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Статті в журналах з теми "Integral simulation"

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Автор: Grafiati

Опубліковано: 12 травня 2022

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1

Teplyakova, S. V., A. A. Kotesova, and N. N. Nikolaev. "Car integral performance index simulation." Vestnik of Don State Technical University 20, no. 2 (July 12, 2020): 150–54. http://dx.doi.org/10.23947/1992-5980-2020-20-2-150-154.

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2

Miller, Bruce N., and Terrence Reese. "Path integral simulation of positronium." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 192, no. 1-2 (May 2002): 176–79. http://dx.doi.org/10.1016/s0168-583x(02)00864-9.

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3

Herrero, C. P., and R. Ramírez. "Path-integral simulation of solids." Journal of Physics: Condensed Matter 26, no. 23 (May 9, 2014): 233201. http://dx.doi.org/10.1088/0953-8984/26/23/233201.

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4

KOSINA, HANS, and MIHAIL NEDJALKOV. "PARTICLE MODELS FOR DEVICE SIMULATION." International Journal of High Speed Electronics and Systems 13, no. 03 (September 2003): 727–69. http://dx.doi.org/10.1142/s0129156403002010.

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A theoretical analysis of the Monte Carlo (MC) method for both semiclassical and quantum device simulation is presented. A link between physically-based MC methods for semiclassical transport calculations and the numerical MC method for solving integrals and integral equations is established. The integral representations of the transient and the stationary Boltzmann equations are presented as well as the respective conjugate equations. The structure of the terms of the Neumann series and their evaluation by MC integration is discussed. Using this formal approach the standard MC algorithms and a variety of new algorithms is derived, such as the backward and the weighted algorithms, and algorithms for linear small-signal analysis. Applying this theoretical framework to the Wigner-Boltzmann equation enables the development of particle models for quantum transport problems.

5

Asuka, Masashi, and Kiyotoshi Komaya. "Train Simulation Method Applying Integral Calculation." IEEJ Transactions on Electronics, Information and Systems 121, no. 1 (2001): 68–75. http://dx.doi.org/10.1541/ieejeiss1987.121.1_68.

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6

Rami´rez, Rafael, and Carlos P. Herrero. "Path-integral simulation of crystalline silicon." Physical Review B 48, no. 19 (November 15, 1993): 14659–62. http://dx.doi.org/10.1103/physrevb.48.14659.

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7

Wallqvist, A., and B. J. Berne. "Path-integral simulation of pure water." Chemical Physics Letters 117, no. 3 (June 1985): 214–19. http://dx.doi.org/10.1016/0009-2614(85)80206-2.

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8

Duan, Jun-Sheng, and YangQuan Chen. "Mechanical response and simulation for constitutive equations with distributed order derivatives." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 04 (December 2017): 1750040. http://dx.doi.org/10.1142/s1793962317500404.

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Mechanical response and simulation for constitutive equation with distributed order derivatives were considered. We investigated the creep compliance, creep recovery, relaxation modulus, stress–strain behavior under harmonic deformation for each case of two constitutive equations. We express these responses and results as easily computable forms and simulate them by using MATHEMATICA 8. The results involve the exponential integral function, convergent improper integrals on the infinite interval [Formula: see text] and the numerical integral method for the convolution integral. For both equations, stress responses to harmonic deformation display hysteresis phenomena and energy dissipation. The two constitutive equations characterize viscoelastic models of fluid-like and solid-like, respectively.

9

GILLAN, M. J., and F. CHRISTODOULOS. "THE PATH-INTEGRAL QUANTUM SIMULATION OF HYDROGEN IN METALS." International Journal of Modern Physics C 04, no. 02 (April 1993): 287–97. http://dx.doi.org/10.1142/s0129183193000306.

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The path-integral method for simulating quantum many-body systems is outlined, emphasising the recently developed quantum transition state theory (QTST) for calculating transition rates. Recent applications of path-integral simulation to metal-hydrogen systems are described. It is shown how QTST applied through path-integral simulation allows the calculation of the temperature-dependent diffusion coefficient of hydrogen and its isotopes in metals. The new methods show that the change of activation energy experimentally observed in some systems arises from the cross-over between quantum and classical behaviour.

