Nonlinear resistance forms

TL;DR

This paper introduces nonlinear resistance forms, defining a family of resistance metrics and demonstrating their additivity in circuits, unifying resistance forms and p-resistance forms within this framework.

Contribution

It presents a new framework for nonlinear resistance forms, extending classical resistance concepts to nonlinear settings and unifying various resistance notions.

Findings

Defined a 1-parameter family of nonlinear resistance metrics

Proved additivity over serial circuits

Unified resistance forms and p-resistance forms within the framework

Abstract

In this paper we introduce the notion of nonlinear resistance forms. We define a $1$-parameter family of nonlinear resistance metrics and show their additivity over serial circuits. Moreover, we prove that resistance forms and $p$-resistance forms fall into our framework.