Relaxation Dynamics
Non-exponential decay functions describe relaxation processes in complex disordered physical systems and dielectric materials. The kohlrausch stretched exponential model parameterizes physical variable recovery over time using a fractional exponent between zero and one. Sensor engineering applies this function to quantify long-term baseline drift, structural strain relaxation, and dielectric absorption effects.
Sourcing evaluation fits experimental decay data against the model to predict long-term calibration stability.
Time Constant
Traditional single-exponential relaxation assumes a single characteristic time constant governing parameter decay. Disordered systems contain a continuous distribution of activation energies, yielding a stretched decay curve over multiple temporal decades. The stretching parameter beta measures the distribution width of underlying relaxation times.
Lower beta values indicate broader distributions of micro-scale relaxation processes within polymers, glasses, and disordered thin films.
Material Aging
Dielectric absorption in precision capacitors and substrate insulations causes voltage recovery following rapid discharge cycles. Piezoresistive sensor substrates exhibit mechanical creep following sudden pressure steps, following stretched exponential dynamics. Temperature changes shift the effective time constant according to Arrhenius kinetics, accelerating or decelerating physical relaxation processes.
Characterizing these decay curves allows digital signal processing algorithms to filter out long-term thermal memory effects.
Fitting Boundary
Model validity requires continuous parameter extraction across at least three decades of temporal data.
