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The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas. The curves on the phase diagram show the points where the free energy (and other derived properties) becomes non-analytic: their derivatives with respect to the coordinates (temperature and ...
The phase plane method refers to graphically determining the existence of limit cycles in the solutions of the differential equation. The solutions to the differential equation are a family of functions. Graphically, this can be plotted in the phase plane like a two-dimensional vector field. Vectors representing the derivatives of the points ...
In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space; a one-dimensional system is called a phase line, while a two-dimensional system is called a phase plane. For every possible state of the system or allowed combination of values of the system's parameters, a point is ...
2-dimensional Hubbard model. The Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. [1] It is particularly useful in solid-state physics. The model is named for John Hubbard. The Hubbard model states that each electron experiences competing forces: one pushes it to tunnel to ...
Wigner crystal. Structure of a two-dimensional Wigner crystal in a parabolic potential trap with 600 electrons. Triangles and squares mark positions of the topological defects. A Wigner crystal is the solid (crystalline) phase of electrons first predicted by Eugene Wigner in 1934. [1][2] A gas of electrons moving in a uniform, inert ...
The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector, the state vector. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
Phase portrait of damped oscillator, with increasing damping strength. The equation of motion is. In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying ...
Stable limit cycle (shown in bold) and two other trajectories spiraling into it Stable limit cycle (shown in bold) for the Van der Pol oscillator. In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as ...