재생 커널법과 몬테 카를로 적분법을 이용한 극초음속 비행체의 Newtonian 공력 계수 계산

조민지,안미치코 한국전산유체공학회 2023 한국전산유체공학회지 Vol.28 No.4

This study proposes a method to calculate a high-precision approximation of the exact Newtonian aerodynamic coefficients for arbitrary shapes by combining the Reproducing Kernel Hilbert Space (RKHS) method and Monte-Carlo integration. The RKHS method was used to obtain the approximation function of hypersonic vehicle geometry from the structured grid points, and the Newtonian aerodynamic coefficients were calculated using Monte-Carlo integration. The effectiveness of the RKHS method was verified by applying it to simple shapes, and it was confirmed that the structured grid points could be well interpolated with random sampling points. The predicted value of the drag coefficient, obtained using Monte-Carlo integration on the sampling point data of the interpolated basic shapes, was evaluated by comparing it with the analytical solutions. Improvements in prediction accuracy were confirmed when compared with the results from the panel method. As an example application to arbitrary shapes, the present methods were examined for the Apollo command module shape, and it was confirmed that the calculated Newtonian aerodynamic coefficients had good accuracy when compared with the analytical solutions, even when considering flow at different angles of attack.

New Monte-Carlo based simulation program suitable for low-energy ions irradiation in pure materials

Al-Malkawi Ghadeer H.,Al-Ajlony Al-Montaser Bellah A.,Al-Shboul Khaled F.,Hassanein Ahmed 한국원자력학회 2023 Nuclear Engineering and Technology Vol.55 No.4

A new Monte-Carlo-based computer program (RDS-BASIC) is developed to simulate the transport of energetic ions in pure matter. This computer program is utilizing an algorithm that uses detailed numerical solutions for the classical scattering integral for evaluating the outcomes of the binary collision processes. This approach is adopted by several prominent similar simulation programs and is known to provide results with higher accuracy compared to other approaches that use approximations to shorten the simulation time. Furthermore, RDS-BASIC simulation program contains special methods to reduce the displacement energy threshold of surface atoms. This implementation is found essential for accurate simulation results for sputtering yield in the case of very low energy ions irradiation (near sputtering energy threshold) and also successfully solve the problem of simultaneously obtaining an acceptable number of atomic displacements per incident ions. Results of our simulation for several irradiation systems are presented and compared with their respective TRIM (SRIM-2013) and the state-of-the-art SDTrimSP simulation results. Our sputtering simulation results were also compared with available experimental data. The simulation execution time for these different simulation programs has also been compared.

Asymptotic Comparison of Latin Hypercube Sampling and Its Stratified Version

Lee, Jooho The Korean Statistical Society 1999 Journal of the Korean Statistical Society Vol.28 No.2

Latin hypercube sampling(LHS) introduced by McKay et al. (1979) is a widely used method for Monte Carlo integration. Stratified Latin hypercube sampling(SLHS) proposed by Choi and Lee(1993) improves LHS by combining it with stratified sampling. In this article it is shown that SLHS yields an asymptotically more accurate than both stratified sampling and LHS.

Numerical Integrations for One-Loop Feynman Integrals of Bilinear Operators with Staggered Fermions

Jongjeong Kim,이원종 한국물리학회 2009 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.55 No.5

