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Journal articles on the topic 'Weak and strong numerical congergence'

Author: Grafiati

Published: 9 September 2022

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1

Mosler, J. "Numerical analyses of discontinuous material bifurcation: strong and weak discontinuities." Computer Methods in Applied Mechanics and Engineering 194, no. 9-11 (2005): 979–1000. http://dx.doi.org/10.1016/j.cma.2004.06.018.

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2

Mavroyannis, Constantine. "A laser-excited three-level atom. II numerical results." Canadian Journal of Physics 68, no. 4-5 (1990): 411–21. http://dx.doi.org/10.1139/p90-065.

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Numerical calculations are presented for the interference spectra of a laser-excited three-level atom, where the strong and the weak atomic transitions are driven by resonant and nonresonant laser fields, respectively. The spectral functions describing the interference spectra for the electric dipole allowed excited state have been considered in the low- and high-intensity limit of the laser field operating in the strong transition. The interference spectra arise from the competition between short-lifetime spontaneous processes and short- and long-lifetime excitations induced by the strong and

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3

Mužík, Juraj. "Numerical Simulation of the Couette Flow Using Meshless Weak-strong Method." Procedia Engineering 91 (2014): 334–39. http://dx.doi.org/10.1016/j.proeng.2014.12.070.

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4

Bunch, James R. "The weak and strong stability of algorithms in numerical linear algebra." Linear Algebra and its Applications 88-89 (April 1987): 49–66. http://dx.doi.org/10.1016/0024-3795(87)90102-9.

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5

Englert, Roman, and Jörg Muschiol. "Numerical Evidence That the Power of Artificial Neural Networks Limits Strong AI." Advances in Artificial Intelligence and Machine Learning 02, no. 02 (2022): 338–46. http://dx.doi.org/10.54364/aaiml.2022.1122.

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A famous definition of AI is based on the terms weak and strong AI from McCarthy. An open question is the characterization of these terms, i.e., the transition from weak to strong. Nearly no research results are known for this complex and important question. In this paper we investigate how the size and structure of a Neural Network (NN) limits the learnability of a training sample, and thus, can be used to discriminate weak and strong AI (domains). Furthermore, the size of the training sample is a primary parameter for the training effort estimation with the big O function. The needed trainin

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Hilke, Michael, Mathieu Massicotte, Eric Whiteway, and Victor Yu. "Weak Localization in Graphene: Theory, Simulations, and Experiments." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/737296.

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We provide a comprehensive picture of magnetotransport in graphene monolayers in the limit of nonquantizing magnetic fields. We discuss the effects of two-carrier transport, weak localization, weak antilocalization, and strong localization for graphene devices of various mobilities, through theory, experiments, and numerical simulations. In particular, we observe a minimum in the weak localization and strong localization length reminiscent of the minimum in the conductivity, which allows us to make the connection between weak and strong localization. This provides a unified framework for both

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7

Kerman, R. A. "Strong and Weak Weighted Convergence of Jacobi Series." Journal of Approximation Theory 88, no. 1 (1997): 1–27. http://dx.doi.org/10.1006/jath.1996.3005.

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8

Ngodock, Hans, Matthew Carrier, Scott Smith, and Innocent Souopgui. "Weak and Strong Constraints Variational Data Assimilation with the NCOM-4DVAR in the Agulhas Region Using the Representer Method." Monthly Weather Review 145, no. 5 (2017): 1755–64. http://dx.doi.org/10.1175/mwr-d-16-0264.1.

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Abstract The difference between the strong and weak constraints four-dimensional variational (4DVAR) analyses is examined using the representer method formulation, which expresses the analysis as the sum of a first guess and a finite linear combination of representer functions. The latter are computed analytically for a single observation under both strong and weak constraints assumptions. Even though the strong constraints representer coefficients are different from their weak constraints counterparts, that difference is unable to help the strong constraints compensate for the loss of informa

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9

Abbasian Arani, Ali Akbar, and Majid Dehghani. "Numerical Comparison of Two and Three Dimensional Flow Regimes in Porous Media." Defect and Diffusion Forum 312-315 (April 2011): 427–32. http://dx.doi.org/10.4028/www.scientific.net/ddf.312-315.427.

