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Topic: Monte Carlo method

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	Monte Carlo method
		Monte Carlo methods are methods for solving various kinds of computational problems by using random numbers (or more often pseudo-random numbers), as opposed to deterministic algorithms.
		Monte Carlo methods are extremely important in computational physics and related applied fields, and have diverse applications from esoteric quantum chromodynamics calculations, to use by engineers in designing heat shields and aerodynamic forms.
		The "Monte Carlo" designation is a reference to the famous casino in that area, and was popularized by early pioneers in the field such as Stanislaw Marcin Ulam, Enrico Fermi, Jon von Neumann and Nick Metropolis[?].
	www.ebroadcast.com.au /lookup/encyclopedia/mo/Monte_Carlo_method.html (596 words)

	Monte Carlo Method
		Monte Carlo methods—named after the famous European gambling casino—are a means of numerically simulating chance events in order to predict the most likely future outcome.
		Monte Carlo simulations are distinguished from other types of simulation techniques by their extensive use of random numbers and repeated trials.
		Advanced Monte Carlo methods involve the use of Markov chains and the Gibbs sampler, statistical tools that consider the probability of moving through a multistage process given multiple variables and uncertainties.
	www.referenceforbusiness.com /encyclopedia/Mor-Off/Monte-Carlo-Method.html (636 words)

	Calculation of Pi Using the Monte Carlo Method (Site not responding. Last check: 2007-11-03)
		The "Monte Carlo Method" is a method of solving problems using statistics.
		Although the Monte Carlo Method is often useful for solving problems in physics and mathematics which cannot be solved by analytical means, it is a rather slow method of calculating pi.
		This method, was known as "The method of the French Lieutenant" or "The method of generating PI casting stones in a Pond".
	www.eveandersson.com /pi/monte-carlo-circle (582 words)

	Monte Carlo method Summary
		Monte Carlo methods are very important in computational physics and related applied fields, and have diverse applications from esoteric quantum chromodynamics calculations to designing heat shields and aerodynamic forms.
		Monte Carlo methods were central to the simulations required for the Manhattan Project, though were strongly limited by the computational tools at the time.
		Uses of Monte Carlo methods require large amounts of random numbers, and it was their use that spurred the development of pseudorandom number generators, which were far quicker to use than the tables of random numbers which had been previously used for statistical sampling.
	www.bookrags.com /Monte_Carlo_method (2780 words)

	Monte Carlo Method \| World of Mathematics
		The Monte Carlo method, used to investigate a wide variety of problems, is a stochastic technique based on the statistics of random events applied to large numbers.
		The Monte Carlo method is one of the most powerful techniques available in terms of the application to such a wide range of problems.
		Although crude Monte Carlo methods were employed in studies that predate that of the development of the atomic bomb the systematic development of Monte Carlo ideas emerged in 1948 when a group of scientists obtained Monte Carlo estimates for the eigenvalues of the Schrödinger equation.
	www.bookrags.com /research/monte-carlo-method-wom (860 words)

	The Monte Carlo method
		Monte Carlo calculation of x-radiation transport is based on stochastic mathematical simulation of the interactions between photons and matter.
		The Monte Carlo method used here calculates the kerma in both components of the skeleton, the active bone marrow and the rest of skeletal material, by dividing the absorbed energy in the whole skeleton into two parts, applying the method of Rosenstein (1976).
		The x-ray spectra are calculated according to the theory of Birch and Marshal (1979) and specified in terms of the x-ray tube voltage (kV), the angle of the tungsten target of the x-ray tube, and filtration.
	www.stuk.fi /sateilyn_kayttajille/ohjelmat/PCXMC/en_GB/mc_method/_print (917 words)

	Monte Carlo (Site not responding. Last check: 2007-11-03)
		A Monte Carlo method is a stochastic technique, meaning that it is based on using random numbers and probability to investigate problems.
		Monte Carlo methods are employed in a wide variety of fields including economics, finance, physics, chemistry, engineering, and even the study of traffic flows.
		The Monte Carlo method was then applied to problems related to the atomic bomb." (Simulation and the Monte Carlo Method by Reuven Y. Rubinstein, John Wiley and Sons, Inc., New York, 1981, p.11.) For a brief history of Monte Carlo Methods see http://stud2.tuwien.ac.at/~e9527412/history.html.
	astro.temple.edu /~dhill001/montecarlo/monte.html (1330 words)

	Monte Carlo Techniques
		The method calls for a random walk, or a guided random walk, in phase space during which the integrand is evaluated at each step and averaged over.
		The Monte Carlo approach is implemented by enclosing the circle in a square of side 2 and using random numbers in the interval x = (-1,1) and y = (-1,1).
		A parallel implementation of the Monte Carlo integration must have the random sequence distributed to the different nodes, either by communication or by a local generation of the sequence.
	einstein.drexel.edu /courses/PHYS405/Monte_Carlo (1885 words)