The lattice regularization of quantum chromodynamics (QCD) allows us to study the nonperturbative nature of the strong interaction by using numerical simulations. In order to extract physical information from data of lattice simulations, one must to match lattice operators with continuum operators. For sufficiently small lattice spacing, the matching factor can be calculated perturbatively. Here, we study the numerical integration of the Feynman diagrams at the one-loop level, which are necessary to obtain the matching factors. We use the quadrature method and the Monte Carlo method for numerical integration. We compare these two methods and discuss their efficiency. We also study the advantage of using HYP/Fat7 links and an improved gluon action. As a result, we compare the sizes of the integrals in the following four cases: (1) thin links with an unimproved gluon action, (2) HYP/Fat7 links with an unimproved gluon action, (3) thin links with an improved gluon action, and (4) HYP/Fat7 links with an improved gluon action. The lattice regularization of quantum chromodynamics (QCD) allows us to study the nonperturbative nature of the strong interaction by using numerical simulations. In order to extract physical information from data of lattice simulations, one must to match lattice operators with continuum operators. For sufficiently small lattice spacing, the matching factor can be calculated perturbatively. Here, we study the numerical integration of the Feynman diagrams at the one-loop level, which are necessary to obtain the matching factors. We use the quadrature method and the Monte Carlo method for numerical integration. We compare these two methods and discuss their efficiency. We also study the advantage of using HYP/Fat7 links and an improved gluon action. As a result, we compare the sizes of the integrals in the following four cases: (1) thin links with an unimproved gluon action, (2) HYP/Fat7 links with an unimproved gluon action, (3) thin links with an improved gluon action, and (4) HYP/Fat7 links with an improved gluon action.

형상 파라미터 공차 변화에 따른 2선 대칭/비대칭 전송선로 크로스토크의 확률적 예측에 대한 연구

이재영(Jaeyoung Lee),이호상(Hosang Lee),나완수(Wansoo Nah) 한국전자파학회 2020 한국전자파학회논문지 Vol.31 No.11

본 논문에서는 형상 파라미터의 제작 공차 변화에 의한 2선 대칭/비대칭 전송선로의 크로스토크 전압을 예측하고자 확률적 예측 기법인 Generalized Polynomial Chaos Method (gPC)를 도입하고, 기존의 확률 예측 기법인 몬테카를로 시뮬레이션 (Monte-Calro simulation)을 이용한 예측을 병행하여 최종적으로 실제 측정된 크로스토크 전압과 비교하였다. 전송선로는 한 쌍의 마이크로스트립 신호선 형태로, 일반적인 대칭선로 구조와 크로스토크 저감 성능을 갖는 비대칭선로 구조를 기준으로 삼았다. 전송선로 구조 내에서 확률 변수 5가지를 정의하였고, 해당 변수들을 매개로 몬테카를로 시뮬레이션과 gPC 방법을 병행하여 진행하였으며, 확률적 예측 결과를 토대로 대칭구조 및 비대칭구조 전송선로에서의 크로스토크 전압 변화를 도출하였으며, 제작 공차에 대하여 어떤 구조가 더 민감한지를 파악하였다. 최종적으로 실제 측정된 크로스토크 전압과 비교하여 확률적 예측 기법의 정합성을 파악하였고, 비대칭 전송선로에서의 크로스토크 저감 성능이 형상 파라미터의 제작 공차에 의하여 크게 훼손되지 않음을 확인하였다. In this study, a generalized polynomial chaos method (gPC), which is a stochastic estimation technique, was used to predict the crosstalk voltage of a two-conductor symmetric/asymmetric transmission line owing to changes in the manufacturing tolerance of the geometrical parameters. In addition, a Monte-Carlo simulation, a conventional estimation method, was conducted in parallel with the gPC, and the results were compared with the actual measured crosstalk. A pair of microstrip signal lines were applied with symmetric and asymmetric structures, achieving a reduction in the crosstalk. A total of five geometrical parameters were defined as random variables, and a stochastic simulation was conducted in parallel for comparison with the crosstalk results of the gPC and Monte-Carlo simulations. Based on the stochastic estimation, we derived the change in crosstalk on the transmission lines and identified which structures are more sensitive to tolerance. Finally, the effectiveness of the stochastic estimation was determined by comparing the actual data, and it was confirmed that the performance in reducing the crosstalk under an asymmetric structure was not significantly hindered based on the manufacturing tolerance of the geometrical parameters.

