Modeling and Simulation of a Fluttering Cantilever in Channel Flow

Characterizing the dynamics of a cantilever in channel flow is relevant to applications ranging from snoring to energy harvesting. Aeroelastic flutter induces large oscillating amplitudes and sharp changes with frequency that impact the operation of these systems. The fluid-structure mechanisms that drive flutter can vary as the system parameters change, with the stability boundary becoming especially sensitive to the channel height and Reynolds number, especially when either or both are small. In this paper, we develop a coupled fluid-structure model for viscous, two-dimensional channel flow of arbitrary shape. Its flutter boundary is then compared to results of two-dimensional direct numerical simulations to explore the model's validity. Provided the non-dimensional channel height remains small, the analysis shows that the model is not only able to replicate DNS results within the parametric limits that ensure the underlying assumptions are met, but also over a wider range of Reynolds numbers and fluid-structure mass ratios. Model predictions also converge toward an inviscid model for the same geometry as Reynolds number increases

Upper and lower bounds for an eigenvalue associated with a positive eigenvector

When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like inequalities and can be applied to non-necessarily purely quadratic Hamiltonians. An application for a magnetic Hamiltonian is given and the case of a discrete Schrodinger operator is also discussed. It is shown how this approach leads to some explicit bounds on the ground-state energy of a system made of an arbitrary number of attractive Coulombian particles

Are collapse models testable with quantum oscillating systems? The case of neutrinos, kaons, chiral molecules

Collapse models provide a theoretical framework for understanding how classical world emerges from quantum mechanics. Their dynamics preserves (practically) quantum linearity for microscopic systems, while it becomes strongly nonlinear when moving towards macroscopic scale. The conventional approach to test collapse models is to create spatial superpositions of mesoscopic systems and then examine the loss of interference, while environmental noises are engineered carefully. Here we investigate a different approach: We study systems that naturally oscillate --creating quantum superpositions-- and thus represent a natural case-study for testing quantum linearity: neutrinos, neutral mesons, and chiral molecules. We will show how spontaneous collapses affect their oscillatory behavior, and will compare them with environmental decoherence effects. We will show that, contrary to what previously predicted, collapse models cannot be tested with neutrinos. The effect is stronger for neutral mesons, but still beyond experimental reach. Instead, chiral molecules can offer promising candidates for testing collapse models.Comment: accepted by NATURE Scientific Reports, 12 pages, 1 figures, 2 table

Control limitations from distributed sensing: theory and Extremely Large Telescope application

We investigate performance bounds for feedback control of distributed plants where the controller can be centralized (i.e. it has access to measurements from the whole plant), but sensors only measure differences between neighboring subsystem outputs. Such "distributed sensing" can be a technological necessity in applications where system size exceeds accuracy requirements by many orders of magnitude. We formulate how distributed sensing generally limits feedback performance robust to measurement noise and to model uncertainty, without assuming any controller restrictions (among others, no "distributed control" restriction). A major practical consequence is the necessity to cut down integral action on some modes. We particularize the results to spatially invariant systems and finally illustrate implications of our developments for stabilizing the segmented primary mirror of the European Extremely Large Telescope.Comment: submitted to Automatic

Relaminarisation of Re_τ=100 channel flow with globally stabilising linear feedback control

The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller’s estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_τ = 100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl’s theory of sheared turbulence

Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of N. N. Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics and condensed matter physics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach, and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem, in which the effect of all the other particles on any given particle is approximated by a single averaged effect, thus reducing a many-body problem to a single-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising and Heisenberg models, superconducting and superfluid systems, strongly correlated systems, etc. It seems likely that these technical advances in the many-body problem will be useful in suggesting new methods for treating and understanding many-particle interacting systems. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects, and for those who are interested in concrete applications.Comment: 60 pages, Refs.25