Cold pools are fundamental ingredients of deep convection. They contribute to organizing the subcloud layer and are considered key elements in triggering convective cells. It was long known that this could happen mechanically, through lifting by the cold pools' fronts. More recently, it has been suggested that convection could also be triggered thermodynamically, by accumulation of moisture around the edges of cold pools. A method based on Lagrangian tracking is here proposed to disentangle the signatures of both forcings and quantify their importance in a given environment. Results from a simulation of radiative‐convective equilibrium over the ocean show that parcels reach their level of free convection through a combination of both forcings, each being dominant at different stages of the ascent. Mechanical forcing is an important player in lifting parcels from the surface, whereas thermodynamic forcing reduces the inhibition encountered by parcels before they reach their level of free convection.

We investigate different toric phases of 2+1 dimensional quiver gauge theories arising from M2-branes probing toric Calabi-Yau 4 folds. A brane tiling for each toric phase is presented. We apply the 'forward algorithm' to obtain the toric data of the mesonic moduli space of vacua and exhibit the equivalence between the vacua of different toric phases of a given singularity. The structures of the Master space, the mesonic moduli space, and the baryonic moduli space are examined in detail. We compute the Hilbert series and use them to verify the toric dualities between different phases. The Hilbert series, R-charges, and generators of the mesonic moduli space are matched between toric phases. arXiv:0903.3234v2 [hep-th] 9 Apr 2009 42 6. Phases of the Q 1,1,1 /Z 2 Theory 43 6.1 Phase I: The Four-Square Model 43 6.2 Phase II: The Two-Square and Two-Octagon Model 50 A. Permanent of the Kasteleyn Matrix and Coordinates of the Points in the Toric Diagram 55 Note added: During the completion of this work, we became aware of two relevant papers: One by Amariti, Forcella, Girardello and Mariotti [49], and one by Franco, Klebanov and Rodriguez-Gomez [50].1 There have also been studies on brane crystals [39,40,41,42], which are three-dimensional bipartite graphs, to establish the relation between 2+1 dimensional gauge theories and their moduli spaces which are Calabi-Yau 4 folds. However, in this paper, we focus only on brane tilings.Parity invariance. The parity operator commutes with the supersymmetry generators. Since all terms in (2.2) come from the second term of the supersymmetric Lagrangian (2.1),

The role of surface heat fluxes underneath cold pools is investigated using cloud‐resolving simulations with either interactive or horizontally homogenous surface heat fluxes over an ocean and a simplified land surface. Over the ocean, there are limited changes in the distribution of the cold pool temperature, humidity, and gust front velocity, yet interactive heat fluxes induce more cold pools, which are smaller, and convection is then less organized. Correspondingly, the updraft mass flux and lateral entrainment are modified. Over the land surface, the heat fluxes underneath cold pools drastically impact the cold pool characteristics with more numerous and smaller pools, which are warmer and more humid and accompanied by smaller gust front velocities. The interactive fluxes also modify the updraft mass flux and reduce convective organization. These results emphasize the importance of interactive surface fluxes instead of prescribed flux boundary conditions, as well as the formulation of surface heat fluxes, when studying convection.