10

Iftikhar, Sabah, Poom Kumam, and Samet Erden. "NEWTON’S-TYPE INTEGRAL INEQUALITIES VIA LOCAL FRACTIONAL INTEGRALS." Fractals 28, no. 03 (May 2020): 2050037. http://dx.doi.org/10.1142/s0218348x20500371.

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We firstly establish an identity involving local fractional integrals. Then, with the help of this equality, some new Newton-type inequalities for functions whose the local fractional derivatives in modulus and their some powers are generalized convex are obtained. Some applications of these inequalities for Simpson’s quadrature rules and generalized special means are also given.

11

Schmidt, T. C., and K. Möhring. "Stochastic path-integral simulation of quantum scattering." Physical Review A 48, no. 5 (November 1, 1993): R3418—R3420. http://dx.doi.org/10.1103/physreva.48.r3418.

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12

Kast, Stefan M. "Combinations of simulation and integral equation theory." Physical Chemistry Chemical Physics 3, no. 23 (November 26, 2001): 5087–92. http://dx.doi.org/10.1039/b106075a.

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13

Nordborg, Henrik, and Gianni Blatter. "Path integral monte carlo simulation of vortices." Czechoslovak Journal of Physics 46, S3 (March 1996): 1817–18. http://dx.doi.org/10.1007/bf02563023.

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14

Abbasov, É. M., and T. S. Kengerli. "Integral Simulation of Oil Displacement by Water." Journal of Engineering Physics and Thermophysics 92, no. 2 (March 2019): 441–49. http://dx.doi.org/10.1007/s10891-019-01949-z.

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15

Yan, Litan, Qinghua Zhang, and Bo Gao. "Hilbert transform of G-Brownian local time." Stochastics and Dynamics 14, no. 04 (September 22, 2014): 1450006. http://dx.doi.org/10.1142/s0219493714500063.

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Let B be a G-Brownian motion with quadratic process 〈B〉 under the G-expectation. In this paper, we consider the integrals [Formula: see text] We show that the integral diverges and the convergence [Formula: see text] exists in 𝕃2 for all a ∈ ℝ, t > 0. This shows that [Formula: see text] coincides with the Hilbert transform of the local time [Formula: see text] of G-Brownian motion B for every t. The functional is a natural extension to classical cases. As a natural result we get a sublinear version of Yamada's formula [Formula: see text] where the integral is the Itô integral under the G-expectation.

16

Chen, Jian Jun, Xiao Xue Li, and Hong Liang Pan. "Investigation on Validity of J-Integral of Edge Crack under Cold Rolling Condition." Applied Mechanics and Materials 556-562 (May 2014): 696–99. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.696.

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In this paper the characterization of the edge crack in the strip steel are studied by using numerical simulation method. The developments of the stress and strain near the crack tip are obtained and the value of the J-integral of edge crack under the rolling process is then examined. FE simulation result shows that the J-integral is not always path independent in the whole rolling process. When the crack is far away from the roller, the J-integral is path independent. When the crack enters the cold rolling region, the unload phenomena will occur near the crack tip which cause the incremental theory of plasticity failed and the conservation of the J-integral is not valid any more. The J-integral failure region is then determined by a series of FE simulations.

17

Karaiev, Artem, and Elena Strelnikova. "Singular integrals in axisymmetric problems of elastostatics." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 01 (February 2020): 2050003. http://dx.doi.org/10.1142/s1793962320500038.

