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Buckminster Fuller found that the cuboctahedron is the only polyhedron in which the distance between its center to the vertex is the same as the distance between its edges. In other words, it has the same length vectors in three-dimensional space, known as vector equilibrium . [ 8 ]
A third consequence of switching to tetrahedral mensuration is Fuller's review of the standard "dimension" concept. Whereas "height, width and depth" have been promulgated as three distinct dimensions within the Euclidean context, each with its own independence, Fuller considered the tetrahedron a minimal starting point for spatial cognition.
Time crystals: A state of matter where an object can have movement even at its lowest energy state. Hidden states of matter: Phases that are unattainable or do not exist in thermal equilibrium, but can be induced e.g. by photoexcitation. Microphase separation: Constituent units forming diverse phases while also keeping united.
The concept of a continuum underlies the mathematical framework for studying large-scale forces and deformations in materials. Although materials are composed of discrete atoms and molecules, separated by empty space or microscopic cracks and crystallographic defects, physical phenomena can often be modeled by considering a substance distributed throughout some region of space.
Classical entropy is defined for a system in its own internal state of thermodynamic equilibrium, which is defined by state variables, with no non-zero fluxes, so that flux variables do not appear as state variables. But for a strongly non-equilibrium system, during a process, the state variables must include non-zero flux variables.
If the equation is used to model a bounded sphere of material in a vacuum, the zero-pressure condition () = and the condition = / should be imposed at the boundary. The second boundary condition is imposed so that the metric at the boundary is continuous with the unique static spherically symmetric solution to the vacuum field equations , the ...
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
The hope is then that any reasonable matter theory will satisfy this condition or at least will preserve the condition if it is satisfied by the starting conditions. Energy conditions are not physical constraints per se , but are rather mathematically imposed boundary conditions that attempt to capture a belief that "energy should be positive ...