On classification of physical effects by the graph types of their mathematical models

Y. B. Karasik,
Thoughts Guiding Systems Corp.,
Ottawa, Canada.
e-mail:karasik@sympatico.ca

Introduction

Physical effects are the way of converting one set of physical quantities into another set, or producing one set of physical quantities from the other one:

(PQ1out, … ,PQnout) = F(PQ1in, … ,PQmin),

where PQiin is the i-th input physical quantity and PQjout is the j-th output physical quantity.

For example, Hall effect converts electric current I in a conductor of width W with charge carrier density of D and magnetic field B across it into a voltage difference V across the conductor:

V = - IB/DWe,

where e is the elementary charge.

Here PQ1in = I, PQ2in = B, PQ3in = D, PQ4in = W, and PQ1out = V.

Physical effects can be classified in various ways:

  1. They can be classified by physical quantities they convert. (For example, all effects that convert mechanical deformation into voltage, such as piezoelectric effect, under this classification have to be placed into one class.)
  2. They can be classified by what can be accomplished with the help of the certain inputs.
    For example, by applying a high pressure the following things can be accomplished:
    • - non-conductors can be converted into conductors [1];
    • - brittle materials can be converted into ductile ones [2];
    • etc.
  3. They can be classified by how to achieve a ceratin result.
    For example, non-conductors can be converted into conductors by:
    • - applying high pressure [1];
    • - immersing them into the atmosphere of bromine vapor;
    • etc.
  4. They can be classified by the type of the dependence between inputs and outputs. (For example, all effects with a linear dependence between inputs and outputs constitute one class under such a classification.)

Classification 1), 2), and 3) are trivial and, in fact, were already partially accomplished by various encyclopedia. Classification of effects by the type of the dependence between inputs and outputs is less obvious and so far has been accomplished by no one. This article is an attempt to fill in this gap and present excerpts from the classification of the latter type.

1. Effects with continuous dependences between inputs and outputs: