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Unlike a traditional bubble chart, such displays don't assign meaning to x- or y-axis positions, but seek to pack circles as tightly as possible to make efficient use of space. These bubble charts were introduced by Fernanda Viegas and Martin Wattenberg [ 6 ] and have since become a popular method of displaying data.
Bubble diagrams, which result in the RPA when summed up. Solid lines stand for interacting or non-interacting Green's functions, dashed lines for two-particle interactions. The random phase approximation (RPA) is an approximation method in condensed matter physics and nuclear physics.
Since this also includes disconnected diagrams with vacuum bubbles, the sum factorizes into (sum over all bubble diagrams) × {\displaystyle \times } (sum of all diagrams with no bubbles). The first term then cancels with the normalization factor in the denominator meaning that the n-point correlation function is the sum of all Feynman diagrams ...
According to quantum field theory, the vacuum between interacting particles is not simply empty space. Rather, it contains short-lived virtual particle–antiparticle pairs (leptons or quarks and gluons). These short-lived pairs are called vacuum bubbles. It can be shown that they have no measurable impact on any process. [9] [nb 1]
The need for exotic matter raises questions about whether one can distribute the matter in an initial spacetime that lacks a warp bubble in such a way that the bubble is created at a later time, although some physicists have proposed models of dynamical warp-drive spacetimes in which a warp bubble is formed in a previously flat space. [4]
In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum surface area than the previous best-known solution, the Kelvin structure.
The configuration space of all unordered pairs of points on the circle is the Möbius strip. In mathematics, a configuration space is a construction closely related to state spaces or phase spaces in physics. In physics, these are used to describe the state of a whole system as a single point in a high-dimensional space.
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