Journal articles: '3d nonlinear models'

1

Kurths, J., A. Brandenburg, U. Feudel, and W. Jansen. "Chaos in Nonlinear Dynamo Models." Symposium - International Astronomical Union 157 (1993): 83–89. http://dx.doi.org/10.1017/s0074180900173917.

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Two nonlinear dynamos have been analyzed by numerical means: 3D-simulation of the magneto-hydrodynamic equations and qualitative analysis of a simplified low-dimensional mean field model. It turns out that both are capable of deterministic chaos in a certain parameter range. As the basic tool the calculation of Lyapunov exponents has been used.

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Pupure, Liva, Leonids Pakrastins, and Janis Varna. "Challenges in developing of 3D nonlinear viscoelastic models." IOP Conference Series: Materials Science and Engineering 1190, no. 1 (October 1, 2021): 012005. http://dx.doi.org/10.1088/1757-899x/1190/1/012005.

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Davids, William G., and George M. Turkiyyah. "Multigrid Preconditioner for Unstructured Nonlinear 3D FE Models." Journal of Engineering Mechanics 125, no. 2 (February 1999): 186–96. http://dx.doi.org/10.1061/(asce)0733-9399(1999)125:2(186).

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Zakrzewski, Kazimierz, Bronisław Tomczuk, and Andrzej Waindok. "Nonlinear scaled models in 3D calculation of transformer magnetic circuits." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 25, no. 1 (January 2006): 91–101. http://dx.doi.org/10.1108/03321640610634362.

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Kou, X. Y., S. T. Tan, and Hod Lipson. "A Data-Driven Process for Estimating Nonlinear Material Models." Applied Mechanics and Materials 50-51 (February 2011): 599–604. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.599.

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Driven by the wide range of new material properties offered by multi-material 3D printing, there is emerging need to create predictive material models for these materials. A data driven process for estimating nonlinear material model is presented in this paper. In contrast with classical methods which derive the engineering stress-strain relationship assuming constant cross-section area and fixed length of a specimen, the proposed approach takes full advantage of 3D geometry of the specimen to estimate the material models. Give a hypothetical material model, virtual tensile tests are performed using Finite Element Analysis (FEA) method, and the parameters of the material model are estimated by minimizing the discrepancies of the virtual responses and the experimental results. The detailed material models, numerical algorithms as well as the optimization approaches are presented and finally preliminary results are offered.

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Makeeva, G. S., and O. A. Golovanov. "Mathematical Models of Microwave and Photonic Devices Engaging Strong Nonlinearities Using Decomposition on Nonlinear Autonomous Blocks." WSEAS TRANSACTIONS ON COMMUNICATIONS 20 (March 17, 2021): 44–51. http://dx.doi.org/10.37394/23204.2021.20.6.

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Mathematical modeling technique based on solving the nonlinear Maxwell’s equations (Eqs.) rigorously using the decomposition approach on nonlinear autonomous blocks partially filled by the nonlinear media with a “strong” nonlinearity (NABs) and reliable engineering method for numerical computation of microwave and photonic nonlinear 3D devices engaging strong nonlinearities, applicable in CAD, were developed. To determine the NAB descriptors the iterative computational process for solving the nonlinear 3D diffraction boundary problems with the non-asymptotic radiation boundary conditions on the NAB bounds was performed using the projection method. The iteration method of recomposition of NABs is developed using the linearization of its descriptors. Using the computational algorithm for solving nonlinear diffraction boundary problems performed as NABs and improved computation algorithm of determination of bifurcation points the nonlinearity thresholds in the magnetic nanoarrays at microwaves were numerically simulated.

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Jiang, Huan Jun, and Lao Er Liu. "Numerical Analysis of RC Shear Walls under Cyclic Loading by PERFORM-3D." Advanced Materials Research 250-253 (May 2011): 2253–57. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.2253.

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For engineering practice purpose, the macroscopic model capable of simulating the main characteristics of nonlinear behavior is desirable to reduce computational efforts in nonlinear structural analysis. Several different types of macroscopic models for shear walls have been developed. The shear wall element used in the commercial program PERFORM-3D is one types of macroscopic models for reinforced concrete shear walls. The application of PERFORM-3D in the nonlinear static analysis of reinforced concrete shear walls is introduced in this study. The selection of constitutive models and the determination of related parameters of the constituent material are presented in detail. The applicability of the shear wall element is verified by numerical simulation on three reinforced concrete shear wall specimens under cyclic loading. The comparison between the numerical analysis and test results leads to the conclusion that the shear wall element with appropriate constitutive models can capture the nonlinear behavior of reinforced concrete shear wall well and be conveniently applied in engineering practice.

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Saldívar, Mauricio Cruz, Eugeni L. Doubrovski, Mohammad J. Mirzaali, and Amir A. Zadpoor. "Nonlinear coarse-graining models for 3D printed multi-material biomimetic composites." Additive Manufacturing 58 (October 2022): 103062. http://dx.doi.org/10.1016/j.addma.2022.103062.

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Mahfouz, Mohamed, Ahmed Badawi, Brandon Merkl, Emam E. Abdel Fatah, Emily Pritchard, Katherine Kesler, Megan Moore, Richard Jantz, and Lee Jantz. "Patella sex determination by 3D statistical shape models and nonlinear classifiers." Forensic Science International 173, no. 2-3 (December 2007): 161–70. http://dx.doi.org/10.1016/j.forsciint.2007.02.024.

