On the dynamics created by a time--dependent Aharonov-Bohm flux

We study the dynamics of classical and quantum particles moving in a punctured plane under the influence of a homogeneous magnetic field and driven by a time-dependent singular flux tube through the hole

Dynamics of a classical Hall system driven by a time-dependent Aharonov--Bohm flux

We study the dynamics of a classical particle moving in a punctured plane under the influence of a strong homogeneous magnetic field, an electrical background, and driven by a time-dependent singular flux tube through the hole. We exhibit a striking classical (de)localization effect: in the far past the trajectories are spirals around a bound center; the particle moves inward towards the flux tube loosing kinetic energy. After hitting the puncture it becomes ``conducting'': the motion is a cycloid around a center whose drift is outgoing, orthogonal to the electric field, diffusive, and without energy loss

Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux

We study the dynamics of a quantum particle moving in a plane under the influence of a constant magnetic field and driven by a slowly time-dependent singular flux tube through a puncture. The known adiabatic results do not cover these models as the Hamiltonian has time dependent domain. We give a meaning to the propagator and prove an adiabatic theorem. To this end we introduce and develop the new notion of a propagator weakly associated to a time-dependent Hamiltonian.Comment: Title and Abstract changed, will appear in Journal of Mathematical Physic

A constant of quantum motion in two dimensions in crossed magnetic and electric fields

We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial invariant of motion. Do to so we proof that the Hamiltonian is unitarily equivalent to an effective Hamiltonian which commutes with the observable of kinetic energy.Comment: 18 pages, 2 figures; the title was changed and several typos corrected; to appear in J. Phys. A: Math. Theor. 43 (2010

Unanimity Rule on networks

We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e. a node will change its (binary) state only if all of its neighbours have the same corresponding state. It is shown that a transition takes place depending on the initial condition of the problem. In particular, a critical number of initially activated nodes is needed so that the whole system gets activated in the long-time limit. The influence of the degree distribution of the nodes is naturally taken into account. For simple network topologies we solve the model analytically, the cases of random, small-world and scale-free are studied in detail.Comment: 7 pages 4 fig

Adjoint approach to the physical characterization of a shallow-water environment

In underwater acoustics a variety of different applications of adjoint models has been proposed in recent years. Adjoints have been derived for normal modes and for both the standard parabolic equation and Claerbout’s wide-angle approximation. This paper reviews the analytic nonlocal boundary control approach proposed in an earlier paper by the authors [Meyer & Hermand, ‘‘Optimal nonlocal boundary control of the wide-angle parabolic equation for inversion of a waveguide acoustic field,’’ J. Acoust. Soc. Am. 117, 2937–2948 (2005)] and presents a numerical extension that allows direct inversion of the geoacoustic parameters that are embedded in a discrete representation of the nonlocal boundary condition at the water-sediment interface. The effectiveness of this numerical adjoint approach for the physical characterization of a shallow-water environment is illustrated with applications for geoacoustic inversion and ocean acoustic tomography. In particular, it is shown how a joint inversion across multiple frequencies can enhance the performance of the optimization process, especially for the case of a sparse receiver array spanning part of the water column. In an additional example we combine the two applications and discuss the feasibility of geoacoustic inversion in the presence of an uncertain sound-speed profile

A numerical adjoint parabolic equation (PE) method for tomography and geoacoustic inversion in shallow water

Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937–2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK ’94 experimental conditions

Validation of adjoint-generated environmental gradients for the acoustic monitoring of a shallow water area

In the framework of the recent Maritime Rapid Environmental Assessment sea trial MREA07/BP'07 [Le Gac&Hermand, 2007] that was conducted in the same area south of the island of Elba as the earlier Yellow Shark trial (YS94), this paper examines the original YS94 acoustic data and the recent MREA07 oceanographic data to demonstrate adjoint-based acoustic monitoring of environmental parameters in Mediterranean shallow waters. First, adjoint-generated environmental gradients are validated for the application in geoacoustic inversion where the bottom acoustic parameters of the YS94 layered seabed are determined from the long-range waterborne propagation of a multi-frequency signal. Then, for the application in ocean acoustic tomography, the temporal variability of the MREA07/BP'07 oceanographic data is analyzed in terms of empirical orthogonal functions and the adjoint-based inversion scheme is used to track the time-varying sound speed profile of the experimental transect

A variational approach for geoacoustic inversion using adjoint modeling of a PE approximation model with non local impedance boundary conditions

The adjoint model method of control theory is known to give accurate and efficient data assimilation processes in oceanography and meteorology. However, it has rarely been applied in underwater acoustics for inversion purposes. Based on the back-propagation of the mismatch between observations and their predictions, the adjoint model can produce the corrections to the associated direct forward model input parameters. In this paper, the adjoint of a parabolic equation propagation model with non local impedance boundary conditions at the water sediment interface is used in order to determine an acoustically equivalent representation of the seabed. The bottom is represented by these boundary conditions that play the role of the control parameter