scholarly journals Advanced Differential Approximation Formulation of the PN Method for Radiative Transfer

2009 ◽  
Author(s):  
Michael F. Modest ◽  
Gopalendu Pal
Keyword(s):  
Monte Carlo ◽  
Energy Equation ◽  
Rapid Change ◽  
Differential Approximation ◽  
Major Drawback ◽  
New Approach ◽  
Exact Analytical Solutions ◽  
Concentric Spheres ◽  
Standard Models ◽  
Grazing Angles

The spherical harmonics (PN) method, especially its lowest order, i.e., the P1 or differential approximation, enjoys great popularity because of its relative simplicity and compatibility with standard models for the solution of the (overall) energy equation. Low-order PN approximations perform poorly in the presence of strongly nonisotropic intensity distributions, especially in optically thin situations within nonisothermal enclosures (due to variation in surface radiosities across the enclosure surface, causing rapid change of irradiation over incoming directions). A previous modification of the PN approximation, i.e., the modified differential approximation (MDA), separates wall emission from medium emission to reduce the nonisotropy of intensity. Although successful, the major drawback of this method is that the intensity at the walls is set to zero into outward directions, while incoming intensity is nonzero, resulting in a discontinuity at grazing angles. To alleviate this problem, a new approach, termed here the “advanced differential approximation (ADA),” is developed, in which the directional gradient of the intensity at the wall is minimized. This makes the intensity distribution continuous for the P1 method and mostly continuous for higher-order PN methods. The new method is tested for a 1-D slab and concentric spheres, and for a 2-D medium. Results are compared with the exact analytical solutions for the 1-D slab as well as the Monte Carlo-based simulations for 2-D media.

scholarly journals Advanced Differential Approximation Formulation of the PN Method for Radiative Transfer

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Gopalendu Pal ◽  
Michael F. Modest
Keyword(s):  
Monte Carlo ◽  
Energy Equation ◽  
Rapid Change ◽  
Differential Approximation ◽  
Major Drawback ◽  
New Approach ◽  
Exact Analytical Solutions ◽  
Concentric Spheres ◽  
Standard Models ◽  
Grazing Angles

The spherical harmonics (PN) method, especially its lowest order, i.e., the P1 or differential approximation, enjoys great popularity because of its relative simplicity and compatibility with standard models for the solution of the (overall) energy equation. Low-order PN approximations perform poorly in the presence of strongly nonisotropic intensity distributions, especially in optically thin situations within nonisothermal enclosures (due to variation in surface radiosities across the enclosure surface, causing rapid change of irradiation over incoming directions). A previous modification of the PN approximation, i.e., the modified differential approximation (MDA), separates wall emission from medium emission to reduce the nonisotropy of intensity. Although successful, the major drawback of this method is that the intensity at the walls is set to zero into outward directions, while incoming intensity is nonzero, resulting in a discontinuity at grazing angles. To alleviate this problem, a new approach, termed here the “advanced differential approximation (ADA),” is developed, in which the directional gradient of the intensity at the wall is minimized. This makes the intensity distribution continuous for the P1 method and mostly continuous for higher-order PN methods. The new method is tested for a 1D slab and concentric spheres and for a 2D medium. Results are compared with the exact analytical solutions for the 1D slab as well as the Monte Carlo-based simulations for 2D media.

scholarly journals A Monte Carlo Method of Solving Heat Conduction Problems

1980 ◽  
Vol 102 (1) ◽  
pp. 121-125 ◽  
Author(s):  
S. K. Fraley ◽  
T. J. Hoffman ◽  
P. N. Stevens
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Monte Carlo Method ◽  
Transport Equation ◽  
Heat Conduction Equation ◽  
Analytical Techniques ◽  
Conduction Equation ◽  
Geometric Complexity ◽  
New Approach ◽  
Temperature Distributions

A new approach in the use of Monte Carlo to solve heat conduction problems is developed using a transport equation approximation to the heat conduction equation. A variety of problems is analyzed with this method and their solutions are compared to those obtained with analytical techniques. This Monte Carlo approach appears to be limited to the calculation of temperatures at specific points rather than temperature distributions. The method is applicable to the solution of multimedia problems with no inherent limitations as to the geometric complexity of the problem.

Improved estimation is a prerequisite for successful terminal guidance

2005 ◽  
Vol 219 (2) ◽  
pp. 145-156 ◽  
Author(s):  
J Shinar ◽  
V Turetsky
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Estimation Errors ◽  
New Approach ◽  
Target Acceleration ◽  
The Future ◽  
New Ideas ◽  
Estimation System ◽  
Terminal Guidance

Successful interception of manoeuvring anti-surface missiles that are expected in the future can be achieved only if the estimation errors against manoeuvring targets can be minimized. The paper raises new ideas for an improved estimation concept by separating the tasks of the estimation system and by explicit use of the time-to-go in the process. The outcome of the new approach is illustrated by results of Monte Carlo simulations in generic interception scenarios. The results indicate that if an eventual ‘jump’ in the commanded target acceleration is detected sufficiently rapidly, small estimation errors and consequently precise guidance can be obtained.