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The purpose of this work is to study the fluid flow regimes in a porous media with high enough velocities (in the range of laminar flow). In our study, the results obtained from expanding Darcy’s equation to Forchheimer’s equation with volume averaging method have been used for studdying the fluid flow behavior in 2D and 3D models. Results of numerical simulations show that in all cases, there are weak inertial regime, strong inertial regime and transition zone. In all the cases, the domain of weak inertial regime is relatively narrow, and this problem is intensified in the 3D numerical simula

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Siopacha, Maria, and Josef Teichmann. "Weak and strong Taylor methods for numerical solutions of stochastic differential equations." Quantitative Finance 11, no. 4 (2011): 517–28. http://dx.doi.org/10.1080/14697680903493573.

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11

Dormy, Emmanuel. "Strong-field spherical dynamos." Journal of Fluid Mechanics 789 (January 22, 2016): 500–513. http://dx.doi.org/10.1017/jfm.2015.747.

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Numerical models of the geodynamo are usually classified into two categories: dipolar modes, observed when the inertial term is small enough; and multipolar fluctuating dynamos, for stronger forcing. We show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong-field limit. This solution coexists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set

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12

Legay, A., H. W. Wang, and T. Belytschko. "Strong and weak arbitrary discontinuities in spectral finite elements." International Journal for Numerical Methods in Engineering 64, no. 8 (2005): 991–1008. http://dx.doi.org/10.1002/nme.1388.

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13

Ewald, Brian. "Weak Versions of Stochastic Adams-Bashforth and Semi-implicit Leapfrog Schemes for SDEs." Computational Methods in Applied Mathematics 12, no. 1 (2012): 23–31. http://dx.doi.org/10.2478/cmam-2012-0002.

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AbstractWe consider the weak analogues of certain strong stochastic numerical schemes, namely an Adams-Bashforth scheme and a semi-implicit leapfrog scheme. We show that the weak version of the Adams-Bashforth scheme converges weakly with order 2, and the weak version of the semi-implicit leapfrog scheme converges weakly with order 1. We also note that the weak schemes are computationally simpler and easier to implement than the corresponding strong schemes, resulting in savings in both programming and computational effort.

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14

Fantuzzi, Nicholas, Lorenzo Leonetti, Patrizia Trovalusci, and Francesco Tornabene. "Some Novel Numerical Applications of Cosserat Continua." International Journal of Computational Methods 15, no. 06 (2018): 1850054. http://dx.doi.org/10.1142/s0219876218500548.

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Cosserat continua demonstrated to have peculiar mechanical properties, with respect to classic Cauchy continua, because they are able to more accurately describe heterogeneous materials, as particle composites and masonry-like material, taking into account size effects. Many studies have been devoted to their numerical implementation. In this paper, some reference benchmarks, referred to an isotropic heterogeneous sample, are shown by comparing the solutions provided by strong and weak formulations. The strong formulation finite element method (SFEM), implemented in MATLAB®, is compared to the

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15

Kiefer, Michael T., Matthew D. Parker, and Joseph J. Charney. "Regimes of Dry Convection above Wildfires: Idealized Numerical Simulations and Dimensional Analysis*." Journal of the Atmospheric Sciences 66, no. 4 (2009): 806–36. http://dx.doi.org/10.1175/2008jas2896.1.

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Abstract Wildfires are capable of inducing atmospheric circulations that result predominantly from large temperature anomalies produced by the fire. The fundamental dynamics through which a forest fire and the atmosphere interact to yield different convective regimes is still not well understood. This study uses the Advanced Regional Prediction System (ARPS) model to investigate the impact of the environmental (i.e., far upstream, undisturbed by fire) wind profile on dry convection above a prescribed heat source of an intensity and spatial scale comparable to a wildfire. Dimensional analysis o

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16

Kitiashvili, I. N., A. G. Kosovichev, A. A. Wray, and N. N. Mansour. "Numerical simulations of magnetic structures." Proceedings of the International Astronomical Union 6, S273 (2010): 315–19. http://dx.doi.org/10.1017/s1743921311015444.