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Singular integral equations arisen in axisymmetric problems of elastostatics are under consideration in this paper. These equations are received after applying the integral transformation and Gauss–Ostrogradsky’s theorem to the Green tensor for equilibrium equations of the infinite isotropic medium. Initially, three-dimensional problems expressed in Cartesian coordinates are transformed to cylindrical ones and integrated with respect to the circumference coordinate. So, the three-dimensional axisymmetric problems are reduced to systems of one-dimensional singular integral equations requiring the evaluation of linear integrals only. The thorough analysis of both displacement and traction kernels is accomplished, and similarity in behavior of both kernels is established. The kernels are expressed in terms of complete elliptic integrals of first and second kinds. The second kind elliptic integrals are nonsingular, and standard Gaussian quadratures are applied for their numerical evaluation. Analysis of external integrals proved the existence of logarithmic and Cauchy’s singularities. The numerical treatment of these integrals takes into account the presence of this integrable singularity. The numerical examples are provided to testify accuracy and efficiency of the proposed method including integrals with logarithmic singularity, Catalan’s constant, the Gaussian surface integral. The comparison between analytical and numerical data has proved high precision and availability of the proposed method.

18

Franklin, Ashley E., and Nicole Petsas Blodgett. "Simulation in Undergraduate Education." Annual Review of Nursing Research 39, no. 1 (December 1, 2020): 3–31. http://dx.doi.org/10.1891/0739-6686.39.3.

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Simulation is an integral component of undergraduate nursing education because it allows for a safe, timely, and prescriptive approach to meet learning objectives at the levels of individual simulations, courses, and academic programs. This review of the literature provides an overview of steps taken to move simulation forward in undergraduate nursing education, and it highlights educational theories, research, best practices, and policy statements underpinning modern nursing simulation. This chapter outlines simulation and curriculum integration approaches and provides examples of participant, course, and program outcomes.

19

Franklin, Ashley E., and Nicole Petsas Blodgett. "Simulation in Undergraduate Education." Annual Review of Nursing Research 39, no. 1 (December 1, 2020): 3–31. http://dx.doi.org/10.1891/0739-6686.39.3.

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Simulation is an integral component of undergraduate nursing education because it allows for a safe, timely, and prescriptive approach to meet learning objectives at the levels of individual simulations, courses, and academic programs. This review of the literature provides an overview of steps taken to move simulation forward in undergraduate nursing education, and it highlights educational theories, research, best practices, and policy statements underpinning modern nursing simulation. This chapter outlines simulation and curriculum integration approaches and provides examples of participant, course, and program outcomes.

20

Latt, Kaido. "THE FINITE PART OF DIVERGENT INTEGRALS WITH LOGARITHMIC FACTORS." Mathematical Modelling and Analysis 16, no. 4 (November 22, 2011): 537–57. http://dx.doi.org/10.3846/13926292.2011.627951.

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The concepts of the finite part (f.p.) and analytic finite part (a.f.p.) of divergent integrals are defined in the situation where the singular function in the integral has a logarithmic factor. The change of variables in f.p.- and a.f.p-integrals is examined.

21

Fan, Tai-Hsi, Edward J. Mayle, Peter A. Kottke, and Andrei G. Fedorov. "Simulation of electroanalysis using the boundary integral method." TrAC Trends in Analytical Chemistry 25, no. 1 (January 2006): 52–65. http://dx.doi.org/10.1016/j.trac.2005.03.020.

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22

van Dorsselaere, J. P., C. Seropian, P. Chatelard, F. Jacq, J. Fleurot, P. Giordano, N. Reinke, B. Schwinges, H. J. Allelein, and W. Luther. "The ASTEC Integral Code for Severe Accident Simulation." Nuclear Technology 165, no. 3 (March 2009): 293–307. http://dx.doi.org/10.13182/nt09-a4102.

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23

Slabanja, Mattias, and Göran Wahnström. "Quantum path-integral simulation of poly(propylene oxide)." Chemical Physics Letters 342, no. 5-6 (July 2001): 593–98. http://dx.doi.org/10.1016/s0009-2614(01)00651-0.

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24

Farnoosh, Rahman, and Ebrahimi Morteza. "Monte Carlo simulation for solving Fredholm integral equations." Kybernetes 38, no. 9 (October 16, 2009): 1621–29. http://dx.doi.org/10.1108/03684920910991577.

