When the high price of Russian-made nuclear fuel jeopardized the future of important research, Oregon State engineers fashioned a solution using techniques whose roots can be traced to a game of solitaire played 70 years ago.

For decades, scientists around the world have conducted experiments at the research reactor operated by the Institute of Nuclear Physics in the capital city of Tashkent, Uzbekistan. Their work includes tests to investigate various facets of nuclear security and is funded by the United States Department of Energy.

Unfortunately, Russia is the sole supplier of the particular uranium-based fuel that powers the reactor, and it has priced Uzbekistan out of the market.

“Russia has a monopoly on this type of fuel,” said Todd Palmer, professor of nuclear engineering. Uzbekistan recently announced that it will decommission the reactor, which means that researchers are losing a reliable and inexpensive testing venue that can complete experiments on short notice. Many Uzbeks are losing their jobs, and their country’s prestige in the scientific community will take a hit as a result. Although research reactors in the United States are capable of filling the gap, most of them are booked many months in advance.

Long before the decommissioning, Palmer and his colleagues were considering another option: replace the current plate-type fuel — so called because of its flat, rectangular shape — with plentiful and cheap pin-type fuel made in South Korea, which is configured in long, cylindrical aluminum rods. He likened the change to yanking a car’s engine and slotting in another. “Hopefully, you’ll get the same performance and the brakes and safety systems still work,” he said.

But physically replacing the fuel assembly without knowing the outcome is risky business that would entail enormous political commitments and many millions of dollars. So to test the potential solution, Palmer simulated the fuel substitution using a technique called the Monte Carlo method, which relies on probability to model physical and conceptual systems.

Instead of producing a single answer, Monte Carlo simulations produce a range of possible outcomes and their likelihoods. “It’s the most mathematically simple, physically intuitive approach for solving very complicated problems that cannot be solved analytically,” said Palmer.

**The Monte Carlo method**

The Monte Carlo method was born out of a simple card game. In 1946, the visionary mathematician and Manhattan Project veteran Stanislaw Ulam was playing solitaire while recovering from a serious illness. He casually wondered what his chances were of winning a game and figured out that simulating the play 100 times and counting the number of wins made far more sense than trying to calculate the odds using a purely mathematical approach.

“This was already possible to envisage with the beginning of the new era of fast computers,” Ulam said in 1983, “and I immediately thought of problems of neutron diffusion and other questions of mathematical physics.”

The name Monte Carlo refers to the casino where Ulam’s uncle supposedly gambled away large sums.

Today, Monte Carlo simulations turn up in any field where probability and statistics play a role:physical sciences, finance, biology, computer graphics, artificial intelligence, petroleum reserves management, investing, election forecasting, climate modeling, sports, and more. It’s been used to determine the most efficient process for boarding commercial airliners.

At its most basic level, Monte Carlo simulation predicts the outcome of flipping a coin thousands or even millions of times. Marginally more interesting is estimating the value of pi by simulating random dart throws at a circle inscribed within a square board, counting the number of hits inside the circle, then finishing with some middle school-level geometry operations. Things get notably more difficult when using Monte Carlo to approximate the odds, for example, of winning a baseball game.

Let’s say a team is down a run in the bottom of the ninth inning, with one out and a runner at first base. Is there a greater chance of scoring if, 1) the runner tries to steal second; 2) the batter tries to bunt the runner to second; or 3) the batter swings for a hit? At least a handful of variables must be quantified and plugged into the Monte Carlo software, such as the runner’s success rate for stealing against the opposing pitcher, the catcher’s record of throwing out base runners, and the hitter’s batting average and bunting ability. Even weather could play a factor. As the number of variables grows, confidence in the solution increases and the margin of error decreases. The simulation will produce a distribution of many thousands of data points from which the Monte Carlo algorithm will determine the most likely outcomes.

**Using Monte Carlo in nuclear research**

Where Monte Carlo simulations really shine is in addressing messy problems involving loads of variables and many possible outcomes — and where the stakes are high. Nuclear scientists use them to model the production and flow of energy in reactors and weapons, discover how radiation travels through and interacts with its surroundings, or assess the reliability of pumps, pipes, and other structures in nuclear plants.

A Monte Carlo simulation for a commercial nuclear reactor, for instance, calls for something in the neighborhood of two billion individual pieces of data to produce trustworthy results. The price of such fidelity is time, and Monte Carlo simulation is the tortoise of the data science world.

“Of all the algorithms, it’s easily one of the slowest ways of solving these types of problems,” said Palmer. Intricate simulations that incorporate the element of time, such as the rate of fuel depletion within a reactor core, can gobble up weeks of uninterrupted computer processing. The high-speed computers that make Monte Carlo simulation possible at all originated at the dawn of the atomic age in tandem with nuclear engineering, which is a point of pride for Palmer.

“The development of modern computers is more closely connected to nuclear engineering than with any other discipline,” he said. “The two sprang from the same well, and I feel a strong familial kinship to that.”

Scientists of the Manhattan Project, who faced mathematical challenges of mind-boggling complexity, relied heavily on mechanical tabulating machines, which frequently broke down from overuse. At the time, a “computer” was a human being. Roomfuls of human computers, mostly women, worked out calculations all day. Half a dozen of them later became the first programmers of ENIAC, the world’s first general purpose electronic computer, which secretly went into service in 1946 and soon after was enlisted by the nuclear scientists who created the hydrogen bomb.

**A potential solution**

For the Uzbekistan reactor, a time-tested Monte Carlo algorithm (also with roots in the Manhattan Project) provided a clear answer to the original proposition: the reactor would indeed perform just as well and as safely with the alternate fuel supply from South Korea.

“Based on what we have found, we could say with confidence that it would work in the real world,” said Palmer.

Even so, Uzbekistan will close the reactor. Fuel costs may well have been a factor in the decision, but the advanced age of the reactor, which opened in 1959, may also have been a consideration. Palmer had hoped to brief someone at the Department of Energy about the advantages, to science and the United States, of keeping the reactor running, but events overtook his plans.

“As scientists and engineers, we tend to stop after the calculations are made,” he added. “But a policymaker has to take that information and ask ‘what does this mean?’ and then make decisions based on the answer. It’s not just numbers.”

In addition to applying Monte Carlo simulations in his work, Palmer is also seeking ways to improve the algorithms themselves, particularly in the development of radiation source detectors. Placed at a border crossing, these detectors could conceivably pinpoint radioactive cargo hidden in vehicles trying to sneak across a frontier, but they must be exquisitely sensitive in order to pick up the tiny amounts of radiation that slip through shielding material that smugglers are sure to use to avoid discovery.

“To design detectors, you need simulations,” he said. “We want to be able to complete these simulations as fast and accurately as we can to design the detectors as well as possible.”