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Note that subcritical and supercritical describe the stability of the outer lines of the pitchfork (dashed or solid, respectively) and are not dependent on which direction the pitchfork faces. For example, the negative of the first ODE above, x ˙ = x 3 − r x {\displaystyle {\dot {x}}=x^{3}-rx} , faces the same direction as the first picture ...
Complex eigenvalues of an arbitrary map (dots). In case of the Hopf bifurcation, two complex conjugate eigenvalues cross the imaginary axis. In the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a periodic solution arises. [1]
In a supercritical regime, in contrary to the subcritical regime the network has a giant component. In the special case of = the network is complete (see complete graph). A random network is in a supercritical regime if the average degree exceeds the critical point, that is if
Critical carbon dioxide exuding fog while cooling from supercritical to critical temperature. The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822 [ 10 ] [ 11 ] and named by Dmitri Mendeleev in 1860 [ 12 ] [ 13 ] and Thomas Andrews in 1869. [ 14 ]
As water hits the sink, it disperses, increasing in depth to a critical radius where the flow (supercritical with low depth, high velocity, and a Froude number greater than 1) must suddenly jump to a greater, subcritical depth (high depth, low velocity, and a Froude number less than 1) that is known to conserve momentum. Figure 2.
A transcritical cycle is a closed thermodynamic cycle where the working fluid goes through both subcritical and supercritical states. In particular, for power cycles the working fluid is kept in the liquid region during the compression phase and in vapour and/or supercritical conditions during the expansion phase.
In this plot, the depth where the minimum energy occurs is known as the critical depth. Consequently, this depth corresponds to a Froude Number ( F n ) {\displaystyle (F_{n})} of 1. Depths greater than critical depth are considered “subcritical” and have a Froude Number less than 1, while depths less than critical depth are considered ...
Using careful control rod movements, it is thus possible to achieve a supercritical reactor core without reaching an unsafe prompt-critical state. Once a reactor plant is operating at its target or design power level, it can be operated to maintain its critical condition for long periods of time.