Monte Carlo Type Simulations Research Articles

Channeling-like effects due to the macroscopic structure of porous silicon

When performing Rutherford Backscattering Spectrometry (RBS) measurements combined with channeling on “columnar” porous Si samples with the beam aligned to the direction of the pores, an additional yield decrease appears due to the macroscopic structure. Changes in the stopping power as the ions cross holes and material walls will also result in an additional spread in the ion energy. This work presents both experimental results and Monte Carlo type simulations showing the above structural effects. The simulations were done by a currently developed code, RBS-MAST, which is able to treat arbitrary structures on a nm-μm scale.

Uncertainty in economic models of climate-change impacts

Uncertainty is poorly represented in existing studies of climate-change impacts. Methods that have been used to characterize uncertainty in the literature are described and the limitations of each discussed. It is found that two broad characterizations are useful. A large number of studies are based on several specific scenarios or attempt to randomize selected variables in their deterministic economic models. Other studies describe individual or collective reaction to risk. The first category falls short of an adequate representation of uncertainty by focusing primarily on a few values of variables included to capture variability. The second group of studies tend to focus more on behavior than impacts. What is needed are Monte Carlo type simulations where randomness is apparent in a series of independent draws from a distribution suitably adjusted for climate change. Some of the benefits of improvements in the characterization of uncertainty are discussed.

Sampling and analysis of gut contents in relation to environmental variability and diel vertical migration by herbivorous zooplankton

The accuracy of standard sampling and analysis procedures for estimating ingestion by herbi- vorous zooplankton was assessed using models. Artificial environments were created in a computer model, allowing for depth-dependent variability in temperature, chlorophyll and primary production. Model zooplankton were simulated within these artificial environments using individual-based models. The model zooplankton feed and defaecate at rates determined by temperature and food con- centrations, and also exhibit diel vertical migration (DVM) according to a variety of migration models. The computer model was run for different combinations of these nine environmental and five DVM models. Data were 'sampled' from the model output, similar to field sampling of mesozooplankt on grazing. Dairy ingestion was calculated from the gut 'samples' using standard procedures for analysing gut fluorescence. The sample results were compared with the actual ingestion values in the model, and some causes of discrepancies were noted, (i) If incorrect temperatures were assumed when calculat- ing the gut evacuation rate (K), then estimates of ingestion were wrong by up to 40%. (ii) Non-uniform food environments gave errors of up to 30% because of the large variability of measured gut contents among individuals, (iii) Sampling from only part of the total depth range (eg. at the chlorophyll maximum) resulted in estimates of ingestion being only 5% of the real value. This sampling practice should be discouraged, because the sample is not random, (iv) If sampling is not frequent enough, erron can be as large as 45%, but more usually were -10% for realistic sampling frequencies. We describe an analysis procedure that uses Monte Carlo-type simulations in a computer spreadsheet to estimate population consumption. These calculations take into account natural variability due to popu- lations, samples and assumptions. We urge that results should be presented as ranges of possible values, rather than as single 'mean' values, to allow for easier recognition of meaningful differences among samples and systems.

Experiments in concurrent stochastic simulation: The EcliPSe paradigm

This paper presents results on the performance of a novel and flexible concurrent simulation environment known as EcliPSe. The paradigm we advocate is based on the premise that replication based simulations, either nondistributed or minimally distributed, yield excellent speedups. The approach used makes concurrent simulation easily accessible to researchers because its use does not require knowledge of parallel programming. The experiments we report include Monte Carlo type simulations (e.g., estimating integrals, order-statistics), Markov-chain simulations (hitting-times, distributed algorithms), and discrete-event simulation (e.g., tail probabilities in queues, FDDI token ring performance, and simulations of high performance software testing techniques on SIMD machines).

Decoding metrics for slow frequency-hopped DPSK systems

A variety of soft-decision decoding metrics for slow frequency-hopped, differential phase shift keyed spread-spectrum systems are studied. The computational cut-off rates in the presence of partial band noise jamming for these metrics are analysed. The usefulness of various degrees of side information, the effectiveness of limiting and quantisation when side information is not available, and the importance of a judicious choice of the quantisation step size are demonstrated. Monte-Carlo type simulations for the system encoded by Odenwalder's (7, 1/2) code are conducted, the resulting BERs reveal that close approximations can be attained by estimations calculated from a known closed-form formula.

