Abstract
The first part of this report deals with a new linear model of the capacitor. It is based entirely on old concepts and results that have not been combined before. The model current after a voltage step at t = 0 is proportional to t−n where n is a number less than but close to one. In the frequency domain losses are distributed to all frequencies. Both of these qualities adhere to real capacitors.
The major result can be expressed in the integral equation
q(t) = C0 · u(t) + Cχ · (dn-1u(t)/dtn-1) t > 0
which replaces the traditional equation q(t) = C · u(t). Cχ is a constant and the time/frequency dependence lies in the fractional derivative, eq. (15).
Application of these concepts imply neglibible changes to the majority of the results obtained hitherto by conventional methods but several effects that are not explicable by these methods follow from the model. The most important of these is the memory effect and that particular discussion ends in the conclusion that dielectrics have memory. The memory involves a weight factor, t−n, which makes it impossible to replace the memory of past voltages with a single initial value in order to predict the future behaviour of the dielectric.
In the last part of the report it is found that the same model applies to the theory of elasticity and to many, if not all, other systems. The conclusion is that matter has memory. It appears that there is a common memory that can be influenced by many means, e.g., electric fields, mechanical stress, magnetic fields, temperature etc.
Export citation and abstract BibTeX RIS