Journal articles: 'Weak and strong numerical congergence'

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

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Mavroyannis, Constantine. "A laser-excited three-level atom. II numerical results." Canadian Journal of Physics 68, no. 4-5 (April 1, 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 the weak laser fields, respectively. Both laser fields have been treated as quantized and as classical entities. The computed spectra have been presented graphically for different values of the Rabi frequencies and detunings of the weak laser field. It is shown that the decrease in the intensity of the short-lifetime excitation may provide a measure of the spectral width of the long-lifetime excitation.

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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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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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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 training repetitions may also limit the learning tractability and will be investigated. The results are illustrated with an analysis of a feedforward NN and a training sample for language with 1,000 words including the effort for the training repetitions.

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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 localizations, which explains the observed experimental features. We compare these results to numerical simulation and find a remarkable agreement between theory, experiment, and numerics. Various graphene devices were used in this study, including graphene on different substrates, such as glass and silicon, as well as low and high mobility devices.

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

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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 (April 17, 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 information that the weak constraints includes. Numerical experiments carried out in the Agulhas retroflection for single and multiobservation assimilations clearly show that the weak constraint 4DVAR produces analyses that fit the observations with significantly higher accuracy than the strong constraints.

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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 simulations. This could be the reason of missing the weak inertial regime in experimental studies on inertial fluid flow in porous media. The domain of strong inertial regime in 3D models is so wide that after Darcy’s regime, the governed regime is the strong inertial regime. To obtain more accurate and analytical results, more studies should be done on the 2D and the 3D flow regimes.

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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 (April 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 the dominant length scale, and the strong-field branch, in which viscous and inertial effects are largely negligible. These results indicate that a distinguished limit needs to be sought to produce numerical models relevant to the geodynamo and that the usual approach of minimising the magnetic Prandtl number (ratio of the fluid kinematic viscosity to its magnetic diffusivity) at a given Ekman number is misleading.

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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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Fantuzzi, Nicholas, Lorenzo Leonetti, Patrizia Trovalusci, and Francesco Tornabene. "Some Novel Numerical Applications of Cosserat Continua." International Journal of Computational Methods 15, no. 06 (September 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 finite element method (FEM), given by COMSOL® Multiphysics, and the advantages of the two approaches are highlighted and discussed.

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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 (April 1, 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 of the fire–atmosphere problem provides two relevant parameters: a surface buoyancy parameter that addresses the amount of heat a parcel of air receives in transiting above the fire and an advection parameter that addresses the degree to which the environmental wind advects updrafts away from the fire. Two-dimensional simulations are performed in which the upstream surface wind speed and mixed layer mean wind speed are varied independently to better understand the fundamental processes governing the organizational mode and updraft strength. The result of these experiments is the identification of two primary classes of dry convection: plume and multicell. Simulated plume cases exhibit weak advection by the mean wind and are subdivided into intense plume and hybrid classes based on the degree of steadiness within the convection column. Hybrid cases contain columns of largely discrete updrafts versus the more continuous updraft column associated with the intense plume mode. Multicell cases develop with strong mixed layer advection and are subdivided into strong and weak classes based on the depth of convection. Intense plume and strong multicell (hybrid and weak multicell) cases occur when the surface buoyancy is large (small). Parcel analyses are performed to more closely examine the forcing of convection within different areas of the parameter space. The multicell (strong and weak) and intense plume modes are forced by a combination of buoyancy and dynamic pressure gradient forcing associated with the perturbation wind field, whereas the hybrid mode is forced by a combination of buoyancy and dynamic pressure gradient forcing associated with the strong background shear. The paper concludes with a discussion of the degree of nonlinearity that is likely to exist at the fire front for each of the convective modes; nonlinear fire behavior is most likely for the hybrid mode and least likely for the weak multicell mode. Knowledge of the sensitivity of the convective mode to upstream conditions can provide information about the degree of nonlinear or erratic fire behavior expected for a given wind profile upstream of the fire.

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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 (August 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 domain. The process starts concentration of magnetic patches at the boundaries of granular cells, which are subsequently merged together into a stable large-scale structure by converging downdrafts below the surface. The resulting structure represents a compact concentration of strong magnetic field, reaching 6 kG in the interior. It has a cluster-like internal structurization, and is maintained by strong downdrafts extending into the deep layers.