RELTSYS: A computer program for life prediction of deteriorating systems

Enright, Michael P.,Frangopol, Dan M. Techno-Press 2000 Structural Engineering and Mechanics, An Int'l Jou Vol.9 No.6

As time-variant reliability approaches become increasingly used for service life prediction of the aging infrastructure, the demand for computer solution methods continues to increase. Effcient computer techniques have become well established for the reliability analysis of structural systems. Thus far, however, this is largely limited to time-invariant reliability problems. Therefore, the requirements for time-variant reliability prediction of deteriorating structural systems under time-variant loads have remained incomplete. This study presents a computer program for $\underline{REL}$iability of $\underline{T}$ime-Variant $\underline{SYS}$tems, RELTSYS. This program uses a combined technique of adaptive importance sampling, numerical integration, and fault tree analysis to compute time-variant reliabilities of individual components and systems. Time-invariant quantities are generated using Monte Carlo simulation, whereas time-variant quantities are evaluated using numerical integration. Load distribution and post-failure redistribution are considered using fault tree analysis. The strengths and limitations of RELTSYS are presented via a numerical example.

Time stepwise local volatility

배형옥,임현철 대한수학회 2022 대한수학회보 Vol.59 No.2

We propose a path integral method to construct a time stepwise local volatility for the stock index market under Dupire's model. Our method is focused on the pricing with the Monte Carlo Method (MCM). We solve the problem of randomness of MCM by applying numerical integration. We reconstruct this task as a matrix equation. Our method provides the analytic Jacobian and Hessian required by the nonlinear optimization solver, resulting in stable and fast calculations.

원통형 조사창에서의 양끝내포선 길이분포를 이용한 절리크기분포 추정 연구

서가현(Ga Hyun Suh),송재준(Jae-Joon Song) 한국암반공학회 2016 터널과지하공간 Vol.26 No.3

본 연구에서는 3차원 원통형 조사창에서의 양끝내포선 길이 분포를 이용하여 절리 직경 분포 추정을 수행하였다. 추정 결과의 수치적인 오차를 줄이기 위하여, 보조변수를 도입한 개선된 방안을 제시하였다. 몬테-카를로 시뮬레이션으로 검증한 결과, 보조변수의 변화에 따라 추정 분포의 진동이 줄어들어 오차가 크게 감소한 것을 확인하였다. 또한 절리 직경의 최적 분포 및 적정한 보조변수 값을 찾기 위한 알고리즘을 제안하였다. A method for estimating rock joint size distribution using contained traces length distribution from 3D cylindrical window survey was suggested. To reduce the numerical error, an improved technique was applied. The accuracy was verified by referring to Monte-Carlo simulation and it was found that the error can be decreased with suitable gamma values.

Path-integral Monte Carlo Study of Asymmetric Quantum Quadrupolar Rotors with Fourth-order Propagators

박성진,신현덕,권용경 한국물리학회 2012 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.61 No.4

The recently-proposed fourth-order propagator based on the multi-product expansion has been applied to path-integral Monte Carlo calculations for asymmetric quantum quadruploar rotors fixed at face-centered cubic lattice sites. The rotors are observed to undergo an orientational orderdisorder phase transition at a low temperature when the electric quadrupole-quadrupole interaction is strong enough. At intermediate interaction strength, a further decrease of temperature after the first transition to the ordered phase results in a reentrant transition back to the disordered phase. The theoretical phase diagram of these asymmetric rotors determined by using fourth-order path-integral Monte Carlo calculations is found to be in good quantitative agreement with the experimental one for solid hydrogen deuteride. This leads us to conclude that the fourth-order propagator can be effectively implemented for an accurate path-integral Monte Carlo calculation of a quantum many-body system with rotational degrees of freedom.

Valuation of step-down knock-in in one stock linked security using numerical and Monte Carlo integration

( Gyehong Kim ) 한국파생상품학회 2023 선물연구 Vol.31 No.1

This paper shows a new methodology for evaluating the value and sensitivity of autocall knock-in type equitylinked securities. While the existing evaluation methods, Monte Carlo simulation and finite difference method, have limitations in underestimating the knock-in effect, which is one of the important characteristics of this type, this paper presents a precise joint probability formula for multiple autocall chances and knock-in events. Based on this, the calculation results obtained by utilizing numerical and Monte Carlo integration are presented and compared with those of existing models. The results of the proposed model show notable improvements in terms of accuracy and calculation time.