Effect of weak fluid inertia upon Jeffery orbits

We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the "Jeffery orbits". We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. We analyse how the linear stability of the \lq log-rolling\rq{} orbit depends on particle shape and find it to be unstable for prolate spheroids. This resolves a puzzle in the interpretation of direct numerical simulations of the problem. In general both unsteady and non-linear terms in the Navier-Stokes equations are important.Comment: 5 pages, 2 figure

Settling of an asymmetric dumbbell in a quiescent fluid

We compute the hydrodynamic torque on a dumbbell (two spheres linked by a massless rigid rod) settling in a quiescent fluid at small but finite Reynolds number. The spheres have the same mass densities but different sizes. When the sizes are quite different the dumbbell settles vertically, aligned with the direction of gravity, the largest sphere first. But when the size difference is sufficiently small then its steady-state angle is determined by a competition between the size difference and the Reynolds number. When the sizes of the spheres are exactly equal then fluid inertia causes the dumbbell to settle in a horizontal orientation.Comment: 11 pages, 1 figure, as publishe

Rotation of a spheroid in a simple shear at small Reynolds number

We derive an effective equation of motion for the orientational dynamics of a neutrally buoyant spheroid suspended in a simple shear flow, valid for arbitrary particle aspect ratios and to linear order in the shear Reynolds number. We show how inertial effects lift the degeneracy of the Jeffery orbits and determine the stabilities of the log-rolling and tumbling orbits at infinitesimal shear Reynolds numbers. For prolate spheroids we find stable tumbling in the shear plane, log-rolling is unstable. For oblate particles, by contrast, log-rolling is stable and tumbling is unstable provided that the aspect ratio is larger than a critical value. When the aspect ratio is smaller than this value tumbling turns stable, and an unstable limit cycle is born.Comment: 25 pages, 5 figure

The role of inertia for the rotation of a nearly spherical particle in a general linear flow

We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur

Direct Calculation of the Spin Stiffness in the J1J_1--J2J_2 Heisenberg Antiferromagnet

We calculate the spin stiffness $\rho_s$ for the frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on a square lattice by exact diagonalizations on finite clusters of up to $36$ sites followed by extrapolations to the thermodynamic limit. For the non-frustrated case, we find that $\rho_s = (0.183\pm 0.003)J_1$, in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated stiffness vanishes for $0.4 \lesssim J_2/J_1 \lesssim 0.6$. In this intermediate region, the finite-size scaling works poorly -- an additional sign that their is neither N\'eel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the N\'eel-ordered region.Comment: 4 pages, uuencoded compressed ps-file (made with uufiles

Glacio-isostatic deformation around the Vatnajokull ice cap, Iceland, induced by recent climate warming: GPS observations and finite element modeling

Glaciers in Iceland began retreating around 1890, and since then the Vatnajökull ice cap has lost over 400 km3 of ice. The associated unloading of the crust induces a glacio‐isostatic response. From 1996 to 2004 a GPS network was measured around the southern edge of Vatnajökull. These measurements, together with more extended time series at several other GPS sites, indicate vertical velocities around the ice cap ranging from 9 to 25 mm/yr, and horizontal velocities in the range 3 to 4 mm/yr. The vertical velocities have been modeled using the finite element method (FEM) in order to constrain the viscosity structure beneath Vatnajökull. We use an axisymmetric Earth model with an elastic plate over a uniform viscoelastic half‐space. The observations are consistent with predictions based on an Earth model made up of an elastic plate with a thickness of 10–20 km and an underlying viscosity in the range 4–10 × 1018 Pa s. Knowledge of the Earth structure allows us to predict uplift around Vatnajökull in the next decades. According to our estimates of the rheological parameters, and assuming that ice thinning will continue at a similar rate during this century (about 4 km3/year), a minimum uplift of 2.5 meters between 2000 to 2100 is expected near the current ice cap edge. If the thinning rates were to double in response to global warming (about 8 km3/year), then the minimum uplift between 2000 to 2100 near the current ice cap edge is expected to be 3.7 meters

Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene

We have measured a strictly linear pi-plasmon dispersion along the axis of individualized single wall carbon nanotubes, which is completely different from plasmon dispersions of graphite or bundled single wall carbon nanotubes. Comparative ab initio studies on graphene based systems allow us to reproduce the different dispersions. This suggests that individualized nanotubes provide viable experimental access to collective electronic excitations of graphene, and it validates the use of graphene to understand electronic excitations of carbon nanotubes. In particular, the calculations reveal that local field effects (LFE) cause a mixing of electronic transitions, including the 'Dirac cone', resulting in the observed linear dispersion

Modified Spin Wave Thoery of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The ground state of the square lattice bilayer quantum antiferromagnet with nearest and next-nearest neighbour intralayer interaction is studied by means of the modified spin wave method. For weak interlayer coupling, the ground state is found to be always magnetically ordered while the quantum disordered phase appear for large enough interlayer coupling. The properties of the disordered phase vary according to the strength of the frustration. In the regime of weak frustration, the disordered ground state is an almost uncorrelated assembly of interlayer dimers, while in the strongly frustrated regime the quantum spin liquid phase which has considerable N\'eel type short range order appears. The behavior of the sublattice magnetization and spin-spin correlation length in each phase is discussed.Comment: 15 pages, revtex, figures upon reques

Quantum Phase Transition in the Frustrated Heisenberg Antiferromagnet

Using the J_1-J_2 model, we present a description of quantum phase transition from Neel ordered to the spin-liquid state based on the modified spin wave theory. The general expression for the gap in the spectrum in the spin-liquid phase is presented.Comment: 8 pages of REVTeX 3.0, one PostScript file appended (Eq. 15 corrected, two recent references added, + some minor changes

Anomalous Spin Dynamics observed by High Frequency ESR in Honeycomb Lattice Antiferromagnet InCu2/3V1/3O3

High-frequency ESR results on the S=1/2 Heisenberg hexagonal antiferromagnet InCu2/3V1/3O3 are reported. This compound appears to be a rare model substance for the honeycomb lattice antiferromagnet with very weak interlayer couplings. The high-temperature magnetic susceptibility can be interpreted by the S=1/2 honeycomb lattice antiferromagnet, and it shows a magnetic-order-like anomaly at TN=38 K. Although, the resonance field of our high-frequency ESR shows the typical behavior of the antiferromagnetic resonance, the linewidth of our high-frequency ESR continues to increase below TN, while it tends to decrease as the temperature in a conventional three-dimensional antiferromagnet decreases. In general, a honeycomb lattice antiferromagnet is expected to show a simple antiferromagnetic order similar to that of a square lattice antiferromagnet theoretically because both antiferromagnets are bipartite lattices. However, we suggest that the observed anomalous spin dynamics below TN is the peculiar feature of the honeycomb lattice antiferromagnet that is not observed in the square lattice antiferromagnet.Comment: 5 pages, 5 figure