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Relaxation (iterative Methods)
Relaxation stands quite generally for a release of tension, a return to equilibrium. In the sciences, the term is used in the following ways: * Relaxation (physics), and more in particular: ** Relaxation (NMR), processes by which nuclear magnetization returns to the equilibrium distribution ** Dielectric relaxation, the delay in the dielectric constant of a material ** Vibrational energy relaxation, the process by which molecules in high energy quantum states return to the Maxwell-Boltzmann distribution ** Chemical relaxation (physics), relaxation methods, related to temperature jump ** Relaxation oscillator, a type of electronic oscillator In mathematics: :* Relaxation (approximation), a technique for transforming hard constraints into easier ones :* Relaxation (iterative method), a technique for the numerical solution of equations :* Mathematical optimization#Relaxation (extension method), Relaxation (extension method), a technique for a natural extension in mathematical optimiza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relaxation (physics)
In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium. Each relaxation process can be categorized by a relaxation time τ. The simplest theoretical description of relaxation as function of time ''t'' is an exponential law ( exponential decay). In simple linear systems Mechanics: Damped unforced oscillator Let the homogeneous differential equation: :m\frac+\gamma\frac+ky=0 model damped unforced oscillations of a weight on a spring. The displacement will then be of the form y(t) = A e^ \cos(\mu t - \delta). The constant T (=2m/\gamma) is called the relaxation time of the system and the constant μ is the quasi-frequency. Electronics: RC circuit In an RC circuit containing a charged capacitor and a resistor, the voltage decays exponentially: : V(t)=V_0 e^ \ , The constant \tau = RC\ is called the ''relaxation time'' or RC time constant of the circuit. A nonlinear oscillator circuit which generates a repeating waveform ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |