La Boîte de Schrödinger - Expérience 1 (French Edition)
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Download PDF La Boîte de Schrödinger - Partie 1 (French Edition)
Planck Stars and Loop Gravity. I summarise the recent developments of Loop Quantum Gravity and the state of the art of theory, and I describe an idea on a possible window for observation of astrophysical quantum gravitational effects. Unlikely events matter. Various aspects of this approach are discussed including a numerical realization on sparse grids. Using an explicit formula for solutions, we prove a stability criterion for the non-autonomous system.
Corresponding stability criteria for transport and wave propagation on networks with variable coefficients are derived by expressing these systems as difference equations.
We present during this talk an overview of the questions, and recent positive and negative results on the control, stabilization and inverse problems for coupled systems. For each of these problems, we consider situations for which the number of controls, feedbacks and measurements is strictly less than the number of unknowns or of equations. Namely the controls or the measurements for these systems are limited only to certain components of the state-vector. This is called indirect control or indirect inverse problems.
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The challenging questions are then, to determine whether it is possible to drive back the full system, that is all the components of the state-vector, to a desired state in finite time or asymptotically, or to derive stability estimates in the case of inverse problems. We present positive results as well as negative results, stress the influence of the coupling operators, the geometric aspects and show how the situation varies compared to the scalar case.
We study controlled alignment models in finite dimension and we explore how to enforce pattern formation or convergence to consensus in a group of interacting agents. These sparsity features are desirable in view of practical issues. Han-Kwan et M. We study Carleman estimate. The pseudo convexity condition is well known to have this estimate. From the point of views in inverse problems we review the theory of Carleman estimates under weak pseudo convexity related to the limiting Carleman weights.
The space of admissible paths connecting two points is contractible if we do not care about the length of the paths and may have a nontrivial topology if the length is constrained. We try to understand what happens when the points are very close and the length is small.
We study, from a control theoretic view point, a simplified 1D model of fluid-structure interactions. More precisely we consider a point mass moving in a pipe filled with a fluid. The control variable is a force acting on the mass point. The main result of the paper asserts that for any initial data there exist a time T and a control such that, at time T, the point reaches approximately its destination, whereas the velocities of the fluid and of the point mass simultaneously vanish.
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Therefore, within this simplified model, the fluid can be exactely controlled by inputs acting on the moving point only. We consider inverse problems for the Einstein equation with a time-depending metric on a 4-dimensional globally hyperbolic Lorentzian manifold. We formulate the concept of active measurements for relativistic models. We do this by coupling Einstein equations with equations for scalar fields. The inverse problem we study is the question, do the observations of the solutions of the coupled system in an open subset U of the space-time with the sources supported in U determine the properties of the metric in a larger domain?
To study this problem we define the concept of light observation sets and show that these sets determine the conformal class of the metric.
This corresponds to passive observations from a distant area of space which is filled by light sources. We will also consider inverse problems for other non-linear hyperbolic equations.
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This is joint work with Y. Kurylev and M. This talk is a survey on some applications of Carleman estimates to control and stabilization problems. We recall the proof of unique continuation using Carleman estimates. This allows also to give an interpolation estimate, i. A first application of the interpolation estimate is an estimate on eigenfunctions of Laplace-Beltrami operator on a Riemannian manifold without boundary. This estimate is a model to the estimates obtained below. To obtain same kind of results on bounded domain, we give Carleman estimates with boundary terms.
This allows to prove interpolation estimate up the boundary in bounded domains. From this, we give estimate on finite sum of eigenfunctions. As a consequence we can prove control for heat equation. Another application is the estimate of energy decreasing for damped wave equation. In this lecture we address the problem of the optimal placement of sensors and actuators for wave propagation problems. We also explain how closely this topic is related to the fine properties of the high frequency behavior of the eigenfunctions of the Laplacian which is intimately linked to the ergodicity properties of the dynamical system generated by the corresponding billiard.
We shall also discuss the same problem for heat processes showing that, in that frame, according to intuition, the problem is governed by a finite number of Fourier modes. These results will be illustrated by numerical simulations. It is based on recent joint work in collaboration with Y.