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AbstractWe use 3D radiative MHD simulations of the upper turbulent convection layer for investigation of physical mechanisms of formation of magnetic structures on the Sun. The simulations include all essential physical processes, and are based of the LES (Large-Eddy Simulations) approach for describing the sub-grid scale turbulence. The simulation domain covers the top layer of the convection zone and the lower atmosphere. The results reveal a process of spontaneous formation of stable magnetic structures from an initially weak vertical magnetic field, uniformly distributed in the simulation

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17

Saha, Nilanjan, and D. Roy. "Higher order weak linearizations of stochastically driven nonlinear oscillators." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2083 (2007): 1827–56. http://dx.doi.org/10.1098/rspa.2007.1852.

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We present derivative-free weak and strong solutions of stochastically driven nonlinear oscillators of engineering interest using higher order forms of the locally transversal linearization (LTL) method. Unlike strong solutions, weak stochastic solutions attempt to predict only mathematical expectations of functions of the true solution and are obtainable with much less computational effort. The linearized equations corresponding to the higher order implicit LTL schemes are arrived at using backward Euler–Maruyama and Newmark expansions in order to conditionally replace nonlinear drift and mul

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18

Cai, Xing Hui, Cheng Ying Shi, Peng Xu, Man Lin Zhu, and Guo Liang Wang. "A Meshfree Weak-Strong-Form Method for Magnetohydrodynamic Flow in a Pipe." Advanced Materials Research 490-495 (March 2012): 1883–87. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.1883.

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In this paper, a meshfree weak-strong form method is presented to compute the fully developed magnetohydrodynmic flow in a pipe. The radial basis function point interpolation approximation is adopted to construct the shape functions. For the nodes whose local quadrature domain is intersect with the natural boundaries, a local weak form of radial point interpolation method is applied. Otherwise, a strong form of meshfree point collocation method is employed. Numerical simulations are carried out for fully developed magnetohydrodynmic flow in a rectangular pipe with arbitrary electrical conducti

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19

Weber, C., A. Stasiak, P. De Los Rios, and G. Dietler. "Numerical Simulation of Gel Electrophoresis of DNA Knots in Weak and Strong Electric Fields." Biophysical Journal 90, no. 9 (2006): 3100–3105. http://dx.doi.org/10.1529/biophysj.105.070128.

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20

Naimie, Christopher E. "Georges Bank residual circulation during weak and strong stratification periods: Prognostic numerical model results." Journal of Geophysical Research: Oceans 101, no. C3 (1996): 6469–86. http://dx.doi.org/10.1029/95jc03698.

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21

Lehtola, Susi, Maria Dimitrova, and Dage Sundholm. "Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields." Molecular Physics 118, no. 2 (2019): e1597989. http://dx.doi.org/10.1080/00268976.2019.1597989.

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22

Wang, B. R., J. T. Liu, S. T. Gu, and Q. C. He. "Numerical evaluation of the effective conductivities of composites with interfacial weak and strong discontinuities." International Journal of Thermal Sciences 93 (July 2015): 1–20. http://dx.doi.org/10.1016/j.ijthermalsci.2014.12.025.

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23

MA, GUOWEI, XINMEI AN, and LEI HE. "THE NUMERICAL MANIFOLD METHOD: A REVIEW." International Journal of Computational Methods 07, no. 01 (2010): 1–32. http://dx.doi.org/10.1142/s0219876210002040.

