Curl free pressure gradients over orography in a solution of the fully compressible Euler equations with implicit treatment of acoustic and gravity waves

Steep orography can cause noisy solutions and instability in models of the atmosphere. A new technique for modelling flow over orography is introduced which guarantees curl free gradients on arbitrary grids, implying that the pressure gradient term is not a spurious source of vorticity. This mimetic property leads to better hydrostatic balance and better energy conservation on test cases using terrain following grids. Curl-free gradients are achieved by using the co-variant components of velocity over orography rather than the usual horizontal and vertical components. In addition, gravity and acoustic waves are treated implicitly without the need for mean and perturbation variables or a hydrostatic reference profile. This enables a straightforward description of the implicit treatment of gravity waves. Results are presented of a resting atmosphere over orography and the curl-free pressure gradient formulation is advantageous. Results of gravity waves over orography are insensitive to the placement of terrain-following layers. The model with implicit gravity waves is stable in strongly stratified conditions, with N∆t up to at least 10 (where N is the Brunt-V ̈ais ̈al ̈a frequency). A warm bubble rising over orography is simulated and the curl free pressure gradient formulation gives much more accurate results for this test case than a model without this mimetic property.

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Distinct behavioral phenotypes in male mice lacking the thyroid hormone receptor alpha1 or beta isoforms

Thyroid hormones influence both neuronal development and anxiety via the thyroid hormone receptors (TRs). The TRs are encoded by two different genes, TRalpha and TRbeta. The loss of TRalpha1 is implicated in increased anxiety in males, possibly via a hippocampal increase in GABAergic activity. We compared both social behaviors and two underlying and related non-social behaviors, state anxiety and responses to acoustic and tactile startle in the gonadally intact TRalpha1 knockout (alpha1KO) and TRbeta (betaKO) male mice to their wild-type counterparts. For the first time, we show an opposing effect of the two TR isoforms, TRalpha1 and TRbeta, in the regulation of state anxiety, with alpha1 knockout animals (alpha1KO) showing higher levels of anxiety and betaKO males showing less anxiety compared to respective wild-type mice. At odds with the increased anxiety in non-social environments, alpha1KO males also show lower levels of responsiveness to acoustic and tactile startle stimuli. Consistent with the data that T4 is inhibitory to lordosis in female mice, we show subtly increased sex behavior in alpha1KO male mice. These behaviors support the idea that TRalpha1 could be inhibitory to ERalpha driven transcription that ultimately impacts ERalpha driven behaviors such as lordosis. The behavioral phenotypes point to novel roles for the TRs, particularly in non-social behaviors such as state anxiety and startle.