to be silent has a cost in terms of memory space, while, in the context of self-stabilization, where every node constantly checks the states of its neighbors, the silence property can be of limited practical interest. In fact, it is known that relaxing this requirement results in algorithms with smaller space-complexity.
In this paper, we are aiming at measuring how much gain in terms of memory can be expected by using arbitrary deterministic self-stabilizing algorithms, not necessarily silent. To our knowledge, the only known lower bound on the memory requirement for deterministic general algorithms, also established at the end of the 90\u27s, is due to Beauquier et al. [PODC \u2799] who proved that registers of constant size are not sufficient for leader election algorithms. We improve this result by establishing the lower bound Omega(log log n) bits per register for deterministic self-stabilizing algorithms solving (Delta+1)-coloring, leader election or constructing a spanning tree in networks of maximum degree Delta
Memory lower bounds for deterministic self-stabilization
In the context of self-stabilization, a \emph{silent} algorithm guarantees
that the register of every node does not change once the algorithm has
stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that,
for finding the centers of a graph, for electing a leader, or for constructing
a spanning tree, every silent algorithm must use a memory of
bits per register in -node networks. Similarly, Korman et al. [Dist. Comp.
'07] proved, using the notion of proof-labeling-scheme, that, for constructing
a minimum-weight spanning trees (MST), every silent algorithm must use a memory
of bits per register. It follows that requiring the algorithm
to be silent has a cost in terms of memory space, while, in the context of
self-stabilization, where every node constantly checks the states of its
neighbors, the silence property can be of limited practical interest. In fact,
it is known that relaxing this requirement results in algorithms with smaller
space-complexity.
In this paper, we are aiming at measuring how much gain in terms of memory
can be expected by using arbitrary self-stabilizing algorithms, not necessarily
silent. To our knowledge, the only known lower bound on the memory requirement
for general algorithms, also established at the end of the 90's, is due to
Beauquier et al.~[PODC '99] who proved that registers of constant size are not
sufficient for leader election algorithms. We improve this result by
establishing a tight lower bound of bits per
register for self-stabilizing algorithms solving -coloring or
constructing a spanning tree in networks of maximum degree~. The lower
bound bits per register also holds for leader election
Large Eddy Simulations of gaseous flames in gas turbine combustion chambers
Recent developments in numerical schemes, turbulent combustion models and the regular increase of computing power allow Large Eddy Simulation (LES) to be applied to real industrial burners. In this paper, two types of LES in complex geometry combustors and of specific interest for aeronautical gas turbine burners are reviewed: (1) laboratory-scale combustors, without compressor or turbine, in which advanced measurements are possible and (2) combustion chambers of existing engines operated in realistic operating conditions. Laboratory-scale burners are designed to assess modeling and funda- mental flow aspects in controlled configurations. They are necessary to gauge LES strategies and identify potential limitations. In specific circumstances, they even offer near model-free or DNS-like LES computations. LES in real engines illustrate the potential of the approach in the context of industrial burners but are more difficult to validate due to the limited set of available measurements. Usual approaches for turbulence and combustion sub-grid models including chemistry modeling are first recalled. Limiting cases and range of validity of the models are specifically recalled before a discussion on the numerical breakthrough which have allowed LES to be applied to these complex cases. Specific issues linked to real gas turbine chambers are discussed: multi-perforation, complex acoustic impedances at inlet and outlet, annular chambers.. Examples are provided for mean flow predictions (velocity, temperature and species) as well as unsteady mechanisms (quenching, ignition, combustion instabil- ities). Finally, potential perspectives are proposed to further improve the use of LES for real gas turbine combustor designs
An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach
We present a numerical method to accurately simulate particle size
distributions within the formalism of rate equation cluster dynamics. This
method is based on a discretization of the associated Fokker-Planck equation.