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This paper presents a review on the numerical manifold method (NMM), which covers the basic theories of the NMM, such as NMM components, NMM displacement approximation, formulations of the discrete system of equations, integration scheme, imposition of the boundary conditions, treatment of contact problems involved in the NMM, and also the recent developments and applications of the NMM. Modeling the strong discontinuities within the framework of the NMM is specially emphasized. Several examples demonstrating the capability of the NMM in modeling discrete block system, strong discontinuities,

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24

Булат, П. В., К. Н. Волков, and М. С. Яковчук. "Flow visualization with strong and weak gas dynamic discontinuities in computational fluid dynamics." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 3 (September 20, 2016): 245–57. http://dx.doi.org/10.26089/nummet.v17r323.

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Рассматриваются методы визуализации течений с газодинамическими разрывами, позволяющие проводить сравнение результатов численного моделирования с данными физического эксперимента. Дается обзор методов оптической визуализации течений сжимаемого газа (теневые картины, шлирен-изображения, интерферограммы). Приводятся примеры визуального представления решений ряда задач газовой динамики, связанных с расчетами течений, содержащих слабые и сильные газодинамические разрывы. Для повышения наглядности результирующего образа применяются топологические методы визуализации, позволяющие определить положени

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25

Alzahrani, Faris, Aatef Hobiny, Ibrahim Abbas, and Marin Marin. "An Eigenvalues Approach for a Two-Dimensional Porous Medium Based Upon Weak, Normal and Strong Thermal Conductivities." Symmetry 12, no. 5 (2020): 848. http://dx.doi.org/10.3390/sym12050848.

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This work is devoted to the investigation of a two-dimensional porous material under weak, strong and normal conductivity, using the eigenvalues method. By using Laplace–Fourier transformations with the eigenvalues technique, the variables are analytically obtained. The derived technique is assessed with numerical results that are obtained from the porous mediums using simplified symmetric geometry. The results, including the displacements, temperature, stresses and the change in the volume fraction field, are offered graphically. Comparisons are made among the outcomes obtained under weak, no

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26

Francq, Christian, and Jean-Michel Zakoïan. "HAC estimation and strong linearity testing in weak ARMA models." Journal of Multivariate Analysis 98, no. 1 (2007): 114–44. http://dx.doi.org/10.1016/j.jmva.2006.02.003.

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27

Lu, Qiuying, and Vincent Naudot. "Bifurcation Complexity from Orbit-Flip Homoclinic Orbit of Weak Type." International Journal of Bifurcation and Chaos 26, no. 04 (2016): 1650059. http://dx.doi.org/10.1142/s0218127416500590.

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In this paper, we study the unfolding of a three-dimensional vector field having an orbit-flip homoclinic orbit of weak type. Such a homoclinic orbit is a degenerate version of the so-called orbit-flip homoclinic orbit. We show the existence of inclination-flip homoclinic orbits of arbitrary higher order bifurcating from the unperturbed system. Our strategy consists of using the local moving coordinates method and blow up in the parameter space. In addition, the numerical existence of the orbit-flip homoclinic orbit of weak type is presented based on the truncated Taylor expansion and the nume

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28

Kovács, Mihály, Annika Lang, and Andreas Petersson. "Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 6 (2020): 2199–227. http://dx.doi.org/10.1051/m2an/2020012.

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The numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise is considered. A standard finite element method is employed for the spatial approximation and a a rational approximation of the exponential function for the temporal approximation. First, strong convergence of this approximation in both positive and negative order norms is proven. With the help of Malliavin calculus techniques this result is then used to deduce weak convergence rates for the class of twice continuously differentiable test functions with polynomially bounded deriva

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29

Xue, Jianyang, Xin Zhang, Rui Ren, Lei Zhai, and Linlin Ma. "Experimental and numerical study on seismic performance of steel reinforced recycled concrete frame structure under low-cyclic reversed loading." Advances in Structural Engineering 21, no. 12 (2018): 1895–910. http://dx.doi.org/10.1177/1369433218759080.