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Zhao, Yong. "Finite Element Modeling and Analysis of Nonlinear Impact and Frictional Motion Responses Including Fluid—Structure Coupling Effects." Shock and Vibration 4, no. 5-6 (1997): 311–25. http://dx.doi.org/10.1155/1997/496945.

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A nonlinear three dimensional (3D) single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP) to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI) using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1) the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2) the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3) the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC) criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.

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Naqeeb, Muhammad, Amjad Hussain, and Ahmad Mohammed Alghamdi. "Blow-up criteria for different fluid models in anisotropic Lorentz spaces." AIMS Mathematics 8, no. 2 (2022): 4700–4713. http://dx.doi.org/10.3934/math.2023232.

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<abstract><p>This paper establishes new blow-up criteria, in anisotropic Lorentz spaces, via one-directional derivatives of the velocity and magnetic fields for the Cauchy problem to the 3D magneto-micropolar model and via one-directional derivative of velocity for the Cauchy problem to the 3D nonlinear dissipative system.</p></abstract>

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Zanazzi, Elena, Eva Coïsson, Daniele Ferretti, and Alessio Lorenzelli. "Masonry Spires: 3D Models to Understand their Seismic Vulnerability." Key Engineering Materials 817 (August 2019): 317–24. http://dx.doi.org/10.4028/www.scientific.net/kem.817.317.

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The May 2012 Emilia earthquake has highlighted the important vulnerability of masonry spires at the top of bell towers of churches. Indeed, almost half of those in the epicentral area have shown a typical damage mechanism consisting in the shear sliding and overturning of the top of the spire. Given the recurrence of this phenomenon, the present paper tries to provide a contribution to the comprehension of the seismic behaviour of the spires through the numerical analysis of three case studies. In particular, the work analyses the spires of the churches of San Nicola di Bari in Cortile, near Carpi (MO); Sant'Egidio in Cavezzo (MO), and Sant'Agostino in Sant'Agostino (FE). The numerical models of these masonry structures were made using Abaqus Finite Element software. After the creation of the three-dimensional geometric models, a first nonlinear static analysis of the entire bell tower was performed adopting for masonry the Abaqus “concrete damage plasticity model”. Once the stability of the bell tower was verified for dead loads, the non-linear time-step dynamic analysis was faced. This required the definition of the seismic input at the base of the tower, through the accelerograms recorded by the closest stations. The nonlinear dynamic analysis of the global model of the bell tower provided the floor response spectra at the base and at the top of the spire. Indeed the comparison between spectra at the ground and at the top highlights the filter effect of the stem of the bell tower with a significant increase in accelerations at the top. This effect may explain the widespread damage observed at the top of the spires. Eventually, three different non-invasive intervention techniques were proposed in compliance with the principles of restoration and were modelled to compare their behaviour.

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Wei, Xiangzhi, Xianda Li, Shanshan Wen, Yu Zheng, and Yaobin Tian. "Channel design for 3D models with applications in powder-bed additive manufacturing." Rapid Prototyping Journal 25, no. 9 (October 14, 2019): 1536–44. http://dx.doi.org/10.1108/rpj-06-2018-0156.

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Purpose For any 3D model with chambers to be fabricated in powder-bed additive manufacturing processes such as SLM and SLS, powders are trapped in the chambers of the finished model. This paper aims to design a shortest network with the least number of outlets for efficiently leaking the trapped powders. Design/methodology/approach This paper proposes a nonlinear objective with linear constraints for solving the channel design problem and a particle swarm optimization algorithm to solve the nonlinear system. Findings Structural optimization for the channel network leads to fairly short channels in the interior of the 3D models and very few outlets on the model surface, which achieves the cleaning of the powders while causing almost the least changes to the model. Originality/value This paper reveals the NP-harness of computing the shortest channel network with the least number of outlets. The proposed approach helps the design of lightweight models using the powder-bed additive manufacturing techniques.

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Golovnich, A. K. "MODELS OF STATIONS WITH FUNCTIONALITY OF PROTOTYPES OF PHYSICAL AND TECHNOLOGICAL PROCESSES." World of Transport and Transportation 15, no. 5 (October 28, 2017): 6–13. http://dx.doi.org/10.30932/1992-3252-2017-15-5-1.

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[For the English abstract and full text of the article please see the attached PDF-File (English version follows Russian version)].ABSTRACT Possibilities of model reconstructions of railway stations of different complexity level with the reproduction of technology of their operation on the basis of algorithms of correct physics of processes are considered. Realistic construction of models is emphasized by a 3D interpretation of the results of computational procedures, with the help of which a visual image is formed, an ersatz structure of the station is created, and the meaningful properties of the prototyped objects are copied. At the same time, the space-time changes accompanying the modeling correlate with a set of nonlinear phenomena and a multitude of factors of a systemic and non-systemic nature. Keywords: system, 3D station model, prototype, technology, physical processes, nonlinear phenomena, failure prediction.

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LEE, CHAN-SU, and DIMITRIS SAMARAS. "ANALYSIS AND CONTROL OF FACIAL EXPRESSIONS USING DECOMPOSABLE NONLINEAR GENERATIVE MODELS." International Journal of Pattern Recognition and Artificial Intelligence 28, no. 05 (July 31, 2014): 1456009. http://dx.doi.org/10.1142/s0218001414560096.

