Ana Maria Luz - Academia.edu (original) (raw)

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Papers by Ana Maria Luz

Research paper thumbnail of Wave Packet Defocusing Due to a Highly Disordered Bathymetry

Studies in Applied Mathematics, 2013

Slowly modulated water waves are considered in the presence of a strongly disordered bathymetry. ... more Slowly modulated water waves are considered in the presence of a strongly disordered bathymetry. Previous work is extended to the case where the random bottom irregularities are not smooth and are allowed to be of large amplitude. Through the combination of a conformal mapping and a multiplescales asymptotic analysis it is shown that large variations of a disordered bathymetry can affect the nonlinearity coefficient of the resulting damped nonlinear Schrödinger equation. In particular it is shown that as the bathymetry fluctuation level increases the critical point (separating the focusing from the defocusing region) moves to the right, hence enlarging the region where the dynamics is of a defocusing character.

Research paper thumbnail of Nonlinear Stability Criteria for the HMF Model

Archive for Rational Mechanics and Analysis, 2017

We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the ... more We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a specific criterion, we prove the nonlinear stability of steady states which are decreasing functions of the microscopic energy. To achieve this task, we extend to this context the strategy based on generalized rearrangement techniques which was developed recently for the gravitational Vlasov-Poisson equation. Explicit stability inequalities are established and our analysis is able to treat non compactly supported steady states to HMF, which are physically relevant in this context but induces additional difficulties, compared to the Vlasov-Poisson system.

Research paper thumbnail of Nonlinear Instability of Inhomogeneous Steady States Solutions to the HMF Model

Journal of Statistical Physics, 2019

Research paper thumbnail of Wave Packet Defocusing Due to a Highly Disordered Bathymetry

Studies in Applied Mathematics, 2013

Slowly modulated water waves are considered in the presence of a strongly disordered bathymetry. ... more Slowly modulated water waves are considered in the presence of a strongly disordered bathymetry. Previous work is extended to the case where the random bottom irregularities are not smooth and are allowed to be of large amplitude. Through the combination of a conformal mapping and a multiplescales asymptotic analysis it is shown that large variations of a disordered bathymetry can affect the nonlinearity coefficient of the resulting damped nonlinear Schrödinger equation. In particular it is shown that as the bathymetry fluctuation level increases the critical point (separating the focusing from the defocusing region) moves to the right, hence enlarging the region where the dynamics is of a defocusing character.

Research paper thumbnail of Nonlinear Stability Criteria for the HMF Model

Archive for Rational Mechanics and Analysis, 2017

We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the ... more We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a specific criterion, we prove the nonlinear stability of steady states which are decreasing functions of the microscopic energy. To achieve this task, we extend to this context the strategy based on generalized rearrangement techniques which was developed recently for the gravitational Vlasov-Poisson equation. Explicit stability inequalities are established and our analysis is able to treat non compactly supported steady states to HMF, which are physically relevant in this context but induces additional difficulties, compared to the Vlasov-Poisson system.

Research paper thumbnail of Nonlinear Instability of Inhomogeneous Steady States Solutions to the HMF Model

Journal of Statistical Physics, 2019

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