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This article mainly focused on the seismic performance of steel reinforced recycled concrete frame structure under low-cyclic reversed loading. To evaluate seismic performance of steel reinforced recycled concrete frame structure, a two-span three-storied steel reinforced recycled concrete frame was conducted at civil engineering laboratory of Xi’an University of Architecture and Technology. Experimental and numerical studies were implemented to investigate the crack status, failure modes, hysteresis loops, skeleton curves, energy dissipation capacity, load–displacement curves, P-Δ effect, and

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30

Sun, Yabing, Jie Yang, and Weidong Zhao. "Itô-Taylor Schemes for Solving Mean-Field Stochastic Differential Equations." Numerical Mathematics: Theory, Methods and Applications 10, no. 4 (2017): 798–828. http://dx.doi.org/10.4208/nmtma.2017.0007.

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AbstractThis paper is devoted to numerical methods for mean-field stochastic differential equations (MSDEs). We first develop the mean-field Itô formula and mean-field Itô-Taylor expansion. Then based on the new formula and expansion, we propose the Itô-Taylor schemes of strong order γ and weak order η for MSDEs, and theoretically obtain the convergence rate γ of the strong Itô-Taylor scheme, which can be seen as an extension of the well-known fundamental strong convergence theorem to the mean-field SDE setting. Finally some numerical examples are given to verify our theoretical results.

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31

Carrillo, José A., Young-Pil Choi, and Yingping Peng. "Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system." Kinetic and Related Models 15, no. 3 (2022): 355. http://dx.doi.org/10.3934/krm.2021052.

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<p style='text-indent:20px;'>We provide a quantitative asymptotic analysis for the nonlinear Vlasov–Poisson–Fokker–Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often referred to as aggregation-diffusion equations. We show that a weak solution to the Vlasov–Poisson–Fokker–Planck system strongly converges to a strong solution to the diffusive model. Our proof relies on the modulated macroscopic kinetic energy estimate based on the weak-strong uniqueness principle together with a careful analys

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32

Huang, Yan Lu, Xin You Ke, and Yi Bin Li. "Numerical Coupling Analysis of Droplets’ Behaviors in GMAW." Advanced Materials Research 139-141 (October 2010): 981–85. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.981.

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The forming process and dynamic behaviors of droplets in gas metal arc welding (GMAW) were numerically simulated by using weak electromagnetic coupling method, with considering the gravity, the electromagnetic force, the free surface and the turbulent flow in the droplets. The shape update of the droplets was calculated on basis of VOF and CSF theories. The Gaussian electric current density was identified as boundary conditions for calculating electromagnetic force. A weak electromagnetic coupling model was used to study the characteristics of relevant physical variables and their roles in met

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33

Nguyen, Binh Huy, and Giang Song Le. "Comparative study of numerical schemes for strong shock simulation using the Euler equations." Science and Technology Development Journal 18, no. 1 (2015): 73–88. http://dx.doi.org/10.32508/stdj.v18i1.943.

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A numerical study of extremely strong shocks was presented. Various types of numerical schemes with first-order accuracy and higherorder accuracy with adaptive stencils were implemented to solve the one and twodimensional Euler equations based on the explicit finite difference method, including Roe’s first-order upwind, Steger-Warming Flux Vector splitting (FVS), Sweby’s flux-limited and Essentially Non-oscillatory (ENO) scheme. The result comparisons were carried out to discuss which scheme is the most suitable for strong shock problem. The dissipative nature of the firstorder scheme can be e

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34

Lu, Wei, Mingyang Li, Bozo Vazic, Selda Oterkus, Erkan Oterkus, and Qing Wang. "Peridynamic Modelling of Fracture in Polycrystalline Ice." Journal of Mechanics 36, no. 2 (2020): 223–34. http://dx.doi.org/10.1017/jmech.2019.61.