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Facial expressions convey personal characteristics and subtle emotional states. This paper presents a new framework for modeling subtle facial motions of different people with different types of expressions from high-resolution facial expression tracking data to synthesize new stylized subtle facial expressions. A conceptual facial motion manifold is used for a unified representation of facial motion dynamics from three-dimensional (3D) high-resolution facial motions as well as from two-dimensional (2D) low-resolution facial motions. Variant subtle facial motions in different people with different expressions are modeled by nonlinear mappings from the embedded conceptual manifold to input facial motions using empirical kernel maps. We represent facial expressions by a factorized nonlinear generative model, which decomposes expression style factors and expression type factors from different people with multiple expressions. We also provide a mechanism to control the high-resolution facial motion model from low-resolution facial video sequence tracking and analysis. Using the decomposable generative model with a common motion manifold embedding, we can estimate parameters to control 3D high resolution facial expressions from 2D tracking results, which allows performance-driven control of high-resolution facial expressions.

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Ning, Xiao Bin, Ji Sheng Shen, and Bin Meng. "Prediction for Shoe Factor of Drum Brakes Based on Nonlinear 3D Simulation Models." Applied Mechanics and Materials 37-38 (November 2010): 880–85. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.880.

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In order to accurately calculate the braking efficiency factor of drum brake shoe of heavy truck, virtual prototyping of a heavy truck's brake is demonstrated. The requirements for brakes include not only its performance but also its comfort, serviceability and working lifetime, which must be high. The finite element analysis software ANSYS and the multi-body system simulation software MSC.ADAMS were used to establish the drum brake nonlinear 3D simulation model. The model was built by developing joint program module between the rigid shoe and the flexible lining and nonlinear contact force program module between the lining and the rigid drum. Using this model, the simulation was executed for the drum brake of 32t heavy duty truck. The results show that the simulated braking efficiency factor coincides with experimental results of the braking efficiency factor of the heavy truck drum brake.

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Ryzhii, Maxim, and Elena Ryzhii. "Pacemaking function of two simplified cell models." PLOS ONE 17, no. 4 (April 11, 2022): e0257935. http://dx.doi.org/10.1371/journal.pone.0257935.

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Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

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Kuklik, Pavel, Martin Valek, Ivana Bozulic, Pratik Gajjar, Chandrashekhar Mahato, and Jacopo Scacco. "Church enclosure walls bearing capacity estimations and its validation on 3D models." MATEC Web of Conferences 310 (2020): 00023. http://dx.doi.org/10.1051/matecconf/202031000023.

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The paper deals with the nonlinear computational modeling of the baroque enclosure masonry walls. The main tasks are input parameters for efficient advanced numerical tools and techniques, which are based on nonlinear and quasi brittle constitutive FEM modeling. For the work was used the knowledge and results from the Broumov Group Churches survey acquired in the frame of international SAHC university cooperation. The goal of the contribution are real bearing capacity parameters of the composite enclosure walls, which leads from standard homogenization techniques. With regards to the material micro modeling of different wall configuration in longitudinal and transversal direction was done with ATENA 2D software to evaluate the safe bearing capacity of the walls. The set of models aim to assess the bearing capacity of the enclosure wall, which is the main structural element in the church. In detail, we will present results from the numerical investigation, and partial in situ testing, from Vižňov, Ruprechtice and Otovice. Finally, we will present calculation of cracks propagation on full 3D church models. Concerning historical structures, it is one way how to validate the quality of estimations and validate numerical models.

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Li, Xiaoyu, Che Han, and Yulan Wang. "Novel Patterns in Fractional-in-Space Nonlinear Coupled FitzHugh–Nagumo Models with Riesz Fractional Derivative." Fractal and Fractional 6, no. 3 (February 28, 2022): 136. http://dx.doi.org/10.3390/fractalfract6030136.

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In this paper, the Fourier spectral method is used to solve the fractional-in-space nonlinear coupled FitzHugh–Nagumo model.Numerical simulation is carried out to elucidate the diffusion behavior of patterns for the fractional 2D and 3D FitzHugh–Nagumo model. The results of numerical experiments are consistent with the theoretical results of other scholars, which verifies the accuracy of the method. We show that stable spatio-temporal patterns can be sustained for a long time; these patterns are different from any previously obtained in numerical studies. Here, we show that behavior patterns can be described well by the fractional FitzHugh–Nagumo and Gray–Scott models, which have unique properties that integer models do not have. Results show that the Fourier spectral method has strong competitiveness, reliability, and solving ability for solving 2D and 3D fractional-in-space nonlinear reaction-diffusion models.

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NOYER, JEAN-CHARLES, CHRISTOPHE BOUCHER, and MOHAMMED BENJELLOUN. "3D STRUCTURE AND MOTION ESTIMATION FROM RANGE AND INTENSITY IMAGES USING PARTICLE FILTERING." International Journal of Image and Graphics 05, no. 03 (July 2005): 639–61. http://dx.doi.org/10.1142/s0219467805001926.

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This article deals with an estimation method of 3D structure and motion. The object is described by line segments and points assuming that it can be described by a polygonal model. It models the problem which is solved by a nonlinear estimation method: The Particle Filter. This method can account for nonlinear models and non-Gaussian statistics without any linearization stage like the Extended Kalman Filter (EKF), for example. The increase in accuracy is shown on a vision system composed by sensors delivering range and intensity/reflectance image sequences. Finally, the solution is compared with a commonly used state estimation method (EKF).