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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 (May 16, 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 multiplicative diffusion vector fields. We also briefly describe alterations through which explicit forms of such higher order linearizations are obtained. In the weak forms, the Gaussian stochastic integrals, appearing in the linearized solutions, are replaced by random variables with simpler and discrete probability distributions. The resulting local approximations to the true solution are of significantly higher formal order of accuracy, as reflected through local error estimates. Numerical illustrations are presently provided for the Duffing and Van der Pol oscillators driven by additive and multiplicative noises, which are indicative of the numerical accuracy, computational speed and algorithmic simplicity.

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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 conductivity.

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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 (May 2006): 3100–3105. http://dx.doi.org/10.1529/biophysj.105.070128.

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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 (March 15, 1996): 6469–86. http://dx.doi.org/10.1029/95jc03698.

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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 (March 29, 2019): e1597989. http://dx.doi.org/10.1080/00268976.2019.1597989.

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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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MA, GUOWEI, XINMEI AN, and LEI HE. "THE NUMERICAL MANIFOLD METHOD: A REVIEW." International Journal of Computational Methods 07, no. 01 (March 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, as well as weak discontinuities are given. The similarities and distinctions of the NMM with various other numerical methods such as the finite element method (FEM), the extended finite element method (XFEM), the generalized finite element method (GFEM), the discontinuous deformation analysis (DDA), and the distinct element method (DEM) are investigated. Further developments on the NMM are suggested.

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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 положение критических точек, линий отрыва и присоединения потока. A number of methods for the visualization of flows with gas dynamic discontinuities are considered. These methods allow one to perform the direct comparison of numerical results with experimental data. Methods for the optical visualization of compressible gas flows (shadowgraphs, schlieren images, and interferograms) are discussed. Some examples illustrating the visual representation of numerical solutions of gas dynamics problems related to flows containing weak and strong gas dynamic discontinuities are given. Topological methods of visualization are applied to increase the visual representation of resulting images and to define the locations of critical points as well as the separation and attachment lines.

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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 (May 21, 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, normal and strong conductivity.

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

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Lu, Qiuying, and Vincent Naudot. "Bifurcation Complexity from Orbit-Flip Homoclinic Orbit of Weak Type." International Journal of Bifurcation and Chaos 26, no. 04 (April 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 numerical computation for both the strong stable manifold and unstable manifold.

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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 (November 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 derivatives. Under appropriate assumptions on the parameters of the equation, the weak rate is found to be essentially twice the strong rate. This extends earlier work by one of the authors to the semilinear setting. Numerical simulations illustrate the theoretical results.

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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 (February 22, 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 the influence of recycled concrete strength under low-cyclic reversed loading. Results indicate that the steel reinforced recycled concrete frame structure has good seismic behavior during test, and the spindle-shaped hysteresis loops illustrate that the frame has relatively high energy dissipation capacities. The design of steel reinforced recycled concrete frame satisfied the requirements of strong column weak beam, strong shear weak bending, and strong joint weak components. Finally, the simulated results obtained by OpenSees software agree well with the test, which verify the rationality and reliability of the proposed model. The conclusions of this article will be helpful for the design of steel reinforced recycled concrete structures in seismic regions.

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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 (September 12, 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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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 analysis of the Poisson equation.</p>

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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 metal transfer. The simulation results suggest that the maximal value of electric current density lies in the neck of droplets, and the electromagnetic force has great effects of accelerating droplets’ contraction and shortening their falling time. Under the action of strong electromagnetic force, the metal transfer is in a spray form rather than a globular one in GMAW process. The simulated results agree well with theoretical analyses and predecessors’ experiments.

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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 (March 31, 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 easily seen from the numerical solutions. High order ENO scheme had the best resolution for the case having weak discontinuity, but it over- predicted the shock wave location for the case of strong discontinuity.

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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 (February 21, 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 boundaries with respect to grain interiors. Numerical results show that the effect of microstructure is significant for weak grain boundaries. On the other hand, for strong grain boundaries, the effect of microstructure is insignificant. The evaluated results have demonstrated that peridynamics can be a very good alternative numerical tool for fracture analysis of polycrystalline ice material.

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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 consistent.