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25

Oh, Hyun Jung, Shi Woo Rhee, and In Seok Kang. "Simulation of CVD Process by Boundary Integral Technique." Journal of The Electrochemical Society 139, no. 6 (June 1, 1992): 1714–20. http://dx.doi.org/10.1149/1.2069482.

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26

Bresme, Fernando. "Integral equations and simulation studies of waterlike models." Journal of Chemical Physics 108, no. 11 (March 15, 1998): 4505–15. http://dx.doi.org/10.1063/1.475862.

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27

Gusmeroli, R., and A. S. Spinelli. "Accurate boundary integral calculation in semiconductor device simulation." IEEE Transactions on Electron Devices 53, no. 7 (July 2006): 1730–33. http://dx.doi.org/10.1109/ted.2006.875806.

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28

Herrero, Carlos P., and Rafael Ramírez. "High-density amorphous ice: A path-integral simulation." Journal of Chemical Physics 137, no. 10 (September 14, 2012): 104505. http://dx.doi.org/10.1063/1.4750027.

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29

Virág, T., G. Gy Halász, and J. B. Zhelev. "Simulation of continuous drying processes by integral equations." Chemical Engineering Science 44, no. 7 (1989): 1529–38. http://dx.doi.org/10.1016/0009-2509(89)80030-2.

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30

Lavrova, Olga, and Viktor Polevikov. "APPLICATION OF COLLOCATION BEM FOR AXISYMMETRIC TRANSMISSION PROBLEMS IN ELECTRO- AND MAGNETOSTATICS." Mathematical Modelling and Analysis 21, no. 1 (January 26, 2016): 16–34. http://dx.doi.org/10.3846/13926292.2016.1128488.

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This paper considers the numerical solution of boundary integral equations for an exterior transmission problem in a three-dimensional axisymmetric domain. The resulting potential problem is formulated in a meridian plane as the second kind integral equation for a boundary potential and the first kind integral equation for a boundary flux. The numerical method is an axisymmetric collocation with equal order approximations of the boundary unknowns on a polygonal boundary. The complete elliptic integrals of the kernels are approximated by polynomials. An asymptotic kernels behavior is analyzed for accurate numerical evaluation of integrals. A piecewise-constant midpoint collocation and a piecewise-linear nodal collocation on a circular arc and on its polygonal interpolation are used for test computations on uniform meshes. We analyze empirically the influence of the polygonal boundary interpolation to the accuracy and the convergence of the presented method. We have found that the polygonal boundary interpolation does not change the convergence behavior on the smooth boundary for the piecewise-constant and the piecewise-linear collocation.

31

Wang, Hong Tao, Man Zhi Li, and You Jian Shen. "Improved Simulation of Double Integrals Based on Monte-Carlo Method." Advanced Materials Research 655-657 (January 2013): 1016–19. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.1016.

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The traditional method of solving double integral by Monte Carlo method is limited with the integral area, it can only be solved the double integral on the rectangular area. To address this limitation, based on the average method of Monte Carlo method,which puts forward that the uniform distribution should be combined with area of the integral region to improve algorithm, the special rectangle integral region is extended to the general integral region.In this way the simulation accuracy and computational efficiency is improved. Practical example shows that improved algorithm simplifies the calculation process, effectively reduces the computational difficulty, Improves the simulation accuracy and computational efficiency.The procedure is simple and easy to debug. The double integral calculation method is simple and effective, so this improved algorithm is more practical.

32

Györi, I., and L. Horváth. "Gronwall-Bellman type integral inequalities for abstract Lebesgue integral." Mathematical and Computer Modelling 25, no. 1 (January 1997): 51–58. http://dx.doi.org/10.1016/s0895-7177(96)00184-7.

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33

DHARSHINNI, N. PRIYA, Amir Saleh, Fadhillah Azmi, and I. Fawwaz. "Design of Simulation Definite Integral Application learning Using Trapezoid Method based on VB.Net." JOURNAL OF INFORMATICS AND TELECOMMUNICATION ENGINEERING 4, no. 1 (July 20, 2020): 193–202. http://dx.doi.org/10.31289/jite.v4i1.3880.