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ABSTRACTIn this study, a peridynamic material model for a polycrystalline ice is utilised to investigate its fracture behaviour under dynamic loading condition. First, the material model was validated by considering a single grain, double grains and polycrystalline structure under tension loading condition. Peridynamic results are compared against finite element analysis results without allowing failure. After validating the material model, dynamic analysis of a polycrystalline ice material with two pre-existing cracks under tension loading is performed by considering weak and strong grain bou

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35

Chen, Hong, Wei Bing Zhu, Run Peng Sun, and Bin Zhang. "Numerical Simulation of Shock Diffraction on Cartesian Grid." Advanced Materials Research 378-379 (October 2011): 11–14. http://dx.doi.org/10.4028/www.scientific.net/amr.378-379.11.

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Shock diffraction over geometric obstacles is performed on two-dimensional cartesian grid using the TVD WAF method in conjunction with the HLLC approximate Riemann solver and dimensional splitting. Present cartesian grid results for popular and challenging two-dimensional shock diffraction problems are presented and compared to experimental photographs. Benchmark and example test cases were chosen to cover a wide variety of Mach numbers for weak and strong shock waves, and for square and circular geometries. The results show that the comparisons between experimental and simulated images are co

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36

Kumar, Pankaj, and Rupali Verma. "Impact of delay parameter on plant-herbivore dynamics under allee effect." Journal of Physics: Conference Series 2267, no. 1 (2022): 012018. http://dx.doi.org/10.1088/1742-6596/2267/1/012018.

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Abstract In this paper, plant-herbivore dynamics have been studied under the Allee effect using delay differential equations. The state variables considered are: plant population and herbivores. The boundedness and positivity of solutions are established. The interior equilibrium point is calculated for both, strong and weak Allee effect. It is shown that both the populations-plant and herbivores perish under the strong Allee effect. The stability of the system around the interior equilibrium under weak Allee effect is checked. Hopf-Bifurcation occurred at the critical value of the delay param

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IMADA, Masatoshi, Yasuhiro HATSUGAI, and Naoto NAGAOSA. "NUMERICAL ANALYSIS OF COUPLED SPIN-FERMION MODEL — PAIRING MECHANISM THROUGH EXTENDED KONDO SINGLET." International Journal of Modern Physics B 02, no. 05 (1988): 959–73. http://dx.doi.org/10.1142/s0217979288000792.

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A coupled spin-fermion model is investigated by the exact diagonalization of finite lattices to discuss magnetic mechanism of superconductivity. An extended cloud of singlet liquid (extended Kondo singlet) is found around the fermion in a strong coupling region characterized by strong Kondo coupling and large transfer. The existence of the bound state of two fermions is found. The relevance of its Cooper pairing to high-Tc superconductivity is discussed. The relation to the weak coupling region and also to the small transfer region in this model is discussed.

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Anh, Nguyen Dong, and Ninh Quang Hai. "Extension of method of moment equation to nonlinear deterministic vibrations." Vietnam Journal of Mechanics 24, no. 3 (2002): 133–41. http://dx.doi.org/10.15625/0866-7136/24/3/6615.

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The paper present the so-called "an extended averaged equation approach" to the investigation of nonlinear vibration problems. The numerical results in analysing the vibration systems with weak, middle and strong non-linearity show the advantages of the method.

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Grudzien, Colin, Marc Bocquet, and Alberto Carrassi. "On the numerical integration of the Lorenz-96 model, with scalar additive noise, for benchmark twin experiments." Geoscientific Model Development 13, no. 4 (2020): 1903–24. http://dx.doi.org/10.5194/gmd-13-1903-2020.

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Abstract. Relatively little attention has been given to the impact of discretization error on twin experiments in the stochastic form of the Lorenz-96 equations when the dynamics are fully resolved but random. We study a simple form of the stochastically forced Lorenz-96 equations that is amenable to higher-order time-discretization schemes in order to investigate these effects. We provide numerical benchmarks for the overall discretization error, in the strong and weak sense, for several commonly used integration schemes and compare these methods for biases introduced into ensemble-based stat

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40

Gavalec, Martin, Ján Plavka, and Daniela Ponce. "Strong, Strongly Universal and Weak Interval Eigenvectors in Max-Plus Algebra." Mathematics 8, no. 8 (2020): 1348. http://dx.doi.org/10.3390/math8081348.