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Fernández-Martínez, Juan Luis, Zulima Fernández-Muñiz, Shan Xu, Ana Cernea, Colette Sirieix, and Joëlle Riss. "Efficient uncertainty analysis of the 3D electrical tomography inverse problem." GEOPHYSICS 84, no. 3 (May 1, 2019): E209—E223. http://dx.doi.org/10.1190/geo2017-0729.1.

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We have evaluated the uncertainty analysis of the 3D electrical tomography inverse problem using model reduction via singular-value decomposition and performed sampling of the nonlinear equivalence region via an explorative member of the particle swarm optimization (PSO) family. The procedure begins with the local inversion of the observed data to find a good resistivity model located in the nonlinear equivalence region. Then, the dimensionality is reduced via the spectral decomposition of the 3D geophysical model. Finally, the exploration of the uncertainty space is performed via an exploratory version of PSO (RR-PSO). This sampling methodology does not prejudge where the initial model comes from as long as this model has a geologic meaning. The 3D subsurface conductivity distribution is arranged as a 2D matrix by ordering the conductivity values contained in a given earth section as a column array and stacking parallel sections as columns of the matrix. There are three basic modes of ordering: mode 1 and mode 2, by using vertical sections in two perpendicular directions, and mode 3, by using horizontal sections. The spectral decomposition is then performed using these three 2D modes. Using this approach, it is possible to sample the uncertainty space of the 3D electrical resistivity inverse problem very efficiently. This methodology is intrinsically parallelizable and could be run for different initial models simultaneously. We found the application to a synthetic data set that is well-known in the literature related to this subject, obtaining a set of surviving geophysical models located in the nonlinear equivalence region that can be used to approximate numerically the posterior distribution of the geophysical model parameters (frequentist approach). Based on these models, it is possible to perform the probabilistic segmentation of the inverse solution found, meanwhile answering geophysical questions with its corresponding uncertainty assessment. This methodology has a general character could be applied to any other 3D nonlinear inverse problems by implementing their corresponding forward model.

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Zheng, Ke Ke, Jun Ning Chen, Corey Scholes, and Qing Li. "Magnetic Resonance Imaging (MRI) Based Finite Element Modeling for Analyzing the Influence of Material Properties on Menisci Responses." Applied Mechanics and Materials 553 (May 2014): 305–9. http://dx.doi.org/10.4028/www.scientific.net/amm.553.305.

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To investigate the importance of the meniscal non-linear behaviour on knee joint finite element analysis (FEA) study, the aim of this study was to compare linear elastic and nonlinear hyperelastic material models on the pressure distribution of meniscus. For this purpose, a 3D finite element (FE) knee model of a healthy living subject was constructed from magnetic resonance imaging (MRI) to simulate contact pressure under axial compressive loading. Differences in meniscal contact pressures were observed between linear elastic and nonlinear hyperelastic models. These findings emphasize the importance of accounting the nonlinear material behaviour of the menisci in knee joint FEA studies.

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Hasenbusch, Martin, Andrea Pelissetto, and Ettore Vicari. "Relaxational dynamics in 3D randomly diluted Ising models." Journal of Statistical Mechanics: Theory and Experiment 2007, no. 11 (November 23, 2007): P11009. http://dx.doi.org/10.1088/1742-5468/2007/11/p11009.

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Iman, Miftahul. "The Steel Truss Tower (Derricks) Structure Evaluation In Buckling Analysis." JUTEKS : Jurnal Teknik Sipil 5, no. 2 (December 29, 2020): 120. http://dx.doi.org/10.32511/juteks.v5i2.735.

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Tarakan was an oil-producing city had been known since 1896 that were explored in first time in authorized by Bataavishe Petroleum Maatchapij (BPM). The derrick was a petroleum drilling facility that were performed in steel truss structure. The derrick prototype had been modeled in 3D truss by utilizing SAP2000. The models had been classified into 2 models: perfect and imperfect models. The imperfections denoted by the percentage of elements loses (IM20, IM24), and IM16). Buckling analysis consisted in linear and nonlinear analysis had been evaluated. The 3D solid model (Abaqus) also performed for single element buckling. The results showed that perfect derrick model satisfied the strength and stability requirement . The percentage of element loss reduced the capacity 9.45%-37.83%. The IM16 model buckled at 4.27 T were based on nonlinear analysis and 18.50 T were based on linear analysis. The single elemen buckling was 20,63% of the largest compressive element

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Thuillier, F. "3D topological models and Heegaard splitting. II. Pontryagin duality and observables." Journal of Mathematical Physics 61, no. 11 (November 1, 2020): 112302. http://dx.doi.org/10.1063/5.0027779.

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Sergeev, S. M. "Functional Equations and Quantum Separation of Variables for 3d Spin Models." Theoretical and Mathematical Physics 138, no. 2 (February 2004): 226–37. http://dx.doi.org/10.1023/b:tamp.0000015070.88403.f9.

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Ren, Zhengyong, and Thomas Kalscheuer. "Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data." Surveys in Geophysics 41, no. 1 (September 24, 2019): 47–112. http://dx.doi.org/10.1007/s10712-019-09567-3.

