The Monte Carlo trolley, or FERMIAC, was an
analog computer
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. ...
invented by physicist
Enrico Fermi
Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" an ...
to aid in his studies of
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
transport.
Operation
The FERMIAC employed the
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...
to model neutron transport in various types of
nuclear
Nuclear may refer to:
Physics
Relating to the nucleus of the atom:
*Nuclear engineering
*Nuclear physics
*Nuclear power
*Nuclear reactor
*Nuclear weapon
*Nuclear medicine
*Radiation therapy
*Nuclear warfare
Mathematics
*Nuclear space
* Nuclear ...
systems. Given an initial distribution of
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
s, the goal of the process is to develop numerous "neutron genealogies", or models of the behavior of individual neutrons, including each collision, scattering, and
fission
Fission, a splitting of something into two or more parts, may refer to:
* Fission (biology), the division of a single entity into two or more parts and the regeneration of those parts into separate entities resembling the original
* Nuclear fissio ...
. When a fission occurs, the number of emerging neutrons is predicted, and the behavior of each of these neutrons is eventually modeled in the same manner as the first. At each stage,
pseudo-random number
A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process.
Background
The generation of random numbers has many uses, such as for random ...
s are used to make decisions that affect the behavior of each neutron.
The FERMIAC used this method to create two-dimensional neutron genealogies on a scale diagram of a nuclear device. A series of drums on the device were set according to the material being crossed and a random choice between
fast and slow neutrons. Random numbers also determined the direction of travel and the distance until the next collision. Once the drums were set, the trolley was rolled across the diagram, drawing a path as it went. Any time a change in material was indicated on the diagram, the drum settings were adjusted accordingly before continuing.
History
In the early 1930s, Italian physicist
Enrico Fermi
Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" an ...
led a team of young scientists, dubbed the "
Via Panisperna boys
Via Panisperna boys (Italian: ''I ragazzi di Via Panisperna'') is the name given to a group of young Italian scientists led by Enrico Fermi, who worked at the Royal Physics Institute of the University of Rome La Sapienza. In 1934 they made the ...
", in their now-famous experiments in
nuclear physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter.
Nuclear physics should not be confused with atomic physics, which studies the ...
. During this time, Fermi developed "statistical sampling" techniques that he effectively employed to predict the results of experiments.

Years later, in 1946, Fermi participated in the initial review of results from the
ENIAC
ENIAC (; Electronic Numerical Integrator and Computer) was the first programmable, electronic, general-purpose digital computer, completed in 1945. There were other computers that had these features, but the ENIAC had all of them in one pac ...
. Among the others present was
Los Alamos mathematician
Stanislaw Ulam
Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapo ...
, who was familiar with the use of statistical sampling techniques similar to those previously developed by Fermi. Such techniques had mainly fallen out of use, due to the long, repetitious calculations required. However, given ENIAC's powers of calculation, Ulam saw an opportunity to resurrect these techniques. He discussed his ideas with
John von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
, who eventually used the ENIAC to implement the
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deter ...
(as the statistical sampling techniques came to be called) to solve a variety of neutron transport problems.
However, before the ENIAC could be employed for this purpose, it first had to be moved to its permanent home at the
Ballistics Research Laboratory
The Ballistic Research Laboratory (BRL) was a leading U.S. Army research establishment situated at Aberdeen Proving Ground, Maryland that specialized in ballistics (interior, exterior, and terminal) as well as vulnerability and lethality analysis. ...
. It was during this interruption in ENIAC operation that Fermi came up with the idea for his analog device. He enlisted his colleague L.D.P. King to build the instrument, which was later given the fitting name FERMIAC. The device was used for approximately two years
The Fermiac is on display in the Bradbury Science Museum in Los Alamos.
In 2015, the
Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”' created a replica of the device.
[{{Cite web, url=https://en.sif.it/journals/sif/ncc/econtents/2016/039/02/article/24, title=The Fermiac or Fermi's Trolley, website=en.sif.it, access-date=2019-08-11]A presentation of the device by Coccetti et al. is available as PDF.
See also
*
Planimeter
A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape.
Construction
There are several kinds of planimeters, but all operate in a similar way. The precise way in whic ...
*
Neutrons
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beha ...
*
Nuclear fission
Nuclear fission is a nuclear reaction, reaction in which the atomic nucleus, nucleus of an atom splits into two or more smaller atomic nucleus, nuclei. The fission process often produces gamma ray, gamma photons, and releases a very large ...
*
Computer simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
Further articles
What is the FERMIAC or Fermi Trolley?by The Bradbury Science Museum is operated by Los Alamos National Laboratory for education, 2017
References
Early computers
Analog computers
Enrico Fermi