	Monte Carlo history for SSI
		Monte Carlo methods have been used for centuries, but only in the past several decades has the technique gained the status of a full-fledged numerical method capable of addressing the most complex applications.
		The Monte Carlo method may be thought of as similar to a political poll, where a carefully selected statistical sample is used to predict the behavior or characteristics of a large group.
		Monte Carlo methods are widely used in modeling of materials and chemicals, from grain growth modeling in metallic alloys, to behavior of nanostrutures and polymers, and protein structure predictions.
	www.csm.ornl.gov /ssi-expo/MChist.html (749 words)

	Monte Carlo method (Site not responding. Last check: 2007-11-03)
		Monte Carlo (MC) methods are stochastic techniques-meaning they are based on the use of random numbers and probability statistics to investigate problems.
		But, strictly speaking, to call something a "Monte Carlo" experiment, all you need to do is use random numbers to examine some problem.
		With MC methods, a large system can be sampled in a number of random configurations, and that data can be used to describe the system as a whole.
	physics.technion.ac.il /~jammia/projectpage/mcmeth.htm (245 words)

	Monte Carlo method
		A method of estimating the true value of a quantity by carrying out a lot of random samples.
		A famous example of using the Monte Carlo method is to calculate pi.
		This process, which they named after the famous Monaco casino town of Monte Carlo, was created by John von Neumann and Stanislaw Ulam.
	www.daviddarling.info /encyclopedia/M/Monte_Carlo_method.html (315 words)

	Monte Carlo Simulation Basics
		Monte Carlo simulation is a method for iteratively evaluating a deterministic model using sets of random numbers as inputs.
		The Monte Carlo method is just one of many methods for analyzing uncertainty propagation, where the goal is to determine how random variation, lack of knowledge, or error affects the sensitivity, performance, or reliability of the system that is being modeled.
		Monte Carlo simulation is categorized as a sampling method because the inputs are randomly generated from probability distributions to simulate the process of sampling from an actual population.
	www.vertex42.com /ExcelArticles/mc/MonteCarloSimulation.html (596 words)

	Monte Carlo Method
		The first thoughts and attempts I made to practice [the Monte Carlo Method] were suggested by a question which occurred to me in 1946 as I was convalescing from an illness and playing solitaires.
		To understand the Monte Carlo method theoretically, it is useful to think of it as a general technique of numerical integration.
		Monte Carlo transformation Describes the use of the Monte Carlo method in VaR measures.
	www.riskglossary.com /link/monte_carlo_method.htm (1715 words)

	HISTORY OF MONTE CARLO METHOD
		Among all numerical methods that rely on N-point evaluations in M-dimensional space to produce an approximate solution, the Monte Carlo method has absolute error of estimate that decreases as N superscript -1/2 whereas, in the absence of exploitable special structure all others have errors that decrease as N superscript -1/M at best.
		The method is called after the city in the Monaco principality, because of a roulette, a simple random number generator.
		The real use of Monte Carlo methods as a research tool stems from work on the atomic bomb during the second world war.
	stud1.tuwien.ac.at /~e9527412/history.html (603 words)

	Monte Carlo Integration
		Monte Carlo methods can be thought of as statistical simulation methods that utilize a sequences of random numbers to perform the simulation.
		The Monte Carlo method can be used to numerically approximate the value of an integral.
		Every time a Monte Carlo simulation is made using the same sample size it will come up with a slightly different value.
	math.fullerton.edu /mathews/n2003/MonteCarloMod.html (501 words)

	Quasi Monte Carlo method (Site not responding. Last check: 2007-11-03)
		This is in contrast to a Monte Carlo method,which is based on sequences of pseudorandom numbers.
		Monte Carlo and quasi-Monte Carlo methods are stated in a similar way.
		Thus it would appear that the accuracy of the quasi-Monte Carlo method increases faster than that of the Monte Carlo method.However, Morokoff and Calflisch cite examples of problems in which the advantage of the quasi-Monte Carlo is less than expectedtheoretically.
	www.therfcc.org /quasi-monte-carlo-method-64340.html (337 words)

	An Introduction to Monte Carlo Methods
		Following this introduction is a section on the Monte Carlo experiment, part of the physical chemistry lab at UNL, which computes the population distribution in the rotational energy levels of HCl and DCl.
		Monte Carlo Calculation of Pi The first figure is simply a unit circle circumscribed by a square.
		The actual Monte Carlo method used in this lab to determine the population distribution among rotational energy levels is simpler than the two-dimensional example of the estimation of pi, as only one random number is generated for each "throw." This will be apparent shortly.
	www.chem.unl.edu /zeng/joy/mclab/mcintro.html (1070 words)