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The definite integral is one of the subjects that is difficult for students to understand because the process of calculating definite integral of functions is quite complicated and long because it requires mastery of some integrating rules so an interactive learning simulation application is needed to make it easier for students to calculate definite integral of functions and the depiction of the area the curve. One method for calculating definite integrals is the trapezoid method. The trapezoid method works by dividing the boundary into 2 intervals namely x = x0 to x = x1. Simulation media application learning will be designed with the VB.Net programming language. This simulation media learning starts with reading and checking data input. The process is continued by displaying the depiction of the input curve and ending with calculating the area of the curve. Simulation media learning provides a facility to store the input data, the results of the calculation of the area and the image of the curve function in the image format of * .bmp. In this media, the media and material expert’s the results of the average are produced by 88.68% included into media category is very valid media and the results of pre-test and post-test trials showed an increase with an average value of 48.3 for pre-test and 87 for the post-test of the passing grade requirement of 70.Keywords: Definite Integral, Trapezoid Method,VB.Net, Media Validation.

34

Kangro, Raul, and Inga Kangro. "ON FULLY DISCRETE COLLOCATION METHODS FOR SOLVING WEAKLY SINGULAR INTEGRAL EQUATIONS." Mathematical Modelling and Analysis 14, no. 1 (March 31, 2009): 69–78. http://dx.doi.org/10.3846/1392-6292.2009.14.69-78.

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A popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be solved. Unfortunately those integrals usually cannot be computed exactly and even when analytic formulas exist, their straightforward application may cause unacceptable roundoff errors resulting in apparent instability of those methods in the case of highly nonuniform grids. In this paper fully discrete analogs of the collocation methods, where integrals are replaced by quadrature formulas, are considered, corresponding error estimates are derived.

35

Nguyen, Hy, and Minh Nguyen. "A simulation of integral and derivative of the solution of a stochastici integral equation." Annales Polonici Mathematici 57, no. 1 (1992): 1–12. http://dx.doi.org/10.4064/ap-57-1-1-12.

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36

Kopec, Ján, Laura Lachvajderová, Marek Kliment, and Peter Trebuňa. "SIMULATION PROCESSES IN COMPANIES USING PLM AND TECNOMATIX PLANT SIMULATION SOFTWARE." Acta Simulatio 7, no. 3 (September 30, 2021): 13–18. http://dx.doi.org/10.22306/asim.v7i3.61.

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This paper aims to demonstrate the use of simulations in the process of improving production processes. With the help of simulations, it is possible to test the efficiency of production in the virtual world, various variants of simulations. The advantage of simulations is the fact that it is possible to make simple and especially cost-effective changes to the production process and thus make it more efficient to the required level. 3D modeling of production halls is already an integral part of improvement. At the same time, this article points out that PLM positively affects the improvement process itself. The final simulation is aimed at improving the production process.

37

Tappe, Stefan. "The Itô Integral with respect to an Infinite Dimensional Lévy Process: A Series Approach." International Journal of Stochastic Analysis 2013 (April 4, 2013): 1–14. http://dx.doi.org/10.1155/2013/703769.

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We present an alternative construction of the infinite dimensional Itô integral with respect to a Hilbert space valued Lévy process. This approach is based on the well-known theory of real-valued stochastic integration, and the respective Itô integral is given by a series of Itô integrals with respect to standard Lévy processes. We also prove that this stochastic integral coincides with the Itô integral that has been developed in the literature.

38

AL-Wagih, Khalil. "A CHAOTIC BAT ALGORITHM FOR SOLVING DEFINITE INTEGRAL." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 14, no. 4 (January 15, 2015): 5592–98. http://dx.doi.org/10.24297/ijct.v14i4.1959.

