Bubble bag end: a bubbly resolution of curvature singularity

We construct a family of smooth charged bubbling solitons in $$ \mathbbm{M} $$ M 4×T2, four-dimensional Minkowski with a two-torus. The solitons are characterized by a degeneration pattern of the torus along a line in $$ \mathbbm{M} $$ M 4 defining a chain of topological cycles. They live in the same parameter regime as non-BPS non-extremal four-dimensional black holes, and are ultracompact with sizes ranging from miscroscopic to macroscopic scales. The six-dimensional framework can be embedded in type IIB supergravity where the solitons are identified with geometric transitions of non-BPS D1-D5-KKm bound states. Interestingly, the geometries admit a minimal surface that smoothly opens up to a bubbly end of space. Away from the solitons, the solutions are indistinguishable from a new class of singular geometries. By taking a limit of large number of bubbles, the soliton geometries can be matched arbitrarily close to the singular spacetimes. This provides the first classical resolution of a curvature singularity beyond the framework of supersymmetry and supergravity by blowing up topological cycles wrapped by fluxes at the vicinity of the singularity.

How do transitions affect the wave overtopping flow locally as well as downstream?

<p>Wave overtopping on grass-covered dikes results in erosion of the dike cover. Once the dike cover is eroded, the core will be washed away and the dike breaches, leading to flooding of the hinterland. Transitions between grass covers and revetments or geometric transitions are vulnerable for cover erosion and are therefore the most likely locations to initiate dike breach. These transitions affect the overtopping flow and thereby the hydraulic load on the dike cover. For example, bed roughness differences can create additional turbulence and slope changes can result in the formation of a jet that increases the load at the jet impact location. Although it is known that dike cover failure often starts at transitions, the effect of transitions on the hydraulic load remains unknown.</p><p>We developed a detailed numerical 2DV model in OpenFOAM for the overtopping flow over the crest and the landward slope of a grass-covered dike. This model is used to study the effects of transitions on the overtopping flow variables including the flow velocity, shear stress, normal stress and pressure. Several types of transitions are studied such as revetment transitions, slope changes and height differences. </p><p>The results show that the shear stress, normal stress and pressure increase significantly at geometric transitions such as the transition from the crest to the slope and at the landward toe. The increase depends on the wave volume and the geometry of the dike such as the steepness and length of the landward slope. Furthermore, the results show that roughness changes at revetment transition on a grass-covered crest has no influence on the maximum shear stress, maximum normal stress and maximum pressure. The flow velocity increases from a rough to a smooth revetment, while the opposite occurs for the transition from a smooth to a rough revetment. The variation in the flow velocity is well described by analytical formulas for the maximum flow velocity along the dike profile. These formulas are also able to describe the variation in flow velocity for a revetment transition on a berm on the landward slope. In this case, the shear stress increases from a smooth to a rough revetment and decreases from a rough to a smooth revetment. This means that a rough revetment can locally reduce the shear stress, however the transitions have no effect on the shear stress downstream.</p><p>These model results are used to obtain relations for the increase in the hydraulic variables at transitions. These relations can be used to describe the effect of transitions on the hydraulic load in models for grass cover failure by overtopping waves. Accurate descriptions of the hydraulic load in these models will improve the failure assessment of grass-covered dikes with transitions.</p>

MODELLING OF WAVE OVERTOPPING FLOW OVER COMPLEX DIKE GEOMETRIES: CASE STUDY OF THE AFSLUITDIJK

Grass cover erosion by overtopping waves is one of the main failure mechanisms of dikes. Transitions in cover type and geometry can increase the hydraulic load and are therefore identified as vulnerable locations for grass cover erosion. Two models are applied to the inner slope of the Afsluitdijk in the Netherlands to show how transitions can be included in overtopping models. Firstly, the analytical grass-erosion model is used to simulate the erosion depth along the profile for a six-hour storm. The model results show that the erosion depth is maximal at the end of the two slopes in the profile. Secondly, the effect of transitions on the hydraulic load is computed with a detailed hydrodynamic model. The model results show that geometric transitions significantly influence the shear stress, the normal stress and the pressure. Four vulnerable locations for grass cover erosion are identified based on the model results that are related to slope changes along the profile. Furthermore, the model results show that the overtopping flow is mainly affected by geometric transitions, while no effect of roughness transitions on the modelled forces was observed.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/t1cPJwf72nE

The ESCRTs – converging on mechanism

ABSTRACTThe endosomal sorting complexes required for transport (ESCRTs) I, -II and –III, and their associated factors are a collection of ∼20 proteins in yeast and ∼30 in mammals, responsible for severing membrane necks in processes that range from multivesicular body formation, HIV release and cytokinesis, to plasma and lysosomal membrane repair. ESCRTs are best known for ‘reverse-topology’ membrane scission, where they act on the inner surface of membrane necks, often when membranes are budded away from the cytosol. These events are driven by membrane-associated assemblies of dozens to hundreds of ESCRT molecules. ESCRT-III proteins form filaments with a variety of geometries and ESCRT-I has now been shown to also form helical structures. The complex nature of the system and the unusual topology of its action has made progress challenging, and led to controversies with regard to its underlying mechanism. This Review will focus on recent advances obtained by structural in vitro reconstitution and in silico mechanistic studies, and places them in their biological context. The field is converging towards a consensus on the broad outlines of a mechanism that is driven by a progressive ATP-dependent treadmilling exchange of ESCRT subunits, as well as compositional change and geometric transitions in ESCRT filaments.

Toric Degenerations and Laurent Polynomials Related to Givental's Landau–Ginzburg Models

For an appropriate class of Fano complete intersections in toric varieties, we prove that there is a concrete relationship between degenerations to speciûc toric subvarieties and expressions for Givental's Landau–Ginzburg models as Laurent polynomials. As a result, we show that Fano varieties presented as complete intersections in partial flag manifolds admit degenerations to Gorenstein toric weak Fano varieties, and their Givental Landau–Ginzburg models can be expressed as corresponding Laurent polynomials.We also use this to show that all of the Laurent polynomials obtained by Coates, Kasprzyk and Prince by the so–called Przyjalkowski method correspond to toric degenerations of the corresponding Fano variety. We discuss applications to geometric transitions of Calabi–Yau varieties.

Deforming geometric transitions

After a quick review of the wild structure of the complex moduli space of Calabi-Yau 3-folds and the role of geometric transitions in this context (the Calabi-Yau web) the concept of deformation equivalence for geometric transitions is introduced to understand the arrows of the Gross–Reid Calabi-Yau web as deformation-equivalence classes of geometric transitions. Then the focus will be on some results and suitable examples to understand under which conditions it is possible to get simple geometric transitions, which are almost the only well-understood geometric transitions both in mathematics and in physics.