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Abstract A meaningful solution to an inversion problem should be composed of the preferred inversion model and its uncertainty and resolution estimates. The model uncertainty estimate describes an equivalent model domain in which each model generates responses which fit the observed data to within a threshold value. The model resolution matrix measures to what extent the unknown true solution maps into the preferred solution. However, most current geophysical electromagnetic (also gravity, magnetic and seismic) inversion studies only offer the preferred inversion model and ignore model uncertainty and resolution estimates, which makes the reliability of the preferred inversion model questionable. This may be caused by the fact that the computation and analysis of an inversion model depend on multiple factors, such as the misfit or objective function, the accuracy of the forward solvers, data coverage and noise, values of trade-off parameters, the initial model, the reference model and the model constraints. Depending on the particular method selected, large computational costs ensue. In this review, we first try to cover linearised model analysis tools such as the sensitivity matrix, the model resolution matrix and the model covariance matrix also providing a partially nonlinear description of the equivalent model domain based on pseudo-hyperellipsoids. Linearised model analysis tools can offer quantitative measures. In particular, the model resolution and covariance matrices measure how far the preferred inversion model is from the true model and how uncertainty in the measurements maps into model uncertainty. We also cover nonlinear model analysis tools including changes to the preferred inversion model (nonlinear sensitivity tests), modifications of the data set (using bootstrap re-sampling and generalised cross-validation), modifications of data uncertainty, variations of model constraints (including changes to the trade-off parameter, reference model and matrix regularisation operator), the edgehog method, most-squares inversion and global searching algorithms. These nonlinear model analysis tools try to explore larger parts of the model domain than linearised model analysis and, hence, may assemble a more comprehensive equivalent model domain. Then, to overcome the bottleneck of computational cost in model analysis, we present several practical algorithms to accelerate the computation. Here, we emphasise linearised model analysis, as efficient computation of nonlinear model uncertainty and resolution estimates is mainly determined by fast forward and inversion solvers. In the last part of our review, we present applications of model analysis to models computed from individual and joint inversions of electromagnetic data; we also describe optimal survey design and inversion grid design as important applications of model analysis. The currently available model uncertainty and resolution analyses are mainly for 1D and 2D problems due to the limitations in computational cost. With significant enhancements of computing power, 3D model analyses are expected to be increasingly used and to help analyse and establish confidence in 3D inversion models.

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Nie, Shao Feng, Tian Hua Zhou, Xiang Bin Liu, and Xiu Mei Wang. "Study on Mechanical Behavior of Concrete-Filled Square Tubular Column and Bolt-Weld Steel Beam Joints with Reduced Beam Section." Advanced Materials Research 163-167 (December 2010): 620–23. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.620.

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The nonlinear FEM models of concrete-filled square tubular column with internal diaphragms and steel beams with reduced beam section bolt-weld joints, involving geometric, materials and contact nonlinear, were established. The 3D models of beam-to-column joints with internal diaphragms by 3D solid elements are founded. The bearing capacity behavior of joints under the monotonic loading are analyzed, including P-Δ curves, the stresses distribution of beam, the dissipating energy ability and destruction form. The analysis results show that the initial stiffness of joint with reduced beam section is close to that of non-reduced beam section joint. The bearing capacities of joints with reduced beam section are lower a little than that of non-reduced beam section joint. The plastic hinge in the joint with reduced beam section is removed to the reduced beam region.

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Georges, A., D. Hansel, P. Le Doussal, and J. M. Maillard. "Dimensional reduction and correlation functions on 3D lattice models." Journal of Physics A: Mathematical and General 20, no. 15 (October 21, 1987): 5299–309. http://dx.doi.org/10.1088/0305-4470/20/15/041.

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Chen, Tzu-Ting, Ying-Tsong Lin, Linus Y. S. Chiu, and William L. Siegmann. "Coupled effects of nonlinear internal gravity waves and seabed properties on underwater sound propagation." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A44. http://dx.doi.org/10.1121/10.0015482.

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Underwater sound propagation can be affected by strong sound speed gradients induced by nonlinear internal waves in the ocean. Meanwhile, geoacoustic properties of the seabed control acoustic reflections. Experimental data collected at the shelfbreak on the northeast of the South China Sea were analyzed to investigate the joint effects. Both two-dimensional (2D) and three-dimensional (3D) numerical sound propagation models with realistic seafloor and oceanographic inputs have been established to study the nonlinear internal wave effects observed on hydrophone vertical line array moorings. Compared to the 3D model, the prediction errors and uncertainties of the 2D scheme neglecting the transversal/azimuth energy propagation are discussed. In addition, the impact of sediment properties on 3D propagation effects affecting underwater soundscapes in the area is investigated. [Work supported by the Office of Naval Research.]

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Eskitaşçıoğlu, Esin İnan, Muhammed Bahadırhan Aktaş, and Haci Mehmet Baskonus. "New Complex and Hyperbolic Forms for Ablowitz–Kaup–Newell–Segur Wave Equation with Fourth Order." Applied Mathematics and Nonlinear Sciences 4, no. 1 (June 24, 2019): 93–100. http://dx.doi.org/10.2478/amns.2019.1.00010.

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AbstractResearching different solutions of nonlinear models has been interesting in different fields of science and application. In this study, we investigated different solutions of fourth-order nonlinear Ablowitz– Kaup–Newell–Segur wave equation. We have used the sine-Gordon expansion method (SGEM) during this research. We have given the 2D, 3D, and contour graphs acquired from the values of the solutions obtained using strong SGEM.

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Sulaiman, Tukur Abdulkadir, Canan Unlu, and Hasan Bulut. "On the wave solutions to the TRLW equation." ITM Web of Conferences 22 (2018): 01033. http://dx.doi.org/10.1051/itmconf/20182201033.