We show that particular care has to be taken to discretize the advection part
of the Fokker-Planck equation, in order to avoid distortions of the
distribution due to numerical diffusion. For this purpose we use the
Kurganov-Noelle-Petrova scheme coupled with the monotonicity-preserving
reconstruction MP5, which leads to very accurate results. The interest of the
method is highlighted on the case of loop coarsening in aluminum. We show that
the choice of the models to describe the energetics of loops does not
significantly change the normalized loop distribution, while the choice of the
models for the absorption coefficients seems to have a significant impact on
it
Control through operators for quantum chemistry
We consider the problem of operator identification in quantum control. The
free Hamiltonian and the dipole moment are searched such that a given target
state is reached at a given time. A local existence result is obtained. As a
by-product, our works reveals necessary conditions on the laser field to make
the identification feasible. In the last part of this work, some algorithms are
proposed to compute effectively these operators
Sparse Support Recovery with Non-smooth Loss Functions
In this paper, we study the support recovery guarantees of underdetermined
sparse regression using the -norm as a regularizer and a non-smooth
loss function for data fidelity. More precisely, we focus in detail on the
cases of and losses, and contrast them with the usual
loss. While these losses are routinely used to account for either
sparse ( loss) or uniform ( loss) noise models, a
theoretical analysis of their performance is still lacking. In this article, we
extend the existing theory from the smooth case to these non-smooth
cases. We derive a sharp condition which ensures that the support of the vector
to recover is stable to small additive noise in the observations, as long as
the loss constraint size is tuned proportionally to the noise level. A
distinctive feature of our theory is that it also explains what happens when
the support is unstable. While the support is not stable anymore, we identify
an "extended support" and show that this extended support is stable to small
additive noise. To exemplify the usefulness of our theory, we give a detailed
numerical analysis of the support stability/instability of compressed sensing
recovery with these different losses. This highlights different parameter
regimes, ranging from total support stability to progressively increasing
support instability.Comment: in Proc. NIPS 201
Biologically Inspired Dynamic Textures for Probing Motion Perception
Perception is often described as a predictive process based on an optimal
inference with respect to a generative model. We study here the principled
construction of a generative model specifically crafted to probe motion
perception. In that context, we first provide an axiomatic, biologically-driven
derivation of the model. This model synthesizes random dynamic textures which
are defined by stationary Gaussian distributions obtained by the random
aggregation of warped patterns. Importantly, we show that this model can
equivalently be described as a stochastic partial differential equation. Using
this characterization of motion in images, it allows us to recast motion-energy
models into a principled Bayesian inference framework. Finally, we apply these
textures in order to psychophysically probe speed perception in humans. In this
framework, while the likelihood is derived from the generative model, the prior
is estimated from the observed results and accounts for the perceptual bias in
a principled fashion.Comment: Twenty-ninth Annual Conference on Neural Information Processing
Systems (NIPS), Dec 2015, Montreal, Canad
LES evaluation of the effects of equivalence ratio fluctuations on the dynamic flame response in a real gas turbine combustion chamber
Large Eddy Simulations (LES) of a lean swirl-stabilized gas turbine burner are used to analyze mechanisms triggering combustion instabilities. To separately study the effect of velocity and equivalence ratio fluctuations, two LES of the same geometry are performed: one where the burner operates in a “technically” premixed mode (methane is injected by holes in the vanes located in the diagonal passage upstream of the chamber) and the second one where the flow is fully premixed in the diagonal passage. The inlet is acoustically modulated and the mechanisms affecting the dynamic flame response are identified. LES reveals that both cases provide similar averaged (non-)pulsated flame shapes. However, even though the mean flames are only slightly modified, the delays change when mixing is not perfect. LES fields and a simple model for the methane jets trajectories show that mixing in the diagonal passage is not sufficient to damp heterogeneities induced by unsteady fuel flow rate and varying fuel jet trajectories. These mixing fluctuations are phased with velocity oscillations and modify the flame response to forcing. Local fields of delays and interaction indices are obtained, showing that the flame is not compact and is affected by fluctuations of mixing
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