Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit

We apply the dynamical approach to the study of the second order semi-linear elliptic boundary value problem in a cylindrical domain with a small parameter at the second derivative with respect to the "time" variable corresponding to the axis of the cylinder. We prove that, under natural assumptions on the nonlinear interaction function and the external forces, this problem possesses the uniform attractors and that these attractors tend to the attractor of the limit parabolic equation. Moreover, in case where the limit attractor is regular, we give the detailed description of the structure of these uniform attractors when the perturbation parameter is small enough, and estimate the symmetric distance between the perturbed and non-perturbed attractors

Ultrafast dynamics in the presence of antiferromagnetic correlations in electron-doped cuprate La2−x_{2-x}Cex_xCuO4±δ_{4\pm\delta}

We used femtosecond optical pump-probe spectroscopy to study the photoinduced change in reflectivity of thin films of the electron-doped cuprate La$_{2-x}$Ce$_x$CuO$_4$ (LCCO) with dopings of x$=$0.08 (underdoped) and x$=$0.11 (optimally doped). Above T$_c$, we observe fluence-dependent relaxation rates which onset at a similar temperature that transport measurements first see signatures of antiferromagnetic correlations. Upon suppressing superconductivity with a magnetic field, it is found that the fluence and temperature dependence of relaxation rates is consistent with bimolecular recombination of electrons and holes across a gap (2$\Delta_{AF}$) originating from antiferromagnetic correlations which comprise the pseudogap in electron-doped cuprates. This can be used to learn about coupling between electrons and high-energy ($\omega>2\Delta_{AF}$) excitations in these compounds and set limits on the timescales on which antiferromagnetic correlations are static

Doping-Dependent Nodal Fermi Velocity in Bi-2212 Revealed by High-Resolution ARPES

The improved resolution of laser-based angle-resolved photoemission spectroscopy (ARPES) allows reliable access to fine structures in the spectrum. We present a systematic, doping-dependent study of a recently discovered low-energy kink in the nodal dispersion of Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} (Bi-2212), which demonstrates the ubiquity and robustness of this kink in underdoped Bi-2212. The renormalization of the nodal velocity due to this kink becomes stronger with underdoping, revealing that the nodal Fermi velocity is non-universal, in contrast to assumed phenomenology. This is used together with laser-ARPES measurements of the gap velocity, v{sub 2}, to resolve discrepancies with thermal conductivity measurements

Dynamics of drag and force distributions for projectile impact in a granular medium

Our experiments and molecular dynamics simulations on a projectile penetrating a two-dimensional granular medium reveal that the mean deceleration of the projectile is constant and proportional to the impact velocity. Thus, the time taken for a projectile to decelerate to a stop is independent of its impact velocity. The simulations show that the probability distribution function of forces on grains is time-independent during a projectile's penetration of the medium. At all times the force distribution function decreases exponentially for large forces.Comment: 4 page

ARPES studies of cuprate Fermiology: superconductivity, pseudogap, and quasiparticle dynamics

We present angle-resolved photoemission spectroscopy (ARPES) studies of the cuprate high-temperature superconductors which elucidate the relation between superconductivity and the pseudogap and highlight low-energy quasiparticle dynamics in the superconducting state. Our experiments suggest that the pseudogap and superconducting gap represent distinct states, which coexist below T$_c$. Studies on Bi-2212 demonstrate that the near-nodal and near-antinodal regions behave differently as a function of temperature and doping, implying that different orders dominate in different momentum-space regions. However, the ubiquity of sharp quasiparticles all around the Fermi surface in Bi-2212 indicates that superconductivity extends into the momentum-space region dominated by the pseudogap, revealing subtlety in this dichotomy. In Bi-2201, the temperature dependence of antinodal spectra reveals particle-hole asymmetry and anomalous spectral broadening, which may constrain the explanation for the pseudogap. Recognizing that electron-boson coupling is an important aspect of cuprate physics, we close with a discussion of the multiple 'kinks' in the nodal dispersion. Understanding these may be important to establishing which excitations are important to superconductivity.Comment: To appear in a focus issue on 'Fermiology of Cuprates' in New Journal of Physic

Analytical Study of Certain Magnetohydrodynamic-alpha Models

In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-alpha (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes-alpha model). Specifically, we show the global well-posedness and regularity of solutions of a certain MHD-alpha model (which is a particular case of the Lagrangian averaged magnetohydrodynamic-alpha model without enhancing the dissipation for the magnetic field). We also introduce other subgrid scale turbulence models, inspired by the Leray-alpha and the modified Leray-alpha models of turbulence. Finally, we discuss the relation of the MHD-alpha model to the MHD equations by proving a convergence theorem, that is, as the length scale alpha tends to zero, a subsequence of solutions of the MHD-alpha equations converges to a certain solution (a Leray-Hopf solution) of the three-dimensional MHD equations.Comment: 26 pages, no figures, will appear in Journal of Math Physics; corrected typos, updated reference