Shape transformations in rotating ferrofluid drops

Floating drops of magnetic fluid can be brought into rotation by applying a rotating magnetic field. We report theoretical and experimental results on the transition from a spheroid equilibrium shape to non-axissymmetrical three-axes ellipsoids at certain values of the external field strength. The transitions are continuous for small values of the magnetic susceptibility and show hysteresis for larger ones. In the non-axissymmetric shape the rotational motion of the drop consists of a vortical flow inside the drop combined with a slow rotation of the shape. Nonlinear magnetization laws are crucial to obtain quantitative agreement between theory and experiment.Comment: 4 pages, 3 figure

The MacMahon R-matrix

We introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs of $3d$ Young diagrams and retains the nice symmetry of the DIM algebra under the permutation of three deformation parameters $q$, $t^{-1}$ and $\frac{t}{q}$. We construct the intertwining operator for a tensor product of the horizontal Fock representation and the vertical MacMahon representation and show that the intertwiners are permuted using the MacMahon $R$-matrix.Comment: 39 page

Some remarks on one-dimensional force-free Vlasov-Maxwell equilibria

The conditions for the existence of force-free non-relativistic translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria are investigated using general properties of the 1D VM equilibrium problem. As has been shown before, the 1D VM equilibrium equations are equivalent to the motion of a pseudo-particle in a conservative pseudo-potential, with the pseudo-potential being proportional to one of the diagonal components of the plasma pressure tensor. The basic equations are here derived in a different way to previous work. Based on this theoretical framework, a necessary condition on the pseudo-potential (plasma pressure) to allow for force-free 1D VM equilibria is formulated. It is shown that linear force-free 1D VM solutions, which so far are the only force-free 1D VM solutions known, correspond to the case where the pseudo-potential is an attractive central potential. A general class of distribution functions leading to central pseudo-potentials is discussed.Comment: Physics of Plasmas, accepte

Entropy rate defined by internal wave scattering in long-range propagation

Author Posting. © Acoustical Society of America, 2015. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 138 (2015): 1353, doi:10.1121/1.4928617.The reduction of information capacity of the ocean sound channel due to scattering by internal waves is a potential problem for acoustic communication, navigation, and remote sensing over long ranges. In spite of recent progress in research on acoustic signal scattering by random internal waves and the fact that random internal waves are ubiquitous in the world oceans, there is no clear understanding of how these waves influence data communication performance. The entropy decrease resulting from scattering by internal waves is an important measure of information loss. Here a rigorous calculation of the entropy is carried out using second moment transport theory equations with random sound-speed perturbations obeying the Garrett–Munk internal-wave model. It is shown that full-wave rate of entropy is of the same order of magnitude as the Kolmogorov–Sinai entropy and Lyapunov exponents for the relevant ray trajectories. The correspondence between full-wave and ray entropies suggests a correspondence between full-wave scattering and ray chaos near statistical saturation. The relatively small level of entropy rate during propagation through the random internal-wave field shows that scattering by internal waves is likely not an essential limitation for data rate and channel capacity.This work was supported in part by Office of Naval Research grant

Giant Intrinsic Carrier Mobilities in Graphene and Its Bilayer

We have studied temperature dependences of electron transport in graphene and its bilayer and found extremely low electron-phonon scattering rates that set the fundamental limit on possible charge carrier mobilities at room temperature. Our measurements have shown that mobilities significantly higher than 200,000 cm2/Vs are achievable, if extrinsic disorder is eliminated. A sharp (threshold-like) increase in resistivity observed above approximately 200K is unexpected but can qualitatively be understood within a model of a rippled graphene sheet in which scattering occurs on intra-ripple flexural phonons

Electric Field Effect in Atomically Thin Carbon Films

We report a naturally-occurring two-dimensional material (graphene that can be viewed as a gigantic flat fullerene molecule, describe its electronic properties and demonstrate all-metallic field-effect transistor, which uniquely exhibits ballistic transport at submicron distances even at room temperature