Computer simulations represent the real world by use of a computer program. These are an interface between theory and experiment and play a vital role in the scientific studies from the conception of an experiment to the final outcome.
The purpose of simulations is to evaluate the feasibility of a proposed experiment by way of optimizing the experimental design, analyzing the collected data samples and evaluating systematic errors and therefore assessing its scientific reach. In order for the simulations to be accepted in the general scientific community these have to mimic the experimental results. If the two data sets reconcile, then these have some credibility.
Monte Carlo (MC) simulation methods are stochastic techniques based on the use of random numbers and probability statistics to investigate problems. These are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.
The expression” Monte Carlo” is actually very general. We can find MC methods used in everything from economics to chemistry to nuclear physics to regulating the flow of traffic. Of course, the way these are applied varies widely from field to field.
Before the Monte Carlo method was developed, simulationstested a previously understood deterministic problem, and statistical samplingwas used to estimate uncertainties in the simulations. Monte Carlo simulationsinverted this approach, solving deterministic problems using a probabilisticanalog.
The use of MC methods to model physical problems allows usto examine more complex systems than we otherwise can do. Solving equationswhich describe the interactions between two atoms is fairly simple but solvingthe same equations for hundreds or thousands of atoms is not so easy. With MCmethods, a large system can be sampled in a number of random configurations andthat data can be used to describe the system as a whole.
When faced with significant uncertainty in the process of making a forecast or estimation, rather than just replacing the uncertain variable with a single average number, the Monte Carlo Simulation might prove to be a better solution. Since business and finance are plagued by random variables, Monte Carlo simulations have a vast array of potential applications in these fields.
They are used to estimate the probability of cost overruns in large projects and the likelihood that an asset price will move in a certain way. Telecoms use them to assess network performance in different scenarios, helping them to optimize the network.
Analysts use them to assess the risk that an entity will default and to analyze derivatives such as options. Insurers and oil well drillers also use them. Monte Carlo simulations have countless applications outside the business and finance, such as in meteorology, astronomy and particle physics.
Monte Carlo simulations are named after the gambling hot spot in Monaco, since chance and random outcomes are central to the modeling technique, much as they are to games like roulette, dice, and slot machines. The technique was first developed by Stanislaw Ulam, a Polish mathematician who worked on the Manhattan Project which was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada.
After the war, while recovering from brain surgery, Ulam entertained himself by playing countless games of solitaire. He became interested in plotting the outcome of each of these games in order to observe their distribution and determine the probability of winning. After he shared his idea with John Von Neumann, the two collaborated to develop the Monte Carlo simulation.
At this great spirit of Ulam, I am recalled of the saying “No difficulty can discourage, no obstacle dismay, no trouble dishearten the man who has acquired the art of being alive. Difficulties are but dares of fate, obstacles but hurdles to try his skill, troubles but bitter tonics to give him strength; and he rises higher and looms greater after each encounter with adversity.”
Therefore not all storms come to disrupt you. Some come toclear your path.
Dr. Qudsia Gani is Assistant Professor, Department of Physics, Cluster University Srinagar