Identification and mechanical control of ferroelastic domain structure in rhombohedral CaMn7_7O12_{12}

We report on observation of ferroelastic domain structure in single crystals of multiferroic CaMn$_7$O$_{12}$ at room temperature. Two types of ferroelastic domain wall are found, consistent with the material's rhombohedral symmetry that is reduced from cubic symmetry at higher temperatures. Using Raman spectroscopy along with other measurements, we develop a systematic method to determine the microscopic domain orientation. Moreover, we find a switching behavior of the domains, which allows us to detwin the crystals conveniently at room temperature using a moderate uniaxial compression. Our result paves the way for further spectroscopic study and domain engineering in CaMn$_7$O$_{12}$.Comment: 7 pages, 4 figure

3D mixing in hot Jupiter atmospheres. I. application to the day/night cold trap in HD 209458b

Hot Jupiters exhibit atmospheric temperatures ranging from hundreds to thousands of Kelvin. Because of their large day-night temperature differences, condensable species that are stable in the gas phase on the dayside, such as TiO and silicates, may condense and gravitationally settle on the nightside. Atmospheric circulation may counterbalance this tendency to gravitationally settle. This three dimensional (3D) mixing of chemical species has not previously been studied for hot Jupiters, yet it is crucial to assess the existence and distribution of TiO and silicates in the atmospheres of these planets. We perform 3D global circulation models of HD209458b including passive tracers that advect with the 3D flow, including a source/sink on the nightside to represent condensation and gravitational settling of haze particles. We show that global advection patterns produce strong vertical mixing that can keep condensable species lofted as long as they are trapped in particles of sizes of a few microns or less on the night side. We show that vertical mixing results not from small-scale convection but from the large-scale circulation driven by the day-night heating contrast. Although this vertical mixing is not diffusive in any rigorous sense, a comparison of our results with idealized diffusion models allows a rough estimate of the vertical diffusion coefficient. Kzz=5x10**4/Sqrt(Pbar) m2/s can be used in 1D models of HD 209458b. Moreover, our models exhibit strong spatial and temporal variability in the tracer concentration that could result in observable variations during transit or secondary eclipse measurements. Finally, we apply our model to the case of TiO in HD209458b and show that the day-night cold trap would deplete TiO if it condenses into particles bigger than a few microns on the planet's night side, making it unable to create the observed stratosphere of the planet.Comment: Accepted in A&A in August 2013 http://dx.doi.org/10.1051/0004-6361/20132113

Soft vibrational mode associated with incommensurate orbital order in multiferroic CaMn7_7O12_{12}

We report inelastic light scattering measurements of lattice dynamics related to the incommensurate orbital order in $\mathrm{CaMn_7O_{12}}$. Below the ordering temperature $T_\mathrm{o} \approx 250 \,\mathrm{K}$, we observe extra phonon peaks as a result of Brillouin-zone folding, as well as a soft vibrational mode with a power-law $T$-dependent energy, $\Omega = \Omega_{0}(1 - T/T_{\mathrm{o}})^{1/2}$. This temperature dependence demonstrates the second-order nature of the transition at $T_\mathrm{o}$, and it indicates that the soft mode can be regarded as the amplitude excitation of the composite order parameter. Our result strongly suggests that the lattice degrees of freedom are actively involved in the orbital-ordering mechanism.Comment: 7 pages, 8 figure

Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains

Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored. This paper aims at developing accurate spectral methods using rational basis (or modified mapped Gegenbauer functions) for such models in unbounded domains. The main building block of the spectral algorithms is the explicit representations for the Fourier transform and fractional Laplacian of the rational basis, derived from some useful integral identites related to modified Bessel functions. With these at our disposal, we can construct rational spectral-Galerkin and direct collocation schemes by pre-computing the associated fractional differentiation matrices. We obtain optimal error estimates of rational spectral approximation in the fractional Sobolev spaces, and analyze the optimal convergence of the proposed Galerkin scheme. We also provide ample numerical results to show that the rational method outperforms the Hermite function approach

Dark matter coupling to electroweak gauge and Higgs bosons: an effective field theory approach

If dark matter is a new species of particle produced in the early universe as a cold thermal relic (a weakly-interacting massive particle-WIMP), its present abundance, its scattering with matter in direct-detection experiments, its present-day annihilation signature in indirect-detection experiments, and its production and detection at colliders, depend crucially on the WIMP coupling to standard-model (SM) particles. It is usually assumed that the WIMP couples to the SM sector through its interactions with quarks and leptons. In this paper we explore the possibility that the WIMP coupling to the SM sector is via electroweak gauge and Higgs bosons. In the absence of an ultraviolet-complete particle-physics model, we employ effective field theory to describe the WIMP--SM coupling. We consider both scalars and Dirac fermions as possible dark-matter candidates. Starting with an exhaustive list of operators up to dimension 8, we present detailed calculation of dark-matter annihilations to all possible final states, including gamma gamma, gamma Z, gamma h, ZZ, Zh, W+ W-, hh, and f fbar, and demonstrate the correlations among them. We compute the mass scale of the effective field theory necessary to obtain the correct dark-matter mass density, and well as the resulting photon line signals