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Kumar, Pankaj, and Rupali Verma. "Impact of delay parameter on plant-herbivore dynamics under allee effect." Journal of Physics: Conference Series 2267, no. 1 (May 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 parameter. Numerical results have been supported graphically using MATLAB.

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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 (October 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 (September 30, 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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39

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 (April 16, 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 statistics and filtering performance. The distinction between strong and weak convergence of the numerical schemes is focused on, highlighting which of the two concepts is relevant based on the problem at hand. Using the above analysis, we suggest a mathematically consistent framework for the treatment of these discretization errors in ensemble forecasting and data assimilation twin experiments for unbiased and computationally efficient benchmark studies. Pursuant to this, we provide a novel derivation of the order 2.0 strong Taylor scheme for numerically generating the truth twin in the stochastically perturbed Lorenz-96 equations.

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Gavalec, Martin, Ján Plavka, and Daniela Ponce. "Strong, Strongly Universal and Weak Interval Eigenvectors in Max-Plus Algebra." Mathematics 8, no. 8 (August 12, 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 and vectors are considered as intervals. The properties and recognition algorithms for several types of interval eigenvectors are studied in this paper. For a given interval matrix and interval vector, a set of generators is defined. Then, the strong and the strongly universal eigenvectors are studied and described as max-plus linear combinations of generators. Moreover, a polynomial recognition algorithm is suggested and its correctness is proved. Similar results are presented for the weak eigenvectors. The results are illustrated by numerical examples. The results have a general character and can be applied in every max-plus algebra and every instance of the interval eigenproblem.

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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 (June 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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Давыдов, С. Ю. "Намагниченность эпитаксиального графена, наведенная магнитной металлической подложкой." Физика твердого тела 62, no. 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 bond. Numerical estimates for the Gr/Ni(111) and Gr/Co(poly) heterostructures are fulfilled and compared with the experimental data for Gr/Ni(111) and numerical calculations for Gr/Co/Ni(111). In the first case we have obtained the quantitative agreement, in the second case only the qualitative correspondence is achieved.

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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 (April 13, 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 surface is oppositely charged with respect to the brush. This segregation gives rise to complex patterns in the dependence of the brush thickness on salt concentration. We demonstrate that adjustable ionization of weak polyelectrolytes weakens their conformational response in terms of the dependence of brush thickness on the amplitude of the applied voltage.

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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 new and challenging problems.

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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 becomes faster than the advection speed, marking the onset of strong fronts. In contrast to weak fronts, turbulent eddies are generated at strong fronts by feeding on the downstream laminar flow. Our study also suggests that temporal fluctuations of production and dissipation at the downstream laminar–turbulent front drive the dynamical switches between the two types of front observed up to $Re\simeq 3200$.

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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 (October 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 collocation methods computationally efficient. In the incremental–iterative process, how to accurately reflect the change in the slope of the load–deflection curve of the structure and remain numerically stable are of major concerns. Thus, we propose a strong-form formulated generalized displacement control method to analyze geometric nonlinear problems, where the radial basis collocation method is adopted. The numerical examples demonstrate the ability of the proposed method for large deformation analysis.

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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 (September 4, 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 identified clearly. The de-noised signal is decomposed into several IMFs by the ICEEMDAN method, with the help of the minimum entropy deconvolution (MED), which works as a pre-filter to increase the kurtosis value by about 3.2 times. The envelope spectrum of the effective IMF selected by the MI-SE method shows almost all fault features clearly. An analogous experiment system was built to verify the feasibility of the proposed scheme, whose results have also shown that the proposed hybrid scheme has better performance compared with ICEEMDAN or MED on the weak fault features extraction under a strong noise background. This paper provides a novel method to diagnose the weak faults of the slow speed and heavy load rolling bearings in a strong noise environment.

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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 (January 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 developed such as critical thought and collaborative work.

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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 rate relative to the case without external jet. When vertical weak jet encounter strong horizontal flow, the horizontal flow is dominant that the jet cannot reach the microchannel bottom wall but imposes resistance to the horizontal flow. The investigation on the jet nozzle location shows that the jet nozzle location closer to the channel inlet gives better heat transfer performance.

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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 numerical examples. Our results are improvements and generalizations of some recent results of Khan et al.[21], Chugh et al.[8] and many others in fixed point theory.

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

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