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A Bethe lattice with coordination number z = 3. In statistical mechanics and mathematics, the Bethe lattice (also called a regular tree) is an infinite symmetric regular tree where all vertices have the same number of neighbors. The Bethe lattice was introduced into the physics literature by Hans Bethe in 1935.
In physics, the Bethe ansatz is an ansatz for finding the exact wavefunctions of certain quantum many-body models, most commonly for one-dimensional lattice models. It was first used by Hans Bethe in 1931 to find the exact eigenvalues and eigenvectors of the one-dimensional antiferromagnetic isotropic (XXX) Heisenberg model .
Bethe lattice; Biham–Middleton–Levine traffic model; ... Lattice density functional theory; Lattice model; Lattice model (biophysics) M. Majumdar–Ghosh model; N.
The Swiss cheese model of accident causation is a model used in risk analysis and risk management. It likens human systems to multiple slices of Swiss cheese , which has randomly placed and sized holes in each slice, stacked side by side, in which the risk of a threat becoming a reality is mitigated by the differing layers and types of defenses ...
Mathematically, the security level access may also be expressed in terms of the lattice (a partial order set) where each object and subject have a greatest lower bound (meet) and least upper bound (join) of access rights. For example, if two subjects A and B need access to an object, the security level is defined as the meet of the levels of A ...
For most infinite lattice graphs, p c cannot be calculated exactly, though in some cases p c there is an exact value. For example: for the square lattice ℤ 2 in two dimensions, p c = 1 / 2 for bond percolation, a fact which was an open question for more than 20 years and was finally resolved by Harry Kesten in the early 1980s, [6] see ...
The idea first appeared in physics (statistical mechanics) in the work of Pierre Curie [6] and Pierre Weiss to describe phase transitions. [7]MFT has been used in the Bragg–Williams approximation, models on Bethe lattice, Landau theory, Curie-Weiss law for magnetic susceptibility, Flory–Huggins solution theory, and Scheutjens–Fleer theory.
In his article "Restructuring Lattice Theory" (1982), [1] initiating formal concept analysis as a mathematical discipline, Wille starts from a discontent with the current lattice theory and pure mathematics in general: The production of theoretical results—often achieved by "elaborate mental gymnastics"—were impressive, but the connections between neighboring domains, even parts of a ...