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In this study, a nonlinear model is investigated, namely; the time regularized long wave equation. Various solitary wave solutions are constructed such as the non-topological, compound topological-non-topological bell-type, singular and compound singular soliton solutions. Under the choice of suitable parameters values, the 2D and 3D graphs to all the obtained solutions are plotted. The reported results in this study may be helpful in explaining the physical meanings of some important nonlinear models arising in the field of nonlinear science.

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SHAKEEL, MUHAMMAD, MUHAMMAD ASAD IQBAL, and SYED TAUSEEF MOHYUD-DIN. "CLOSED FORM SOLUTIONS FOR NONLINEAR BIOLOGICAL POPULATION MODEL." Journal of Biological Systems 26, no. 01 (March 2018): 207–23. http://dx.doi.org/10.1142/s0218339018500109.

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The exploration of closed-form solutions for nonlinear partial differential equations (NLPDEs) is an attractive subject in the different branches of mathematical and biological sciences. In this paper, we have applied a modified exp-function method to calculate closed-form solutions of a degenerate parabolic equation arising in the spatial diffusion of biological populations. The model assists us to comprehend the dynamical process of population variations in population models and delivers prized guesses. It is shown that the obtained solutions are more general and fresh and can be helpful to analyze the inner mechanism of other nonlinear biological models. Moreover, 2D and 3D graphical demonstrations together with the numerical data strengthen the effectiveness of the rummage-sale procedure.

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Aanouz, Ilham, Khalil El Khatabi, Assia BelHassan, Tahar Lakhlifi, Mostafa Elidrissi, and Mohammed Bouachrine. "2D- and 3D-QSAR and Molecular Docking of 2-Hydroxyisoquinoline-1,3-Diones as Inhibitors of HIV Reverse Transcriptase." International Journal of Quantitative Structure-Property Relationships 5, no. 4 (October 2020): 32–52. http://dx.doi.org/10.4018/ijqspr.2020100102.

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The main objective of this study is to develop 2D- and 3D-QSAR statistical models for a series consisting of 28 molecules. The authors started with a 2D study based on principal component analysis (PCA), multiple linear regression (RLM), and nonlinear regression (RNLM). The models were developed using 28 molecules with a pIC50 between 5.70 and 6.70. Then they applied 3D-QSAR analysis based on the partial least squares (PLS) method. For 3D-QSAR, they used the molecular field comparative analysis (CoMFA) and comparative molecular similarity index (CoMSIA) methods. For this analysis, they have worked on a training set of 24 compounds, which then give acceptable and reliable values of Q2 (0.791 and 0.538, respectively) and R2 (0.974 and 0.98, respectively). To determine the quantitative 3D-QSAR, the interpretations were based on the contour maps which are produced by the CoMFA and CoMSIA models. In addition, molecular docking is also one of the most important methods for confirming the binding interactions of predicted molecules with their receptors.

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Gepreel, Khaled A., and Amr M. S. Mahdy. "Algebraic computational methods for solving three nonlinear vital models fractional in mathematical physics." Open Physics 19, no. 1 (January 1, 2021): 152–69. http://dx.doi.org/10.1515/phys-2021-0020.

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Abstract This research paper uses a direct algebraic computational scheme to construct the Jacobi elliptic solutions based on the conformal fractional derivatives for nonlinear partial fractional differential equations (NPFDEs). Three vital models in mathematical physics [the space-time fractional coupled Hirota Satsuma KdV equations, the space-time fractional symmetric regularized long wave (SRLW equation), and the space-time fractional coupled Sakharov–Kuznetsov (S–K) equations] are investigated through the direct algebraic method for more explanation of their novel characterizes. This approach is an easy and powerful way to find elliptical Jacobi solutions to NPFDEs. The hyperbolic function solutions and trigonometric functions where the modulus and, respectively, are degenerated by Jacobi elliptic solutions. In this style, we get many different kinds of traveling wave solutions such as rational wave traveling solutions, periodic, soliton solutions, and Jacobi elliptic solutions to nonlinear evolution equations in mathematical physics. With the suggested method, we were fit to find much explicit wave solutions of nonlinear integral differential equations next converting them into a differential equation. We do the 3D and 2D figures to define the kinds of outcome solutions. This style is moving, reliable, powerful, and easy for solving more difficult nonlinear physics mathematically.

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SHAIKH, DASTGEER, and P. K. SHUKŁA. "Nonlinear electromagnetic wave interactions in Hall–MHD plasmas." Journal of Plasma Physics 76, no. 6 (September 2, 2010): 893–901. http://dx.doi.org/10.1017/s0022377810000486.

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AbstractWe have developed a massively parallelized fully three-dimensional (3D) compressible Hall–magnetohydrodynamic (MHD) code to investigate inertial range electromagnetic wave cascades and dissipative processes in the regime, where characteristic length scales associated with plasma fluctuations are smaller than ion gyroradii. Such regime is ubiquitously present in the solar wind and many other collisionless space plasmas. Particularly, in the solar wind, the high time resolution databases depict a spectral break near the end of the 5/3 spectrum that corresponds to a high-frequency regime where the electromagnetic turbulent cascades cannot be explained by the usual MHD models. This refers to a second inertial range, where turbulent cascades follow a k−7/3 (where k is a wavenumber) spectrum in which the characteristic electromagnetic fluctuations evolve typically on kinetic Alfvén time scales. In this paper, we describe results from our 3D compressible Hall–MHD simulations that explain the observed k−7/3 spectrum in the solar wind plasma, energy cascade, anisotropy, and other spectral features.