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Privat and E. We present some recent results on the optimal control of Hamilton-Jacobi equations. The inspiration for this problem comes from the control of front propagation and has connections with optimal transport theory. The main results include existence, partial uniqueness, and characterization of optimizers. In particular, the optimal solutions are characterized by a mean field games type system of PDEs. Stimulated by the classical transposition method in PDEs, we introduced a new notion of solution, i.
This is something like the generalized function solutions to PDEs. As application of our transposition method, we obtain a new numerical method for solving BSDEs. Our method can be viewed as an analogue of the classical finite element method solving deterministic PDEs. As another application of this transposition method, we establish a Pontryagin-type maximum principle for optimal controls of general infinite dimensional nonlinear stochastic evolution equations, in which both drift and diffusion terms can contain the control variables, and the control domains are allowed to be nonconvex.
In this talk, we focus on the control and observation problems for stochastic partial differential equations, particularly on stochastic heat equations and stochastic wave equations, which is a very open area now. We begin with the formulation of the problems. Then, we explain the main difference between it and the same problems for partial differential equations.
After that, we survey some recent results. This talk will end up with some open problems. The typical measurement is a single internal measurement of the solution in some given observatory. There he faces tests, battles enemies, questions the loyalty of friends and allies, withstands a climactic ordeal, teeters on the brink of failure or death, and ultimately returns to where he began, victorious but in some way transformed.
Many of the NDEs people relate follow some version of this structure.
After spending some time going back and forth between the two realms, he descends one last time into the dark place where he began, only this time the grotesque creatures have been replaced by the faces of people praying for him. It offers the possibility of an escape from something that holds you back, and a transformation into something better.
Nobody at the conference better personified the hope for redemption and transformation than Jeff Olsen, one of the two keynote speakers. Lying in the wreckage with his back broken, one arm nearly torn off, and one leg destroyed, he was for a while conscious enough to register that his 7-year-old son was crying but his wife and infant son were silent. He seemed to find himself in a room with a crib, holding the son who had been killed. This is key to what makes near-death experiences so powerful, and why people cling so strongly to them regardless of the scientific evidence.
conumygent.tk Whether you actually saw a divine being or your brain was merely pumping out chemicals like never before, the experience is so intense and new that it forces you to rethink your place on Earth. If the NDE happened during a tragedy, it provides a way to make sense of that tragedy and rebuild your life. If your life has been a struggle with illness or doubt, an NDE sets you in a different direction: you nearly died, so something has to change.
There appeared to be nobody at the conference who thought that near-death experiences are just a product of physical processes in the brain. But there were several people whose talks promised to address the science of NDEs. Alan Hugenot is a middle-aged mechanical engineer who walks and talks with a kinetic intensity, as if he can barely keep himself from ricocheting off the walls. But what makes them scientists is that they know and maintain the distinction between scientific theories, which must be testable against observable evidence, and mysticism or speculation.
This, Mays said, is the explanation that resolves both the problem of how a series of electrical impulses in the brain becomes the sensation of consciousness and the mystery of near-death experiences.
Mays, at least, was extremely specific about which brain cells he thinks the mind entity interacts with in order to control the brain. For all their differences in style and subject matter, Mays, Hugenot, and others are offering similar visions: large, all-encompassing explanations that link things people know to be true with things they would like to be true and that bring a sense of order to the universe.
It makes sense that NDErs would find such stuff compelling. But why was there so much resistance at the conference to real, solid science? At my breakfast with Diane Corcoran, I asked her why nobody at the conference seemed to be discussing the materialist position. Most people who do that have not investigated the field in any serious way.
At some level, I find this reasonable. A lot of writing about NDEs does not merely question experiencers but ridicules them. Nonetheless, at the conference I encountered not just resistance to but a great many misconceptions about science. In the hotel corridors, I ran into Hugenot. The whole point of scientific theories, I said, is that they have to be testable. Testable means falsifiable: you have to be able in principle to do an experiment that might show a theory to be wrong.
Every time the theory survives such a test, our confidence in it increases. So how, I asked, is a conscious universe testable? But which way is down? If you change perspective and imagine the ground above us, maybe down is up.