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The optimization problems, such as scheduling or project management, in which the objective function depends on the operations maximum and plus, can be naturally formulated and solved in max-plus algebra. A system of discrete events, e.g., activations of processors in parallel computing, or activations of some other cooperating machines, is described by a systems of max-plus linear equations. In particular, if the system is in a steady state, such as a synchronized computer network in data processing, then the state vector is an eigenvector of the system. In reality, the entries of matrices an

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41

KLOEDEN, P. E., E. PLATEN, and H. SCHURZ. "THE NUMERICAL SOLUTION OF NONLINEAR STOCHASTIC DYNAMICAL SYSTEMS: A BRIEF INTRODUCTION." International Journal of Bifurcation and Chaos 01, no. 02 (1991): 277–86. http://dx.doi.org/10.1142/s021812749100021x.

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The numerical analysis of stochastic differential equations, currently undergoing rapid development, differs significantly from its deterministic counterpart due to the peculiarities of stochastic calculus. This article presents a brief, pedagogical introduction to the subject from the perspective of stochastic dynamical systems. The key tool is the stochastic Taylor expansion. Strong, pathwise approximations are distinguished from weak, functional approximations, and their role in stability with Lyapunov exponents and stiffness is discussed.

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42

Давыдов, С. Ю. "Намагниченность эпитаксиального графена, наведенная магнитной металлической подложкой". Физика твердого тела 62, № 2 (2020): 326. http://dx.doi.org/10.21883/ftt.2020.02.48886.602.

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Model of energy diagram for the graphene monolayer (Gr) fabricated on magnetic transition metal (MTM) is proposed. Regimes of the strong and weak Gr-MTM coupling are discussed and corresponding analytical expressions for the substrate induced magnetization of epigraphene are obtained. It is shown that in the case of strong coupling the main contribution in magnetization are given by the quasi-local state which leads to the antiferromagnetic Gr-MTM bond, while in the case of weak coupling the main contribution in magnetization are given by the MTM d-band which leads to the ferromagnetic Gr-MTM

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Okrugin, Boris M., Ralf P. Richter, Frans A. M. Leermakers, Igor M. Neelov, Ekaterina B. Zhulina, and Oleg V. Borisov. "Electroresponsive Polyelectrolyte Brushes Studied by Self-Consistent Field Theory." Polymers 12, no. 4 (2020): 898. http://dx.doi.org/10.3390/polym12040898.

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End-grafting of polyelectrolyte chains to conducting substrates offers an opportunity to fabricate electro-responsive surfaces capable of changing their physical/chemical properties (adhesion, wettability) in response to applied electrical voltage. We use a self-consistent field numerical approach to compare the equilibrium properties of tethered strong and weak (pH-sensitive) polyelectrolytes to applied electrical field in both salt-free and salt-containing solutions. We demonstrate that both strong and weak polyelectrolyte brushes exhibit segregation of polyions in two populations if the sur

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Platen, Eckhard. "An introduction to numerical methods for stochastic differential equations." Acta Numerica 8 (January 1999): 197–246. http://dx.doi.org/10.1017/s0962492900002920.

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This paper aims to give an overview and summary of numerical methods for the solution of stochastic differential equations. It covers discrete time strong and weak approximation methods that are suitable for different applications. A range of approaches and results is discussed within a unified framework. On the one hand, these methods can be interpreted as generalizing the well-developed theory on numerical analysis for deterministic ordinary differential equations. On the other hand they highlight the specific stochastic nature of the equations. In some cases these methods lead to completely

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Song, Baofang, Dwight Barkley, Björn Hof, and Marc Avila. "Speed and structure of turbulent fronts in pipe flow." Journal of Fluid Mechanics 813 (January 27, 2017): 1045–59. http://dx.doi.org/10.1017/jfm.2017.14.

