We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that these solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping.

We study tight-binding models of itinerant electrons in two different bands, with effective on-site interactions expressing Coulomb repulsion and Hund’s rule. We prove that, for sufficiently large on-site exchange anisotropy, all ground states show metallic ferromagnetism: They exhibit a macroscopic magnetization, a macroscopic fraction of the electrons is spatially delocalized, and there is no...

We investigate the possible occurrence of a positive cosmic acceleration in a spatially averaged, expanding, unbound Lemâitre-Tolman-Bondi cosmology. By studying an approximation in which the contribution of three-curvature dominates over the matter density, we construct numerical models which exhibit acceleration.

We investigate the possible occurrence of a positive cosmic acceleration in a spatially averaged, expanding, unbound Lemâıtre-Tolman-Bondi cosmology. By studying an approximation in which the contribution of three-curvature dominates over the matter density, we construct numerical models which exhibit acceleration.

Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local pop...

We compute joint AM-FM models that characterize infrared targets and backgrounds in the modulation domain. We consider spatially localized structures within an IR image as sums of nonstationary, quasi-sinusoidal functions admitting locally narrowband amplitude and frequency modulations. By quantitatively estimating the modulations that dominate the signal spectrum on a spatially local basis, we...