Analytical studies of particle dynamics in bending waves in planetary rings

Particles inside a planetary ring are subject to forcing due to the central planet, moons in inclined orbits, self-gravity of the ring and other forces due to radiation drag, collisional effects and Lorentz force due to magnetic field of the planet. We write down the equations of motion of a single particle inside the ring and solve them analytically. We find that the importance of the shear caused by variation of the radial velocity component with local vertical direction cannot be ignored and it may be responsible for damping of the bending waves in planetary rings as observed by the Voyager data. We present the wave profile resulting from the dissipation. We estimate that the surface mass density of the C ring to be of the order of $\sigma \sim 1.2-1.6$gm cm$^{-2}$, and the height $h \sim 2.2-2.4$m. These theoretical results are in agreement with observations.Comment: 17 pages 3 figures MNRAS (In press

Spatial Structure and Coherent Motion in Dense Planetary Rings Induced by Self-Gravitational Instability

We investigate the formation of spatial structure in dense, self-gravitating particle systems such as Saturn's B-ring through local $N$-body simulations to clarify the intrinsic physics based on individual particle motion. In such a system, Salo (1995) showed that the formation of spatial structure such as wake-like structure and particle grouping (clump) arises spontaneously due to gravitational instability and the radial velocity dispersion increases as the formation of the wake structure. However, intrinsic physics of the phenomena has not been clarified. We performed local $N$-body simulations including mutual gravitational forces between ring particles as well as direct (inelastic) collisions with identical (up to $N\sim40000$) particles. In the wake structure particles no longer move randomly but coherently. We found that particle motion was similar to Keplerian motion even in the wake structure and that the coherent motion was produced since the particles in a clump had similar eccentricity and longitude of perihelion. This coherent motion causes the increase and oscillation in the radial velocity dispersion. The mean velocity dispersion is rather larger in a more dissipative case with a smaller restitution coefficient and/or a larger surface density since the coherence is stronger in the more dissipative case. Our simulations showed that the wavelength of the wake structure was approximately given by the longest wavelength \hs{\lambda}{cr} = 4\pi^2 G\Sigma/\kappa^2 in the linear theory of axisymmetric gravitational instability in a thin disk, where $G$, $\Sigma$, and $\kappa$ are the gravitational constant, surface density, and a epicyclic frequency.Comment: Accepted by Earth, Planets, and Space. 39 pages, 20 figures. PostScript files also available from http://www.geo.titech.ac.jp/nakazawalab/hdaisaka/works

The method of R-functions in the solution of elastic problems on the basis of reissner`s mixed variational principle

A method is presented for solving boundary-value elastic problems on the basis of the variational–structural method of R-functions and Reissner’s mixed variational principle. A mathematical formulation is given to problems on the deformation of elastic bodies under mixed boundary conditions and bodies interacting with smooth rigid dies. Solutions satisfying all the boundary conditions are proposed. For undetermined components of these solutions, the resolving equations are derived and their properties are studied. A posteriori estimation of numerical solutions is made. As examples, solutions are found to a problem on the stress–strain state of a short cylinder and to a contact problem on a cylinder interacting with a smooth die. A numerical method of solving such problems is analyzed for convergence, and the accuracy of the solutions is estimated

Limiting Carleman weights and anisotropic inverse problems

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a complex geometrical optics construction for a class of such manifolds. This is used to prove uniqueness results for anisotropic inverse problems, via the attenuated geodesic X-ray transform. Earlier results in dimension $n \geq 3$ were restricted to real-analytic metrics.Comment: 58 page

Effect of neck strength training on health-related quality of life in females with chronic neck pain: a randomized controlled 1-year follow-up study

Abstract Background Chronic neck pain is a common condition associated not only with a decrease in neck muscle strength, but also with decrease in health-related quality of life (HRQoL). While neck strength training has been shown to be effective in improving neck muscle strength and reducing neck pain, HRQoL among patients with neck pain has been reported as an outcome in only two short-term exercise intervention studies. Thus, reports on the influence of a long-term neck strength training intervention on HRQoL among patients with chronic neck pain have been lacking. This study reports the effect of one-year neck strength training on HRQoL in females with chronic neck pain. Methods One hundred eighty female office workers, 25 to 53 years of age, with chronic neck pain were randomized to a strength training group (STG, n = 60), endurance training group (ETG, n = 60) or control group (CG, n = 60). The STG performed high-intensity isometric neck strengthening exercises with an elastic band while the ETG performed lighter dynamic neck muscle training. The CG received a single session of guidance on stretching exercises. HRQoL was assessed using the generic 15D questionnaire at baseline and after 12 months. Statistical comparisons among the groups were performed using bootstrap-type analysis of covariance (ANCOVA) with baseline values as covariates. Effect sizes were calculated using the Cohen method for paired samples. Results Training led to statistically significant improvement in the 15D total scores for both training groups, whereas no changes occurred for the control group (P = 0.012, between groups). The STG improved significantly in five of 15 dimensions, while the ETG improved significantly in two dimensions. Effect size (and 95% confidence intervals) for the 15D total score was 0.39 (0.13 to 0.72) for the STG, 0.37 (0.08 to 0.67) for the ETG, and -0.06 (-0.25 to 0.15) for the CG. Conclusions One year of either strength or endurance training seemed to moderately enhance the HRQoL. Neck and upper body training can be recommended to improve HRQoL of females with neck pain if they are motivated for long-term regular exercise. Trial Registration ClinicalTrials.gov NCT01057836peerReviewe