Queue simulation of cyclic construction operations

Abstract Cyclic construction operations may be modelled in terms of the waiting times of the entities (typically equipment, plant, materials or manpower) that repeatedly pass through the various phases of the cycle. The relevant model involves recursive expressions linking the waiting times of successive cycles. This permits a Monte Carlo type simulation to be carried out and represents an alternative method to conventional event or time-oriented simulation and queueing theory. The elementary form of the recursive expressions for the waiting times results in a short computer program and minimal computer demands, enabling the simulation to be carried out on the smallest of microcomputers. The paper develops the simulation approach and makes a comparison with queueing theory. Both random sampling and a variance reduction technique are used. Models are developed for earthmovmg, quarrying and open-cut mining applications in elementary cycle form and multiple phase form.

Monte Carlo-type simulation for solving stochastic ordinary differential equations

We outline a method for solving numerically initial-value and boundary-value problems for ordinary differential equations whose coefficients and/or initial and boundary data are random quantities. The method consists of simulating on the computer several realizations of the stochastic processes that appear in the coefficients of the equations and similarly for the data. Such a simulation is based upon generating suitable sequences of random numbers, for which reason the method can be thought of as a Monte Carlo method. We then solve “pathwise” the equation and finally compute the quantities of interest such as expected values, moments, etc. over such realizations. The numerical error can also be estimated. The method is very simple but quite general, moreover it respects the correct probabilistic structure of the problem and is trivially suited to parallel implementation.

The Effect of Finger-joint Dispersion on the Strength of Laminated Beams

SYNOPSIS Finger-joints on the tension side of laminated timber beams weaken the laminate and consequently the beam. In this paper a method of strengthening the laminate by dispersing the effect of the finger-joint is discussed. J This dispersion is effected by the longitudinal sawing of the laminate and the displacement of the strips relative to one another. The paper illustrates the possible advantages that a manufacturer can obtain by using this method. To illustrate the increase in strength due to the dispersing of a finger-joint, a Monte Carlo type simulation is described. Experimental work on laminated beams to validate the theory is outlined. Lastly, the results obtained from the experiments and the simulation are compared.

An Improved Importance Sampling Method for Digital Communication System Simulations

The use of importance sampling techniques can substantially reduce the variance of probability of error estimates obtained by Monte Carlo type simulations of digital communication systems. However, the advantages of importance sampling diminish as the memory length of the system becomes greater. This paper presents a modified importance sampling method which achieves substantial variance reduction for systems with memory.

THE SIMULATION OF DISPERSED-PHASE BREAKAGE PHENOMENA

Abstract Droplet breakage in emulsification occurs as the result of work performed against surface tension by dynamic pressure fluctuations while deaggregation in biological wastewater treatment occurs in response to hydrodynamic stresses imposed by aeration, recirculation, and mixing. Such size reduction in the latter case leads to solids carry-over and poor process performance due to reduced sludge age. Laboratory observations of the disintegration process have shown how the hydrodynamic environment causes breakup and lean, batch breakage studies have indicated the most probable sizes of fragments. A Monte-Carlo type simulation has been used successfully to model the breakage process in both liquid-liquid and solid-liquid systems under high dissipation conditions.

Spatial effects on the stability of a food-limited moth population

Having obtained anomalous results in an attempt to continue the simulation study of moth-wasp interaction in Auslander, Oster and Huffaker (J. Franklin Inst. 297, 345-375), attention was centered on the role of spatial heterogeneity in an environment with the moth (Anagasta kühniella) alone. Because of the probable presence of chaotic components in the population behavior (random appearing behavior that is actually caused by deterministic influences), a statistically-based parameter sensitivity and parameter identification method was used. By defining a binary performance criterion that measured the ability of a model with a specific set of parameters to maintain a stable population, the importance of spatial heterogeneity was confirmed. In addition, the use of Monte-Carlo type simulation studies, combined with a binary performance criterion, was demonstrated to be effective for parameter identification and/or parameter sensitivity determination of at least some systems with chaotic or nearly chaotic behavior.

Monte Carlo modeling of current distribution in shaped electron beams

A Monte Carlo type simulation of electron interaction in a shaped electron beam lithography system has been developed. The simulation has been used to model a shaped beam system using Köhler illumination, and shows correct imaging when electron interaction is neglected. The loss of resolution due to interaction is demonstrated, and it is proposed that this technique may be used for the quantitive assessment of the effects on interaction in shaped beam systems.

A computer simulation of evolutionary forces controlling the size of a multigene family.

