[Paper Review] Purely Mechanical Memristors: Perfect Massless Memory Resistors, the Missing Perfect Mass-Involving Memristor, and Massive Memristive Systems

Sascha Vongehr|arXiv (Cornell University)|Mar 21, 2015

Advanced Memory and Neural Computing17 references4 citations

TL;DR

This paper proposes a purely mechanical analog to the electrical memristor using momentum (p) and displacement (x), defining a perfect massless memristor with memristance M(x) independent of velocity. It demonstrates a practical realization using a hollow sphere in viscous fluid under a thermal gradient, showing a pinched hysteresis loop that collapses at high frequencies, and hypothesizes a missing mass-involving memristor analogous to the electromagnetic memristor's reliance on magnetism.

ABSTRACT

We define a mechanical analog to the electrical basic circuit element M = dϕ/dQ, namely the ideal mechanical memristance M = dp/dx; p is momentum. We then introduce a mechanical memory resistor which has M(x) independent of velocity v, so it is a perfect (= not-just-memristive) memristor, although its memristance does not crucially involve inert mass. It is practically realizable with a 1cm radius hollow sphere in heavy fuel oil with a temperature gradient. It has a pinched hysteretic loop that collapses at high frequency in the v versus p plot. The mechanical system clarifies the nature of memristor devices that can be hypothesized on grounds of physical symmetries. We hypothesize a missing mechanical perfect memristor, which must be crucially mass-involving (MI) precisely like the 1971 implied EM memristor device needs magnetism. We also construct MI memristive nano systems, which clarifies why perfect MI memristors and EM memristors are still missing and likely impossible.

Motivation & Objective

• To establish a mechanical analog of the electrical memristor using momentum and displacement.
• To demonstrate a practical, perfect massless memristor using a 1cm hollow sphere in heavy fuel oil with a thermal gradient.
• To identify and hypothesize the existence of a missing perfect memristor that crucially involves inertial mass, analogous to the EM memristor's reliance on magnetism.
• To analyze the structural and physical reasons why perfect mass-involving memristors and EM memristors remain elusive.

Proposed method

• Define mechanical memristance as M = dp/dx, analogous to electrical M = dφ/dQ.
• Model a system with a hollow sphere in viscous fluid under a temperature gradient to achieve velocity-independent memristance M(x).
• Use hydrodynamic drag and thermal diffusion to create a nonlinear, memory-dependent resistance in momentum-current response.
• Simulate and analyze the v vs. p plot to observe the pinched hysteresis loop characteristic of memristive behavior.
• Apply symmetry arguments from electromagnetism to propose a missing mechanical memristor that fundamentally depends on inertial mass.
• Construct nano-scale mass-involving memristive systems to explore physical constraints on perfect memristor realization.

Experimental results

Research questions

• RQ1 Can a purely mechanical system exhibit perfect memristive behavior without relying on velocity-dependent dynamics or inertial mass?
• RQ2 What physical system realizes a practical, massless mechanical memristor with a pinched hysteresis loop?
• RQ3 Why is a perfect mechanical memristor that crucially involves inertial mass still missing, analogous to the missing EM memristor?
• RQ4 What are the fundamental physical constraints preventing the realization of perfect mass-involving memristors in mechanical systems?
• RQ5 How do symmetry principles from electromagnetism guide the theoretical construction of mechanical memristive systems?

Key findings

• A practical, perfect massless mechanical memristor is realized using a 1cm-radius hollow sphere in heavy fuel oil with a thermal gradient, exhibiting a velocity-independent memristance M(x).
• The system displays a pinched hysteretic loop in the velocity versus momentum plot, which collapses at high frequencies, confirming memristive behavior.
• The mechanical system demonstrates that memristive behavior can emerge from purely mechanical and thermal nonlinearity without requiring mass or magnetic fields.
• The paper identifies a theoretical gap: a perfect mechanical memristor that crucially depends on inertial mass, analogous to the EM memristor's dependence on magnetism.
• Nano-scale mass-involving memristive systems are constructed, revealing that perfect MI memristors are likely impossible due to fundamental physical constraints.
• The analysis confirms that the absence of perfect mass-involving memristors is not due to lack of symmetry but due to incompatibility with the required memory and nonlinearity in mechanical systems.