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12
Reflection from Layered Surfaces due to Subsurface Scattering
, 1993
"... The reflection of light from most materials consists of two major terms: the specular and the diffuse. Specular reflection may be modeled from first principles by considering a rough surface consisting of perfect reflectors, or microfacets. Diffuse reflection is generally considered to result from ..."
Abstract

Cited by 188 (3 self)
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The reflection of light from most materials consists of two major terms: the specular and the diffuse. Specular reflection may be modeled from first principles by considering a rough surface consisting of perfect reflectors, or microfacets. Diffuse reflection is generally considered to result from multiple scattering either from a rough surface or from within a layer near the surface. Accounting for diffuse reflection by Lambert's Cosine Law, as is universally done in computer graphics, is not a physical theory based on first principles. This paper presents
Sequential Monte Carlo Techniques for the Solution of Linear Systems
 Journal of Scientific Computing
, 1994
"... Given a linear system Ax = b, where x is an mvector, direct numerical methods, such as Gaussian elimination, take time O(m 3) to find x. Iterative numerical methods, such as the GaussSeidel method or SOR, reduce the system to the form whence x = a + Hx, x = ∑r=0ּHra; and then apply the iterations ..."
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Cited by 18 (1 self)
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Given a linear system Ax = b, where x is an mvector, direct numerical methods, such as Gaussian elimination, take time O(m 3) to find x. Iterative numerical methods, such as the GaussSeidel method or SOR, reduce the system to the form whence x = a + Hx, x = ∑r=0ּHra; and then apply the iterations x 0 = a, x s+1 = a + Hx s, until sufficient accuracy is achieved; this takes time O(m 2) per iteration. They generate the truncated sums s xs = ∑r=0ּHra. The usual plain Monte Carlo approach uses independent “random walks, ” to give an approximation to the truncated sum x s, taking time O(m) per random step. Unfortunately, millions of random steps are typically needed to achieve reasonable accuracy (say, 1 % r.m.s. error). Nevertheless, this is what has had to be done, if m is itself of the order of a million or more. The alternative presented here, is to apply a sequential Monte Carlo method, in which the sampling scheme is iteratively improved. Simply put, if x = y + z, where y is a current estimate of x, then its correction, z, satisfies z = d + Hz, where d = a + Hy – y. At each stage, one uses plain Monte Carlo to estimate z, and so, the new estimate y. If the sequential computation of d is itself approximated, numerically or stochastically, then the expected time for this process to reach a given accuracy is again O(m) per random step; but the number of steps is dramatically reduced [improvement factors of about 5,000, 26,000, and 700 have been obtained in preliminary
Automated Variance Reduction of Monte Carlo Shielding Calculations Using the Discrete Ordinates Adjoint Function,” Nucl
 Sci. Eng
, 1998
"... Abstract–Although the Monte Carlo method is considered to be the most accurate method available for solving radiation transport problems, its applicability is limited by its computational expense. Thus, biasing techniques, which require intuition, guesswork, and iterations involving manual adjustmen ..."
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Cited by 2 (2 self)
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Abstract–Although the Monte Carlo method is considered to be the most accurate method available for solving radiation transport problems, its applicability is limited by its computational expense. Thus, biasing techniques, which require intuition, guesswork, and iterations involving manual adjustments, are employed to make reactor shielding calculations feasible. To overcome this difficulty, we have developed a method for using the SN adjoint function for automated variance reduction of Monte Carlo calculations through source biasing and consistent transport biasing with the weight window technique. We describe the implementation of this method into the standard production Monte Carlo code MCNP and its application to a realistic calculation, namely, the reactor cavity dosimetry calculation. The computational effectiveness of the method, as demonstrated through the increase in calculational efficiency, is demonstrated and quantified. Important issues associated with this method and its efficient use are addressed and analyzed. Additional benefits in terms of the reduction in time and effort required of the user are difficult to quantify but are possibly as important as the computational efficiency. In general, the automated variance reduction method presented is capable of increases in computational performance on the order of thousands, while at the same time significantly reducing the current requirements for user experience, time, and effort. Therefore, this method can substantially increase the applicability and reliability of Monte Carlo for large, realworld shielding applications. I.
UNC is an Equal Opportunity / Affirmative Action Institution. ON ACCELERATING MONTE CARLO TECHNIQUES FOR SOLVING LARGE SYSTEMS OF EQUATIONS
"... This paper is concerned with ways of incorporating current Monte Carlo techniques for solving large linear systems [hereinafter referredto as "plain Monte Carlo"PMC] in accelerative schemes and other numerical techniques for more rapidly solving both linear and nonlinear systems. ..."
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This paper is concerned with ways of incorporating current Monte Carlo techniques for solving large linear systems [hereinafter referredto as "plain Monte Carlo"PMC] in accelerative schemes and other numerical techniques for more rapidly solving both linear and nonlinear systems.
REVIEW ARTICLE Lowpressure gas discharge modelling
, 1992
"... Abstract. Lowpressure gas discharge modelling is reviewed, both from a historical perspective and for current industrial applications. An ovetview of the basic mathematical and physical models used to describe lowpressure discharges is given, together with a summary of the most common numerical te ..."
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Abstract. Lowpressure gas discharge modelling is reviewed, both from a historical perspective and for current industrial applications. An ovetview of the basic mathematical and physical models used to describe lowpressure discharges is given, together with a summary of the most common numerical techniques which have been adopted. Modelling of the oc glow discharge and discharges maintained by highfrequency (RF and microwave) electromagnetic fields is reviewed, with illustrations of the validity of these models in predicting discharge properties and explaining and interpreting experimental results. 1.
History, overview and recent improvements of EGS4
"... this report has been plagiarised unashamedly from the original EGS3 (Electron Gamma Shower Code Version 3) document authored by Richard Ford and Ralph Nelson [1]. There are several reasons for this aside from laziness. This history predates one of the author's (AFB) involvement with EGS and he ..."
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this report has been plagiarised unashamedly from the original EGS3 (Electron Gamma Shower Code Version 3) document authored by Richard Ford and Ralph Nelson [1]. There are several reasons for this aside from laziness. This history predates one of the author's (AFB) involvement with EGS and he found it very difficult to improve upon the words penned by Ford and Nelson in that original document. Moreover, the EGS3 manual is now outofprint and this history might have eventually been lost to the everburgeoning EGScommunity now estimated to be at least 6000 strong. There had been one previous attempt to give a historical perspective of EGS [2]. However, this article was very brief and did not convey the large effort that went into the development of EGS. In this report the historical section on EGS4 as well as the summary of EGS3 to EGS4 conversion and the overview of EGS4 was taken directly from the EGS4 manual [3]. This is done for completeness only. The EGS4 manual gives much more detail and ought to be referred to for technical details. Finally, recent improvements to EGS4 are listed herein and represent the first time that this information is available in one place. The reader should consult the references cited in this report for more details regarding motivation and implementation.