A Monte Carlo-type simulation of the evolution of a multigene family was performed. The model was designed to study the selective forces which may control the size of a multigene family. As expected, we find that direct selection on the size of the multigene family can control its size. More important, we find that selection acting upon the family as a single functional unit, in conjunction with homologous but unequal crossing over, can also control the size of a multigene family.

K→ M2 radiative Auger-like satellites in first transition metals

We present the current status and first results from a Monte Carlo-type simulation toolbox for Solar System small body dynamics. We also present fundamental methods for evaluating the results of this type of simulations using convergence criteria. The calculations consider a body in the Solar System with a mass loss mechanism that generates smaller particles. In our application the body, or parent body, is a comet and the mass loss mechanism is a sublimation process. In order to study mass propagation from parent bodies to Earth, we use the toolbox to sample the uncertainty distributions of relevant comet parameters and to find the resulting Earth influx distributions. The initial distributions considered represent orbital elements, sublimation distance, cometary and meteoroid densities, comet and meteoroid sizes and cometary surface activity. Simulations include perturbations from all major planets, radiation pressure and the Poynting-Robertson effect. In this paper we present the results of an initial software validation performed by producing synthetic versions of the 1933, 1946, 2011 and 2012 October Draconids meteor outbursts and comparing them with observational data and previous models. The synthetic meteor showers were generated by ejecting and propagating material from the recognized parent body of the October Draconids; the comet 21P/Giacobini-Zinner. Material was ejected during 17 perihelion passages between 1866 and 1972. Each perihelion passage was sampled with 50 clones of the parent body, all producing meteoroid streams. The clones were drawn from a multidimensional Gaussian distribution on the orbital elements, with distribution variances proportional to observational uncertainties. In the simulations, each clone ejected 8000 particles. Each particle was assigned an individual weight proportional to the mass loss it represented. This generated a total of 6.7 million test particles, out of which 43 thousand entered the Earth's Hill sphere during 1900–2020 and were considered encounters. The simulation reproduces the predictions and observations of the 1933, 1946, 2011 and 2012 October Draconids, including the unexpected but measured deviation of the meteoroid mass index from a power law in 2012 as compared to 2011. We show that when convergence is sufficient in the simulation, the fraction between two encountered mass distributions is independent of the assumed input mass distribution. Finally, we predict an outburst for the 2018 October Draconids with a peak on October 8–9 that could be up to twice as large as the 2011 and 2012 outbursts.

A Second Study of the Survival of a Neutral Mutant in a Simulated Amerindian Population

In an earlier publication (Li and Neel 1974), a Monte Carlo-type simulation of a complex of four Amerindian villages suggested that the mean survival time for the new mutations which were ultimately lost from the population (t̄0) was 2.3 generations. A rather extensive revision of that simulation is described, and the revised simulation is used to generate a probability mass function for the transmission of an allele, from which t̄0 is estimated. The new estimate is 2.82. Estimates of effective population size (Ne) have been derived from this value. Estimates of Ne based on mean mutant survival appear to be substantially less than the variance-effective Ne as it is usually derived for such a population.

Approaches to urban model-building

Cowan P., Ireland J. and Fine D. (1967) Approaches to urban model-building, Reg. Studies 1, 163–172. The problem is to construct mathematical models which will reproduce the pattern of office growth in the London area, 1947–1965. Two sets of data are used—Land Use and Planning Permissions. These data are allocted to a 500 m grid system. Two models are described, each based on the “attractiveness” of a grid cell for office space in a given time period. The first model is a Monte Carlo type simulation. The second model develops both deterministic and stochastic approaches to the same problem. The models are now being tested against real world data.

Use of Linearized Nonlinear Regression for Simulations Involving Monte Carlo

The material presented furnishes an extension of regression analysis in two respects. First, a type of nonlinear regression function is developed that seems to (1) have substantial curve-fitting flexibility, (2) be satisfactorily determined from an acceptably small number of observations, (3) permit isolation of important combinations of effects, and (4) be computationally manageable. Second, in conjunction with this general type of regression function, a probability model is developed that is applicable under exceedingly general conditions. Namely, each of the independent observations utilized can be from a different statistical population and the shapes of these populations are not necessarily restricted or related in any specific manner. An important aspect of the model is selection of the kind of “average” that the regression represents Estimates, tests, and confidence intervals are developed for investigating the regression coefficients. The methods and results presented are especially useful for Monte Carlo type simulations that are performed by use of a computer. This paper represents a report of research in progress, since many additional results should be obtainable on the basis of the concepts and methods that are presented.