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Ferreira, Miguel Jorge Bernabé, Pramod Padmanabhan, and Paulo Teotonio-Sobrinho. "2D quantum double models from a 3D perspective." Journal of Physics A: Mathematical and Theoretical 47, no. 37 (August 29, 2014): 375204. http://dx.doi.org/10.1088/1751-8113/47/37/375204.

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Saleh, Mofreh F., Bruce Steven, and David Alabaster. "Three-Dimensional Nonlinear Finite Element Model for Simulating Pavement Response: Study at Canterbury Accelerated Pavement Testing Indoor Facility, New Zealand." Transportation Research Record: Journal of the Transportation Research Board 1823, no. 1 (January 2003): 153–62. http://dx.doi.org/10.3141/1823-17.

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A three-dimensional nonlinear finite element model (3D-FEM) was developed as part of a study of the effect of increasing axle load and tire pressure on pavement deterioration. The measured strains, interface stresses, and deflections were collected from the instrumented Canterbury Accelerated Pavement Testing Indoor Facility in New Zealand. In addition, two multilayer elastic models were used to compare the values from the finite element simulation and the actual measurements. The first elastic multilayer model was developed with ELSYM5 software, and the second model was developed with CIRCLY software. CIRCLY differs from ELSYM5 in the ability to account for material anisotropy; ELSYM5 considers the pavement materials to be isotropic. The actual strains and deformations were measured by Emu strain gauges embedded at different depths in the base and subgrade materials. Both the unbound granular base and the subgrade materials were modeled in 3D-FEM as elastic plastic materials. The results showed that for the unbound base layer, the strains calculated from the two elastic models were in reasonable agreement with the values measured in the instrumented test track, while the 3D-FEM model tended to overestimate the strains at the bottom of the base. While none of the models provided a perfect fit to the measured strains in the subgrade layer because the subgrade is less homogenous than assumed, 3D-FEM provided the closest fit. Also, CIRCLY provided better results than ELSYM5, which underestimated the displacement values compared with values obtained with CIRCLY and 3D-FEM.

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Li, Qinglin, Hongyan Gao, Xiaodong Zhang, Jiheng Ni, and Hanping Mao. "Describing Lettuce Growth Using Morphological Features Combined with Nonlinear Models." Agronomy 12, no. 4 (March 31, 2022): 860. http://dx.doi.org/10.3390/agronomy12040860.

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The aim of this study was to describe the sigmoidal growth behaviour of a lettuce canopy using three nonlinear models. Gompertz, Logistic and grey Verhulst growth models were established for the top projected canopy area (TPCA), top projected canopy perimeter (TPCP) and plant height (PH), which were measured by two machine vision views and 3D point clouds data. Satisfactory growth curve fitting was obtained using two evaluation criteria: the coefficient of determination (R2) and the mean absolute percentage error (MAPE). The grey Verhulst models produced a better fit for the growth of TPCA and TPCP, with higher R2 (RTPCA2=0.9097, RTPCP2=0.8536) and lower MAPE (MAPETPCA=0.0284, MAPETPCP=0.0794) values, whereas the Logistic model produced a better fit for changes in PH (RPH2=0.8991, MAPEPH=0.0344). The maximum growth rate point and the beginning and end points of the rapid growth stage were determined by calculating the second and third derivatives of the models, permitting a more detailed description of their sigmoidal behaviour. The initial growth stage was 1–5.5 days, and the rapid growth stage lasted from 5.6 to 26.2 days. After 26.3 days, lettuce entered the senescent stage. These inflections and critical points can be used to gain a better understanding of the growth behaviour of lettuce, thereby helping researchers or agricultural extension agents to promote growth, determine the optimal harvest period and plan commercial production.

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Shakeel, Muhammad, Attaullah, Nehad Ali Shah, and Jae Dong Chung. "Modified Exp-Function Method to Find Exact Solutions of Microtubules Nonlinear Dynamics Models." Symmetry 15, no. 2 (January 29, 2023): 360. http://dx.doi.org/10.3390/sym15020360.

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In this paper, we use the modified exp−ψθ-function method to observe some of the solitary wave solutions for the microtubules (MTs). By treating the issues as nonlinear model partial differential equations describing microtubules, we were able to solve the problem. We then found specific solutions to the nonlinear evolution equation (NLEE) covering various parameters that are particularly significant in biophysics and nanobiosciences. In addition to the soliton-like pulse solutions, we also find the rational, trigonometric, hyperbolic, and exponential function characteristic solutions for this equation. The validity of the method we developed and the fact that it provides more solutions are demonstrated by comparison to other methods. We next use the software Mathematica 10 to generate 2D, 3D, and contour plots of the precise findings we observed using the suggested technique and the proper parameter values.

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Raoult, Cécile, Marissa L. Yates, and Michel Benoit. "A NONLINEAR AND DISPERSIVE 3D MODEL FOR COASTAL WAVES USING RADIAL BASIS FUNCTIONS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 83. http://dx.doi.org/10.9753/icce.v36.waves.83.

