Soap Bubbles in Outer Space: Interaction of a Domain Wall with a Black Hole

We discuss the generalized Plateau problem in the 3+1 dimensional Schwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane (thin domain wall) is located near a black hole. Considering stationary axially symmetric membranes, three different membrane-topologies are possible depending on the boundary conditions at infinity: 2+1 Minkowski topology, 2+1 wormhole topology and 2+1 black hole topology. Interestingly, we find that the different membrane-topologies are connected via phase transitions of the form first discussed by Choptuik in investigations of scalar field collapse. More precisely, we find a first order phase transition (finite mass gap) between wormhole topology and black hole topology; the intermediate membrane being an unstable wormhole collapsing to a black hole. Moreover, we find a second order phase transition (no mass gap) between Minkowski topology and black hole topology; the intermediate membrane being a naked singularity. For the membranes of black hole topology, we find a mass scaling relation analogous to that originally found by Choptuik. However, in our case the parameter $p$ is replaced by a 2-vector $\vec{p}$ parametrizing the solutions. We find that $Mass\propto|\vec{p}-\vec{p}_*|^\gamma$ where $\gamma\approx 0.66$. We also find a periodic wiggle in the scaling relation. Our results show that black hole formation as a critical phenomenon is far more general than expected.Comment: 15 pages, Latex, 4 figures include

Dual-topology insertion of a dual-topology membrane protein.

Some membrane transporters are dual-topology dimers in which the subunits have inverted transmembrane topology. How a cell manages to generate equal populations of two opposite topologies from the same polypeptide chain remains unclear. For the dual-topology transporter EmrE, the evidence to date remains consistent with two extreme models. A post-translational model posits that topology remains malleable after synthesis and becomes fixed once the dimer forms. A second, co-translational model, posits that the protein inserts in both topologies in equal proportions. Here we show that while there is at least some limited topological malleability, the co-translational model likely dominates under normal circumstances

Toroidal membrane vesicles in spherical confinement

We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane. For small area the vesicle can adopt its free form. When increasing the area, the membrane cannot avoid contact and touches the confining sphere along a circular contact line, which extends to a zone of contact for higher area. The elastic energies of the equilibrium shapes are compared to those of their confined counterparts of spherical topology to predict under which conditions a topology change is favored energetically.Comment: 16 pages, 7 figure

S^1 \times S^2 as a bag membrane and its Einstein-Weyl geometry

In the hybrid skyrmion in which an Anti-de Sitter bag is imbedded into the skyrmion configuration a S^{1}\times S^{2} membrane is lying on the compactified spatial infinity of the bag [H. Rosu, Nuovo Cimento B 108, 313 (1993)]. The connection between the quark degrees of freedom and the mesonic ones is made through the membrane, in a way that should still be clarified from the standpoint of general relativity and topology. The S^1 \times S^2 membrane as a 3-dimensional manifold is at the same time a Weyl-Einstein space. We make here an excursion through the mathematical body of knowledge in the differential geometry and topology of these spaces which is expected to be useful for hadronic membranesComment: 9pp in latex, minor correction

Use of fabric membrane topology as an intermediate environment modifier

This paper describes the pattern of airflow around membrane structures, and how they along with the form of the structure itself affect the ventilation rates within their enclosures or their immediate vicinity. Examples that have successfully used membrane skins in the built environment will be reviewed. The possible use of tensile membrane structures topology and orientation to enhance ventilation rates and natural cooling within the semi-enclosed spaces will be discussed. The use of the indigenous fabric skin to tackle key climatic concerns in a simple, elegant manner is discussed along with the review of the wind tunnel experimental visualisation and measurements carried out by the author. These structures go beyond simply providing shading to illustrate innovative, environmentally friendly fabric Architecture, but if properly understood the fabric’s form and topology can play an effective role in the ventilation and natural cooling of spaces in their immediate vicinity

M-theory and the string genus expansion

The partition function of the membrane is investigated. In particular, the case relevant to perturbative string theory of a membrane with topology $S^1 \times \Sigma$ is examined. The coupling between the string world sheet Euler character and the dilaton is shown to arise from a careful treatment of the membrane partition function measure. This demonstrates that the M-theory origin of the dilaton coupling to the string world sheet is quantum in nature.Comment: 12 pages, late