An EBE finite element method for simulating nonlinear flows in rotating spheroidal cavities

Many planetary and astrophysical bodies are rotating rapidly, fluidic and, as a consequence of rapid rotation, in the shape of an ablate spheroid. We present an efficient element-by-element (EBE) finite element method for the numerical simulation of nonlinear flows in rotating incompressible fluids that are confined in an ablate spheroidal cavity with arbitrary eccentricity. Our focus is placed on temporal and spatial tetrahedral discretization of the EBE finite element method in spheroidal geometry, the EBE parallelization scheme and the validation of the nonlinear spheroidal code via both the constructed exact nonlinear solution and the special resonant forcing in the inviscid limit. Copyright © 2009 John Wiley & Sons, Ltd.postprin

The sidewall-localized mode in a resonant precessing cylinder

ArticleWe investigate, via direct numerical simulation using a finite-element method, the precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. Our numerical simulation, after validating with the asymptotic analytical solution for a weakly precessing cylinder and with the constructed exact solution for the strongly nonlinear problem, focuses on the strongly precessing flow at asymptotically small Ekman numbers. An unusual form of the resonant precessing flow is found when the precessing rate is sufficiently large and the corresponding nonlinearity is sufficiently strong. The nonlinear precessing flow is marked by a sidewall-localized non-axisymmetric traveling wave and a wall-localized axisymmetric shear together with an overwhelmingly dominant interior rigid-body rotation whose direction and magnitude substantially reduce the angular momentum of the rotating fluid system.K.Z. is supported by grants from UK Science and Technology Facilities Council and Natural Environment Research Council. X.L. is supported by National Natural Science Foundation of China/11133004 and Chinese Academy of Sciences under Grant Nos. KZZD-EW-01-3 and XDB09000000

Equatorial Zonal Jets and Jupiter’s Gravity

ArticleThe depth of penetration of Jupiter’s zonal winds into the planet’s interior is unknown. A possible way to determine the depth is to measure the effects of the winds on the planet’s high-order zonal gravitational coefficients, a task to be undertaken by the Juno spacecraft. It is shown here that the equatorial winds alone largely determine these coefficients which are nearly independent of the depth of the non-equatorial winds.X.L. is supported by NSFC/11133004 and CAS under grant numbers KZZD-EW-01-3 and XDB09000000, K.Z. is supported by UK NERC and STFC grants and G.S. is supported by the National Science Foundation under grant NSF AST-0909206. The parallel computation is supported by the Shanghai Supercomputer Center

On nonlinear multiarmed spiral waves in slowly rotating systems

Stable nonlinear equilibria of convection in the form of quasistationary, multiarmed spiral waves, up to a maximum of six spiral arms, are found in a slowly rotating fluid confined within a thin spherical shell governed by the three-dimensional Navier–Stokes equation, driven by a radial unstable temperature gradient and affected by a weak Coriolis force. It is shown that three essential ingredients are generally required for the formation of the multiarmed spirals: the influence of slow rotation, large-aspect-ratio geometry and the effect of weak nonlinearity.published_or_final_versio

The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration

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The shape, internal structure and gravity of the fast spinner β Pictoris b

ArticleA young extrasolar gas giant planet, β Pictoris b, recently discovered in the β Pictoris system, spins substantially faster than the giant gas planets Jupiter and Saturn. Based on the newly measured parameters – the rotation period of the planet, its mass and radius – together with an assumption that the gas planet β Pictoris b is in hydrostatic equilibrium and made of a fully compressible barotropic gas with a polytropic index of unity, we are able to compute, via a hybrid inverse method, its non-spherical shape, internal density/pressure distribution and gravitational zonal coefficients up to degree 8. Since the mass Mβ for the planet β Pictoris b is highly uncertain, various models with different values of Mβ are studied in this Letter, providing the upper and lower bounds for its shape parameter as well as its gravitational zonal coefficients. If Mβ is assumed to be 6MJ with MJ being Jupiter's mass, we show that the shape of the planet β Pictoris b is approximately described by an oblate spheroid whose eccentricity at the one-bar surface is E β =0.36928 Eβ=0.36928 with the gravitational coefficient (J2)β = +15 375.972 × 10−6. It follows that our results open the possibility of constraining or inferring the mass Mβ of the planet β Pictoris b if its shape can be measured or constrained. By assuming that the planet β Pictoris b will shrink to the size of Jupiter in the process of cooling down and, hence, rotate much faster, we also calculate the future shape and internal structure of the planet β Pictoris b.XL is supported by NSFC/11133004 and CAS under grant numbers KZZD-EW-01-3 and XDB09000000, KZ is supported by UK NERC and STFC grants and GS is supported by the National Science Foundation under grant NSF AST-0909206. The parallel computation is supported by the Shanghai Supercomputer Center

π+π+\pi^+\pi^+ and π+π−\pi^+\pi^- colliding in noncommutative space

By studying the scattering process of scalar particle pion on the noncommutative scalar quantum electrodynamics, the non-commutative amendment of differential scattering cross-section is found, which is dependent of polar-angle and the results are significantly different from that in the commutative scalar quantum electrodynamics, particularly when $\cos\theta\sim \pm 1$. The non-commutativity of space is expected to be explored at around $\Lambda_{NC}\sim$TeV.Comment: Latex, 12 page

A Java Graphical User Interface for Large-Scale Scientific Computations in Distributed Systems

Large-scale scientific applications present great challenges to computational scientists in terms of obtaining high performance and in managing large datasets. These applications (most of which are simulations) may employ multiple techniques and resources in a heterogeneously distributed environment. Effective working in such an environment is crucial for modern large-scale simulations. In this paper, we present an integrated Java graphical user interface (IJ-GUI) that provides a control platform for managing complex programs and their large datasets easily. As far as performance is concerned, we present and evaluate our initial implementation of two optimization schemes: data replication and data prediction. Data replication can take advantage of \u27temporal locality\u27 by caching the remote datasets on local disks; data prediction, on the other hand, provides prefetch hints based on the datasets\u27 past activities that are kept in databases. We first introduce the data contiguity concept in such an environment that guides data prediction. The relationship between the two approaches is discussed

The decay rate of ψ(2S)\psi(2S) to Λc+Σ+ˉ\Lambda_c+\bar{\Sigma^+} in SM and beyond

With rapid growth of the database of the BES III and the proposed super flavor factory, measurement on the rare $\psi(2S)$ decays may be feasible, especially the weak decays into baryon final states. In this work we study the decay rate of $\psi(2S)$ to $\Lambda_c+\overline{\Sigma^+}$ in the SM and physics beyond the SM (here we use the unparticle model as an example). The QPC model is employed to describe the creation of a pair of $q\bar q$ from vacuum. We find that the rate of $\psi(2S)\rightarrow \Lambda_c+\overline{\Sigma^+}$ is at order of $10^{-10}$ in the SM, whereas the contribution of the unparticle is too small to be substantial. Therefore if a large branching ratio is observed, it must be due to new physics beyond SM, but by no means the unparticle.Comment: 9 pages, 1 figure