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In this paper, an Improved Bat Algorithm with Chaos (IBACH) is presented for solving definite integral. The IBACH satisfies the question of parallel calculating numerical integration in engineering and those segmentation points that are adaptive. Several numerical simulation results show that the algorithm offers an effective way to calculate numerical value of definite integrals; it has a high convergence rate, a high accuracy and robustness.

39

Jiang, Runjian, Elisa Torresani, Guodong Cui, and Eugene A. Olevsky. "Proportional Integral Derivative Control in Spark Plasma Sintering Simulations." Materials 14, no. 7 (April 3, 2021): 1779. http://dx.doi.org/10.3390/ma14071779.

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The prediction of microstructure evolution and densification behavior during the spark plasma sintering (SPS) process largely depends on accurate temperature regulation. A loop feedback control algorithm called proportional integral derivative (PID) control is a practical simulation tool, but its coefficients are often determined by an inefficient “trial and error” method. This paper is devoted to proposing a numerical method based on the principles of variable coefficients to construct an optimal linear PID controller in SPS electro-thermal simulations. Different types of temperature profiles were applied to evaluate the feasibility of the proposed method. Simulation results showed that, for temperature profiles conventionally used in SPS cycles, the PID output keeps pace with the desired profile. Characterized by an imperfect time delay and overshoot/undershoot, the constructed PID controller needs further advancement to provide a more satisfactory temperature regulation for non-continuous temperature profiles. The first step towards a numerical rule for the optimal PID controller design was undertaken in this work. It is expected to provide a valuable reference for the advanced electro-thermal modeling of SPS.

40

Amini, S., and N. D. Maines. "Regularization of strongly singular integrals in boundary integral equations." Communications in Numerical Methods in Engineering 12, no. 11 (November 1996): 787–93. http://dx.doi.org/10.1002/(sici)1099-0887(199611)12:11<787::aid-cnm19>3.0.co;2-5.

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41

Kristalinskii, V. R. "ABOUT THE APPROXIMATE SOLUTION OF THE USUAL AND GENERALIZED HILBERT BOUNDARY VALUE PROBLEMS FOR ANALYTICAL FUNCTIONS." Mathematical Modelling and Analysis 5, no. 1 (December 15, 2000): 119–26. http://dx.doi.org/10.3846/13926292.2000.9637134.

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In this article the methods for obtaining the approximate solution of usual and generalized Hilbert boundary value problems are proposed. The method of solution of usual Hilbert boundary value problem is based on the theorem about the representation of the kernel of the corresponding integral equation by τ = t and on the earlier proposed method for the computation of the Cauchy‐type integrals. The method for approximate solution of the generalized boundary value problem is based on the method for computation of singular integral of the formproposed by the author. All methods are implemented with the Mathcad and Maple.

42

Bertoco, Juliana, Manoel S. B. de Araújo, Rosalía T. Leiva, Hugo A. C. Sánchez, and Antonio Castelo. "Numerical Simulation of KBKZ Integral Constitutive Equations in Hierarchical Grids." Applied Sciences 11, no. 11 (May 26, 2021): 4875. http://dx.doi.org/10.3390/app11114875.

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In this work, we present the implementation and verification of HiGTree-HiGFlow solver (see for numerical simulation of the KBKZ integral constitutive equation. The numerical method proposed herein is a finite difference technique using tree-based grids. The advantage of using hierarchical grids is that they allow us to achieve great accuracy in local mesh refinements. A moving least squares (MLS) interpolation technique is used to adapt the discretization stencil near the interfaces between grid elements of different sizes. The momentum and mass conservation equations are solved by an implicit method and the Chorin projection method is used for decoupling the velocity and pressure. The Finger tensor is calculated using the deformation fields method and a three-node quadrature formula is used to derive an expression for the integral tensor. The results of velocity and stress fields in channel and contraction-flow problems obtained in our simulations show good agreement with numerical and experimental results found in the literature.

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Zhang, Xiang, Xu Dong Pan, and Guang Lin Wang. "Machining Trajectory Generation and Simulation of Miniature Integral Impeller." Key Engineering Materials 522 (August 2012): 355–58. http://dx.doi.org/10.4028/www.scientific.net/kem.522.355.