New approach to Monte Carlo simulation of photon transport in the frequency domain

1995 ◽  
Author(s):  
Ilya V. Yaroslavsky ◽  
Anna N. Yaroslavsky ◽  
Hans-Joachim Schwarzmaier ◽  
Garif G. Akchurin ◽  
Valery V. Tuchin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Frequency Domain ◽  
New Approach ◽  
Photon Transport

TACKLING THE SIGN PROBLEM

1994 ◽  
Vol 05 (02) ◽  
pp. 275-277
Author(s):  
T D Kieu ◽  
C J Griffin
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
New Approach ◽  
Statistical Errors ◽  
Sign Problem ◽  
Complex Valued ◽  
1D Complex

To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. The 1D complex-coupling Ising model is employed as an illustration.

scholarly journals Measuring hospital spatial wingspan by using a discrete choice model with utility-threshold

2018 ◽  
Author(s):  
Saley Issa ◽  
Ribatet Mathieu ◽  
Molinari Nicolas
Keyword(s):  
Monte Carlo ◽  
Discrete Choice ◽  
Choice Model ◽  
Discrete Choice Models ◽  
Mcmc Methods ◽  
Hospital Competition ◽  
Policy Makers ◽  
New Approach ◽  
Asthma Patients ◽  
The One

AbstractPolicy makers increasingly rely on hospital competition to incentivize patients to choose high-value care. Travel distance is one of the most important drivers of patients’ decision. The paper presents a method to numerically measure, for a given hospital, the distance beyond which no patient is expected to choose the hospital for treatment by using a new approach in discrete choice models. To illustrate, we compared 3 hospitals attractiveness related to this distance for asthma patients admissions in 2009 in Hérault (France), showing, as expected, CHU Montpellier is the one with the most important spatial wingspan. For estimation, Monte Carlo Markov Chain (MCMC) methods are used.

A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling

2004 ◽  
Vol 72 (10) ◽  
pp. 1294-1302 ◽  
Author(s):  
D. P. Landau ◽  
Shan-Ho Tsai ◽  
M. Exler
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Statistical Physics ◽  
New Approach

Evaluation of Secondary Flow between Rotating Concentric Spheres Using a Perturbation Method

2021 ◽  
Vol 412 ◽  
pp. 49-72
Author(s):  
R. Leticia Corral Bustamante ◽  
Antonino H. Pérez ◽  
Alfredo L. Márquez
Keyword(s):  
Perturbation Method ◽  
Secondary Flow ◽  
Analytical Method ◽  
Analytic Solution ◽  
Previous Analysis ◽  
Secondary Flows ◽  
Newtonian Flow ◽  
New Approach ◽  
Concentric Spheres ◽  
Method Show

A new approach to evaluate the Newtonian flow between concentric rotating spheres is introduced in this paper. A general analytic solution to the problem is deduced using a perturbation method that takes into account the primary and secondary flows produced between the spheres, as well as an alternative analytical method. In order to exemplify the results of the previous analysis, six particular cases were studied. The results of the perturbation method show that under certain circumstances the secondary flow is no negligible, as is usually considered, but it is comparable to the value of the primary one. While the analytical method allows us to simulate the flow with results very similar to those of other authors.

Production Yield Estimation by the Metamodel Method With a Boundary-Focused Experiment Design

1997 ◽  
Author(s):  
Chinghsin Tu ◽  
Russell R. Barton
Keyword(s):  
Monte Carlo ◽  
Robust Design ◽  
Simulation Models ◽  
Experiment Design ◽  
Production Yield ◽  
Design Stage ◽  
Yield Estimation ◽  
Simulation Code ◽  
New Approach ◽  
A Priority

Abstract The need for yield estimation strategies in the design stage is a priority recognized by industry. Yield estimates can be employed to assess the manufacturability of a design, and allow for modification to produce a robust design. Therefore, low yield of products can be avoided and costs for manufacturing can be reduced. This paper presents an accurate and time-efficient yield estimation approach for use with simulation models. We use a metamodel-based method, which is time-efficient compared to crude Monte Carlo yield estimation using the original simulation code. The approach employs a boundary-focused experiment design, which overcomes the inaccuracy of yield estimates that can occur when using a metamodel method. The results of two examples demonstrate the effectiveness of this new approach.

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