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

Extensive chaos in Rayleigh-Bénard convection

Using large-scale numerical calculations we explore spatiotemporal chaos in Rayleigh-Bénard convection for experimentally relevant conditions. We calculate the spectrum of Lyapunov exponents and the Lyapunov dimension describing the chaotic dynamics of the convective fluid layer at constant thermal driving over a range of finite system sizes. Our results reveal that the dynamics of fluid convection is truly chaotic for experimental conditions as illustrated by a positive leading-order Lyapunov exponent. We also find the chaos to be extensive over the range of finite-sized systems investigated as indicated by a linear scaling between the Lyapunov dimension of the chaotic attractor and the system size

Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.Comment: 5 pages, 2 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

Impact of Postovulatory Food Deprivation on the Ova Transport, Hormonal Profiles and Metabolic Changes in Sows

The effect of food deprivation on ova transport, hormonal profiles and metabolic changes was studied in 20 crossbred multiparous sows during their second oestrus after weaning. To determine the time of ovulation, transrectal ultrasonographic examination was performed. The sows were divided into 2 groups, one control group (C-group), which was fed according to Swedish standards, and one experimental group (E-group). The E-group sows were deprived of food from the first morning meal after ovulation until slaughter. Blood samples were collected every second hour from about 12 h before expected ovulation in the second oestrus after weaning until slaughter and were analysed for progesterone, prostaglandin F2α-metabolite, insulin, glucose, free fatty acids and triglycerides. All sows were slaughtered approximately 48 h after ovulation and the genital tract was recovered. The isthmic part of the oviduct was divided into 3 equally long segments and flushed separately with phosphate buffered saline (PBS). Uterine horns were also flushed with PBS. A significantly greater number of ova were found in the first and second part of the isthmus in the E-group (p = 0.05) while in the C-group most of the ova were found in the third part of the isthmus or the uterus (p = 0.01). The level of prostaglandin F2α-metabolite was significantly higher in the E-group compared with the C-group. The concentration of progesterone increased in both groups after ovulation but there were no significant differences between the groups. The other blood parameters showed that the food-deprived sows were in a catabolic state. The 48 h period of fasting results, directly or indirectly in an delayed ova transport, which may be due to a delayed relaxation in the smooth circular muscle layer of the isthmus

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

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