	Wave:Monte Carlo (Site not responding. Last check: 2007-11-03)
		The method was also used to determine the empirical formulae for time-averaging and scale-averaging (paper Sections 5a and 5b).
		It is called Monte Carlo because of the gambling casinos in that city, and because the Monte Carlo method is related to rolling dice.
		The method can be generalized to any process where the statistical distribution is unknown, yet one needs to determine confidence or significance levels.
	atoc.colorado.edu /research/wavelets/montecarlo.html (400 words)

	HISTORY OF MONTE CARLO METHOD
		Among all numerical methods that rely on N-point evaluations in M-dimensional space to produce an approximate solution, the Monte Carlo method has absolute error of estimate that decreases as N superscript -1/2 whereas, in the absence of exploitable special structure all others have errors that decrease as N superscript -1/M at best.
		The method is called after the city in the Monaco principality, because of a roulette, a simple random number generator.
		The real use of Monte Carlo methods as a research tool stems from work on the atomic bomb during the second world war.
	stud4.tuwien.ac.at /~e9527412/history.html (603 words)

	Monte Carlo method - HighBeam Encyclopedia (Site not responding. Last check: 2007-11-03)
		For example, to estimate the probability of five heads in five successive coin tosses, an analyst unfamiliar with the binomial test could simulate five coin tosses thousands of times on a computer and count the proportion that consist of five heads.
		Schrodinger goes to Monte Carlo; the 'adaptive Monte Carlo' method seeks solutions for chemical and condensed-matter structures.
		Monte Carlo methods for Bayesian analysis of survival data using mixtures of Dirichlet process priors.
	www.encyclopedia.com /doc/1O87-MonteCarlomethod.html (614 words)

	Monte Carlo Method - Mathematics, Probability Statistics, Monte Carlo Method,
		Atomistic Method Applied to Computational Modeling of Surface Alloys The formation of surface alloys is a growing research field that, in terms of the surface structure of multicomponent systems, defines the frontier both for experimental and theoretical techniques.
		Monte Carlo Simulation of Alloy Design Techniques: Fracture and Welding Studied Using the BFS Method for Alloys Large-scale simulations of dynamic processes at the atomic level have developed into one of the main areas of work in computational materials science.
		Finally, numerical results for transport equation obtained by the Monte Carlo method are compared with those obtained by using the method of discrete ordinates and the geometrical Monte Carlo model.
	www.studysphere.com /Site/Sphere_4011.html (861 words)

	Amazon.fr : The Monte Carlo Method for Semiconductor Device Simulation: Livres en anglais: Carlo Jacoboni,P. Lugli (Site not responding. Last check: 2007-11-03)
		It introduces the reader to the Monte Carlo technique as applied to the study of transport in semiconductors, and to the modelling of semiconductor devices.
		Since use of the Monte Carlo technique requires an accurate knowledge of the physical system under investigation, a general overview of the basis of the physics of transport in semiconductors is also provided.
		The Monte Carlo technique is a fairly new tool in the area of device modelling, traditionally dominated by simulators based on drift-diffusion or on balance-equation models, so a comparison of the characteristics of the different methods is presented, pointing out the areas and limits of applicability of each of them.
	www.amazon.fr /Monte-Method-Semiconductor-Device-Simulation/dp/0387821104 (433 words)

	Amazon.co.uk: A Primer for the Monte Carlo Method: Books: I.M. Sobol (Site not responding. Last check: 2007-11-03)
		The Monte Carlo method is a numerical method of solving mathematical problems through random sampling.
		As a universal numerical technique, the method became possible with the advent of computers, and its application continues to expand with each new computer generation.
		It features the main schemes of the Monte Carlo method and presents various examples of its application, including queuing, quality and reliability estimations, neutron transfer, astrophysics and numerical analysis.
	www.amazon.co.uk /Primer-Monte-Carlo-Method/dp/084938673X (522 words)

	Advanced Monte Carlo Methods
		Monte Carlo methods are numerical methods that use random numbers to compute quantities of interest.
		Thus, Monte Carlo methods themselves are a fruitful source of research problems, and when combined with deterministic methods have the promise to provide many improved numerical methods.
		Of particular importance to students of Monte Carlo methods is that they discuss the solution of the difference approximations for elliptic and parabolic equations through probabilistic methods.
	www.cs.fsu.edu /~mascagni/Advanced_Monte_Carlo_Methods.html (2953 words)

	Dynamic Monte Carlo method at AllExperts
		In chemistry, Dynamic Monte Carlo (DMC) is a method for modeling the dynamic behaviors of molecules by comparing the rates of individual steps with random numbers.
		Unlike the Metropolis Monte Carlo method, which has been employed to study systems at equilibrium, the DMC method is used to investigate nonequilibrium systems such as reaction, diffusion, etc. This method is mainly applied to analyze the behavior of adsorbates on surfaces.
		The DMC method is very similar to the Kinetic Monte Carlo method.
	en.allexperts.com /e/d/dy/dynamic_monte_carlo_method.htm (352 words)

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