# Revisiting the Mousetraps Experiment: Not Just about Nuclear Chain Reactions

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. The Berkeley Experiment

#### 3.2. The Dalton Nuclear Experiment

#### 3.3. The Florence Experiment

#### 3.4. The Mousetrap Mathematical Model

_{1}/dt = −k

_{1}L

_{1}L

_{2}

_{2}/dt = k

_{2}L

_{1}L

_{2}− k

_{3}L

_{2}

_{1}” (“Level 1) stands for the potential energy stored in the traps. It is measured using the number of cocked traps as a proxy. “L

_{2}” (“Level 2”) is the kinetic energy stored in the flying balls, measured in terms of the number of balls in the air. The k

_{s}are constants whose value depends on the unit of measurement of the levels.

_{1}, k

_{2}, and k

_{3}were roughly estimated by considering an exponential decay of the triggered traps (k

_{1}); exponential growth of the flying balls when the reaction chains start (k

_{2}); and an exponential decline of the number of flying balls when traps are almost at the minimum (k

_{3}). Once initialized, the fitting returns with the constant values in Figure 5.

_{1}and k

_{2}are expressed in N

^{−}

^{1}s

^{−}

^{1}units, with N = number of balls. k

_{3}is expressed in s

^{−}

^{1}. Remarkably, the fitting converged by itself to a ratio of k

_{2}/k

_{1}nearly equal to 2, which is what would be expected since every ball that triggers a trap releases two balls. This ratio corresponds to the “reproduction rate” in biological populations. Other experimental runs provided similar results, although in some cases the ratio was slightly higher than 2. It may have been the result of a ball triggering more than a single trap or just of fluctuations in the data.

_{2}L

_{1}L

_{2}generated per unit time divided by the fallen balls for the same unit time, that is k

_{3}L

_{2}. The result is (k

_{2}/k

_{3})L

_{1}. At t = 0 (50 untriggered traps), this number is 1.8, close to 2, as one would expect. For t > 0, the net reproduction rate falls and becomes smaller than one when the population of flying balls does not grow anymore. In this specific run, it occurs at the peak of the flying ball population, for L

_{1}= 28 untriggered traps. The final value of the net reproduction rate is 0.43 for 12 untriggered traps, when there are no more flying balls.

_{1}< 25, the net reproduction rate is smaller than one and the system should not show a chain reaction. We verified this result experimentally, finding that, indeed, for less than 25 traps loaded with balls, the chain reaction either does not start or it involves only 2–3 traps before stopping. Note that no experimental setup shown on the Web appears to use less than 25 traps. This lower limit was found by other authors by trial and error.

## 4. Discussion

^{5}to 10

^{8}and more.

_{t}” rate in epidemiology and to the EROEI, or EROI (energy return for energy invested) [16], for several energy production systems that exploit non-renewable resources, e.g., oil, as we noted in a previous study [17].

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**The Dalton nuclear experiment [6].

**Figure 4.**Typical results of the Florence experiments. This figure shows an average of three tests. The data were fitted with a simple logistic equation (upper curve) and the derivative of a logistic equation (lower curve).

**Figure 5.**Results of the fitting of the data for the Florence experiment using the SCLV model. The Y scale is the number of balls/untriggered traps. The coefficients for this specific fitting were found to be k

_{1}= 0.0604, k

_{2}= 0.1212, k

_{3}= 3.3092.

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**MDPI and ACS Style**

Perissi, I.; Bardi, U.
Revisiting the Mousetraps Experiment: Not Just about Nuclear Chain Reactions. *Systems* **2022**, *10*, 91.
https://doi.org/10.3390/systems10040091

**AMA Style**

Perissi I, Bardi U.
Revisiting the Mousetraps Experiment: Not Just about Nuclear Chain Reactions. *Systems*. 2022; 10(4):91.
https://doi.org/10.3390/systems10040091

**Chicago/Turabian Style**

Perissi, Ilaria, and Ugo Bardi.
2022. "Revisiting the Mousetraps Experiment: Not Just about Nuclear Chain Reactions" *Systems* 10, no. 4: 91.
https://doi.org/10.3390/systems10040091