3,486 research outputs found
Dissipative boundary conditions for nonlinear 1-D hyperbolic systems: sharp conditions through an approach via time-delay systems
We analyse dissipative boundary conditions for nonlinear hyperbolic systems
in one space dimension. We show that a previous known sufficient condition for
exponential stability with respect to the C^1-norm is optimal. In particular a
known weaker sufficient condition for exponential stability with respect to the
H^2-norm is not sufficient for the exponential stability with respect to the
C^1-norm. Hence, due to the nonlinearity, even in the case of classical
solutions, the exponential stability depends strongly on the norm considered.
We also give a new sufficient condition for the exponential stability with
respect to the W^{2,p}-norm. The methods used are inspired from the theory of
the linear time-delay systems and incorporate the characteristic method
Lyapunov functions and finite time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems
Hyperbolic systems in one dimensional space are frequently used in modeling
of many physical systems. In our recent works, we introduced time independent
feedbacks leading to the finite stabilization for the optimal time of
homogeneous linear and quasilinear hyperbolic systems. In this work, we present
Lyapunov's functions for these feedbacks and use estimates for Lyapunov's
functions to rediscover the finite stabilization results.Comment: arXiv admin note: text overlap with arXiv:2005.1326
On the optimal controllability time for linear hyperbolic systems with time-dependent coefficients
The optimal time for the controllability of linear hyperbolic systems in one
dimensional space with one-side controls has been obtained recently for
time-independent coefficients in our previous works. In this paper, we consider
linear hyperbolic systems with time-varying zero-order terms. We show the
possibility that the optimal time for the null-controllability becomes
significantly larger than the one of the time-invariant setting even when the
zero-order term is indefinitely differentiable. When the analyticity with
respect to time is imposed for the zero-order term, we also establish that the
optimal time is the same as in the time-independent setting
Null-controllability of linear hyperbolic systems in one dimensional space
This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously established the optimal time for the null and the exact controllability for this system for a generic source term. In this work, we prove the null-controllability for any time greater than the optimal time and for any source term. Similar results for the exact controllability are also discussed
Formation and Dissociation of Hydrate Plugs in a Water in Oil Emulsion
4 pagesIn this paper, we present experimental results of the formation and dissociation of methane hydrate plugs in a semi-batch reactor. The plugs are done from water in heptane emulsion (water content from 30 %). The experimental results shows that the formation rate and dissociation rate are controlled by the heat transfer at the wall of the reactor. An unexpected behaviour is observed as the temperature decreases under the 0°C temperature during dissociation and seems to form ice which slows down the dissociation rate
Towards quantum simulation with circular Rydberg atoms
The main objective of quantum simulation is an in-depth understanding of
many-body physics. It is important for fundamental issues (quantum phase
transitions, transport, . . . ) and for the development of innovative
materials. Analytic approaches to many-body systems are limited and the huge
size of their Hilbert space makes numerical simulations on classical computers
intractable. A quantum simulator avoids these limitations by transcribing the
system of interest into another, with the same dynamics but with interaction
parameters under control and with experimental access to all relevant
observables. Quantum simulation of spin systems is being explored with trapped
ions, neutral atoms and superconducting devices. We propose here a new paradigm
for quantum simulation of spin-1/2 arrays providing unprecedented flexibility
and allowing one to explore domains beyond the reach of other platforms. It is
based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes
combined with the inhibition of their microwave spontaneous emission and their
low sensitivity to collisions and photoionization make trapping lifetimes in
the minute range realistic with state-of-the-art techniques. Ultra-cold
defect-free circular atom chains can be prepared by a variant of the
evaporative cooling method. This method also leads to the individual detection
of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2
Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz.
All the model parameters can be tuned at will, making a large range of
simulations accessible. The system evolution can be followed over times in the
range of seconds, long enough to be relevant for ground-state adiabatic
preparation and for the study of thermalization, disorder or Floquet time
crystals. This platform presents unrivaled features for quantum simulation
Microwave probes Dipole Blockade and van der Waals Forces in a Cold Rydberg Gas
We show that microwave spectroscopy of a dense Rydberg gas trapped on a
superconducting atom chip in the dipole blockade regime reveals directly the
dipole-dipole many-body interaction energy spectrum. We use this method to
investigate the expansion of the Rydberg cloud under the effect of repulsive
van der Waals forces and the breakdown of the frozen gas approximation. This
study opens a promising route for quantum simulation of many-body systems and
quantum information transport in chains of strongly interacting Rydberg atoms.Comment: PACS: 03.67.-a, 32.80.Ee, 32.30.-
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