An inhibitory ternary system contains two terms in its free energy: the interface energy that favors micro-domain growth and the longer ranging confinement energy that prevents unlimited spreading. In a parameter regime where two constituents are small in size compared to the third constituent and the longer ranging energy does not dominate, there is a double bubble like stable critical point o...

A ternary inhibitory system contains two terms in its free energy: the interface energy that favors micro-domain growth and the longer ranging confinement energy that prevents unlimited spreading. In a parameter regime where two constituents are small in size compared to the third constituent and the longer ranging energy does not dominate, there is a double-bubble-like stable stationary point ...

The double bubble sign in neonates is seen on plain abdominal radiographs in a variety of conditions. It represents gas distended dilated stomach and proximal duodenum, and implies congenital proximal bowel obstruction. A newborn with a double bubble and no distal bowel gas can be presumed to have duodenal atresia and in most cases no further imaging is required. If double bubble is present wit...

The classical isoperimetric inequality states that the surface of smallest area enclosing a given volume in R3 is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 2π/3.

We explore the bubble spacetimes which can be obtained from double analytic continuations of static and rotating black holes in anti-de Sitter space. In particular, we find that rotating black holes with elliptic horizon lead to bubble spacetimes only in dimension greater than five. For dimension greater than seven, the topology of the bubble can be non-spherical. However, a bubble spacetime is...

Main result. It is well known that of all surfaces surrounding an area with a given volume V, the sphere has the smallest area. This result explains, e.g., why a soap bubble tends to become a sphere. More than a hundred years ago, the Belgian physicist J. Plateaux asked a similar question: what is the least area surface enclosing two equal volumes? Physical experiments with bubbles seem to indi...

Abstract A 29-year-old woman of Lithuanian heritage was referred to dermatology with a 3-year history recurrent blistering the hands and, occasionally, feet. The patient’s own photographs revealed small, tense blisters on sides her fingers and one foot. In general clinic, she noted have acrylic nails, which had been applying at home gel nail kit for over 5 years. recent years, patient noticed t...

We establish the Gaussian Multi-Bubble Conjecture: least Gaussian-weighted perimeter way to decompose $\mathbb{R}^n$ into $q$ cells of prescribed (positive) measure when $2\le q\le n+1$, is use a ``simplicial cluster," obtained from Voronoi equidistant points. Moreover, we prove that simplicial clusters are unique isoperimetric minimizers (up null-sets). In particular, case $q=3$ confirms Doubl...