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This paper describes machining trajectory generation and simulation of miniature integral impeller. Taking into account the closed and miniature of integral impeller, and low stiffness of the micro-milling tool, in order to avoid interference in the processing, through reasonably division of the impeller blade surface, generate the miniature integral impeller machining trajectory. Then impeller machining NC code is generated, and is simulated in Vericut software. Simulation result shows that the machining programs generated in this paper are effective, and the simulation machined workpiece surface is relatively smooth.

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Vaz, P. T., and S. G. Deo. "On a Volterra Stieltjes integral equation." Journal of Applied Mathematics and Stochastic Analysis 3, no. 3 (January 1, 1990): 177–91. http://dx.doi.org/10.1155/s104895339000017x.

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The paper deals with a study of linear Volterra integral equations involving Lebesgue-Stieltjes integrals in two independent variables. The authors prove an existence theorem using the Banach fixed-point principle. An explicit example is also considered.

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Orekhov, V. I. "Steady motions and integral manifolds of systems with quadratic integrals." Journal of Applied Mathematics and Mechanics 54, no. 6 (January 1990): 751–55. http://dx.doi.org/10.1016/0021-8928(90)90004-t.

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Radenac, Emmanuel, Rémi Harry, and Philippe Villedieu. "A Galerkin Method for the Simulation of Laminar Boundary Layers on Heated Walls." Energies 15, no. 9 (April 29, 2022): 3267. http://dx.doi.org/10.3390/en15093267.

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This paper presents a new solution method for the calculation of laminar thermal boundary layers. The method consists of a coupling between a modal method (Galerkin method) in the direction normal to the wall and a finite volume method in the direction(s) tangential to the wall. It is similar to an integral method in the sense that only a surface mesh is required and that the unknowns are integral quantities (corresponding to the moments up to a fixed order of the temperature profile in the direction normal to the wall). A specificity of the Galerkin method used is that the domain over which the integrals are computed has a variable size that is also an unknown of the problem. Using a series of numerical tests (representative of situations that can be encountered in aeronautics in the case of a wing equipped with a thermal ice protection system), we show that the new method allows us to predict the quantities of interest with a maximum error of a few percent, while a usual integral method (with only one unknown per mesh cell) is unable to treat the case of boundary layers on heated walls with a strong longitudinal temperature gradient, as shown in the literature.

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de Ruiter, M. J., and T. J. J. van der Zee. "Improved Simulation of Wave Loads on Offshore Structures in Integral Design Load Case Simulations." Energy Procedia 94 (September 2016): 199–206. http://dx.doi.org/10.1016/j.egypro.2016.09.224.

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Brieuc, Fabien, Hichem Dammak, and Marc Hayoun. "Quantum Thermal Bath for Path Integral Molecular Dynamics Simulation." Journal of Chemical Theory and Computation 12, no. 3 (February 8, 2016): 1351–59. http://dx.doi.org/10.1021/acs.jctc.5b01146.

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Hadiningrat, Mahendra Satria. "Feynman Path Integral in Multiple-Slit and its Simulation." SPECTA Journal of Technology 2, no. 1 (November 27, 2019): 63–70. http://dx.doi.org/10.35718/specta.v2i1.96.

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In this article we hold on an analytic solution of the well-known cases of difraction and interference of electrons through one and two slits (simply that, the one-dimensional case is assumed only). In addition, we hold an approximations of the electron distribution which offer the interpretation of the results. Our derivation is based on the Feynman path integral formula and this work could also serve an awesome introduction to multiple slits interference. Then it is comparing between theoretical results and simulation in order to get interference pattern of it.

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Liu, Zhi-Hua, and Jeremy Broughton. "Path-integral simulation of positronium in a hard sphere." Physical Review B 40, no. 1 (July 1, 1989): 571–77. http://dx.doi.org/10.1103/physrevb.40.571.

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