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Using extensive direct numerical simulations, the dynamics of laminar–turbulent fronts in pipe flow is investigated for Reynolds numbers between $Re=2000$ and 5500. We here investigate the physical distinction between the fronts of weak and strong slugs both by analysing the turbulent kinetic energy budget and by comparing the downstream front motion to the advection speed of bulk turbulent structures. Our study shows that weak downstream fronts travel slower than turbulent structures in the bulk and correspond to decaying turbulence at the front. At $Re\simeq 2900$ the downstream front speed

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Yang, Judy P., and Jian-Yu Chen. "Strong-Form Formulated Generalized Displacement Control Method for Large Deformation Analysis." International Journal of Applied Mechanics 09, no. 07 (2017): 1750101. http://dx.doi.org/10.1142/s1758825117501010.

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The traditional analysis of geometric nonlinearity is mostly based on the weak-formulated Galerkin method such as the finite element method. The element nature has limited its application as a result of numerical integration in the governing equation and quality control of deformed mesh. In the middle of 1990s, the meshfree methods have been developed and become one leading research topic in computational mechanics. Especially, the strong form collocation methods require no additional efforts to process numerical integration and impose Dirichlet boundary condition, thereby making the collocati

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Yang, Fen, Ziming Kou, Juan Wu, and Tengyu Li. "Application of Mutual Information-Sample Entropy Based MED-ICEEMDAN De-Noising Scheme for Weak Fault Diagnosis of Hoist Bearing." Entropy 20, no. 9 (2018): 667. http://dx.doi.org/10.3390/e20090667.

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In this paper, a novel weak fault features extraction scheme is proposed to extract weak fault features in head sheave bearings of floor-type multi-rope friction mine hoists in strong noise environments. A mutual information-based sample entropy (MI-SE) is proposed to select the effective intrinsic mode function (IMF). The numerical simulation presented in this paper has demonstrated that the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) has a poor performance on weak signals processing under a strong noise background, and fault features cannot be ident

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Parra-Santos, M. Teresa, and Francisco Castro. "Benchmarking for Practical Training in Computational Fluid Dynamics." Journal of Cases on Information Technology 17, no. 1 (2015): 1–12. http://dx.doi.org/10.4018/jcit.2015010101.

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Computational Fluid Dynamics (CFD) is the useful design tool for engineers that requests strong knowledge of fluid mechanics and numerical skills. Learning by doing has significant impact on the success rate of this difficult subject. This paper presents a workshop developed for engineering degree where different scaled down projects is accomplished by students and peers evaluated. Students improve their understanding of the strong and weak points of the numerical models and gain an insight into the fluid dynamics processes learnt in the classroom. Beside, other transversal skills are develope

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Wong, Kok Cheong. "Numerical Investigation of a Crossflow Jet in a Rectangular Microchannel." Applied Mechanics and Materials 284-287 (January 2013): 849–53. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.849.

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The present numerical study is conducted in three dimensional to investigate the crossflow of an external round jet and a horizontal stream of microchannel flow. The results of heat transfer performance for the cases with and without transverse jet are compared. The patterns of different crossflow jet were analyzed to understand the flow and heat transfer characteristics. The effect of jet nozzle position on the heat transfer is investigated. Generally, the heat transfer performance increases with the jet Reynolds number. However, some cases of weak jet are found to cause lower heat transfer r

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Hussain, Nawab, Vivek Kumar, Preety Malik, and Renu Chugh. "Jungck-type implicit iterative algorithms with numerical examples." Filomat 31, no. 8 (2017): 2303–20. http://dx.doi.org/10.2298/fil1708303h.

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We introduce a new Jungck-type implicit iterative scheme and study its strong convergence, stability under weak parametric restrictions in generalized convex metric spaces and data dependency in generalized hyperbolic spaces. We show thatnewintroduced iterative scheme has better convergence rate as compared to well known Jungck implicit Mann, Jungck implicit Ishikawa and Jungck implicit Noor iterative schemes. It is also shown that Jungck implicit iterative schemes converge faster than the corresponding Jungck explicit iterative schemes. Validity of our analytic proofs is shown through numeric

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