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Accurate wave propagation models are required for the design of coastal structures and the evaluation of coastal risks. Nonlinear and dispersive effects are particularly important in the nearshore environment. Two-dimensional cross-shore (2DV) wave models can be used as a preliminary step in coastal studies, but 3D models are needed to capture fully the effects of alongshore bathymetric variations, variable wave incidence, the presence of coastal or harbor structures, etc. Yates and Benoit (2015) developed a numerical model based on fully nonlinear potential flow theory. By assuming non-overturning waves, the kinematic and dynamic free surface boundary conditions are expressed as evolution equations of the free surface elevation and velocity potential, following Zakharov (1968). At each time step, the free surface vertical velocity is estimated by solving the Laplace equation for the velocity potential in the domain. Following Tian and Sato (2008), a spectral approach is used to expand the velocity potential in the vertical as a linear combination of Chebyshev polynomials. The accuracy of the 2DV model was validated with several non-breaking experimental test cases (Benoit et al., 2014; Raoult et al., 2016). Here the model is extended to 3D using scattered nodes (for flexibility) to discretize the horizontal domain. Spatial derivatives are estimated at each node using a linear combination of the function values at neighboring points using Radial Basis Functions (RBF) (Wright and Fornberg, 2006). The accuracy of the method depends on the number of neighboring nodes (Nsten) and the chosen RBF type (e.g. multiquadric, Gaussian, polyharmonic spline (PHS), thin plate spline, etc.), with associated shape factor C for some of them.

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Chae, Dongho, and In-Jee Jeong. "Active vector models generalising 3D Euler and electron–MHD equations." Nonlinearity 36, no. 1 (December 9, 2022): 458–75. http://dx.doi.org/10.1088/1361-6544/aca73e.

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Abstract We introduce an active vector system, which generalises both the 3D Euler equations and the electron–magnetohydrodynamic equations (E–MHD). We may as well view the system as singularised systems for the 3D Euler equations, in which case the equations of (E–MHD) correspond to the order two more singular one than the 3D Euler equations. The generalised surface quasi-geostrophic equation (gSQG) can be also embedded into a special case of our system when the unknown functions are constant in one coordinate direction. We investigate some basic properties of this system as well as the conservation laws. In the case when the system corresponds up to order one more singular than the 3D Euler equations, we prove local well-posedness in the standard Sobolev spaces. The proof crucially depends on a sharp commutator estimate similar to the one used for (gSQG) in Chae et al (2012 Commun. Pure Appl. Math. 65 1037–66). Since the system covers many areas of both physically and mathematically interesting cases, one can expect that there are various related problems to be investigated, parts of which are discussed here.

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Seo, Junwon, and Daniel G. Linzell. "Nonlinear Seismic Response and Parametric Examination of Horizontally Curved Steel Bridges Using 3D Computational Models." Journal of Bridge Engineering 18, no. 3 (March 2013): 220–31. http://dx.doi.org/10.1061/(asce)be.1943-5592.0000345.

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Khorram, Saeed, and Mahede Vahedi. "Evaluating uncertainty in nonlinear hydrological models using VIC-3D model on the Umeå River basin." International Journal of Water 12, no. 4 (2018): 287. http://dx.doi.org/10.1504/ijw.2018.095382.

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Khorram, Saeed, and Mahede Vahedi. "Evaluating uncertainty in nonlinear hydrological models using VIC-3D model on the Umeå River basin." International Journal of Water 12, no. 4 (2018): 287. http://dx.doi.org/10.1504/ijw.2018.10016229.

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Khazal, Ammar S. "Mesh Size Effects in Nonlinear Dynamic 3d- Analysis of Reinforced Concrete Beam Under Impact Loads." Tikrit Journal of Engineering Sciences 15, no. 3 (September 30, 2008): 76–92. http://dx.doi.org/10.25130/tjes.15.3.06.

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The investigation into the effect of mesh size in nonlinear 3D-analysis of reinforced concrete beam under dynamic load presents in this paper. The behavior of reinforced concrete beam under dynamic loads are supported by intensive numerical simulations, and the effect of various parameters on the results is of great interest. Finite element simulations were performed in the nonlinear dynamic domain with modified concrete and steel constitutive models. To eliminate the dependence of the computed results on the mesh size, a procedure for calculating the ultimate tensile strain of concrete was developed and implemented into nonlinear dynamic analysis. The proposed model gives good agreement with the experimental results. In particular, the new model can be used effectively with relatively mesh size in reasonable accuracy.

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Swensen, Daniel J., and Sashi K. Kunnath. "Consequences of Modeling Choices in Seismic Performance Assessment of Buildings." Earthquake Spectra 34, no. 2 (May 2018): 423–40. http://dx.doi.org/10.1193/030217eqs044ep.

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Performance-based approaches utilizing nonlinear analyses have become increasingly popular for seismic evaluation of buildings. Nonlinear simulations of building response require various assumptions and modeling decisions—from choice of software to model parameters—which opens the door to differences in demand assessments from what essentially could be very similar computational models. This study examines nonlinear response sensitivity of three steel moment frame structures to variations in basic nonlinear modeling parameters using three different software platforms: OpenSees, Perform-3D, and SAP2000. The building models were analyzed in the inelastic range using a suite of near-fault and far-fault ground motions, and response sensitivity was assessed using interstory drift and plastic rotation demands. Findings from the study indicate that sensitivity to modeling assumptions and choice of software are more pronounced at the local/element level than at the global/system level and can have an impact in performance-based seismic assessment.

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Forcellini, Davide. "Probabilistic-Based Assessment of Liquefaction-Induced Damage with Analytical Fragility Curves." Geosciences 10, no. 8 (August 15, 2020): 315. http://dx.doi.org/10.3390/geosciences10080315.

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Soil liquefaction may cause severe damages to structures mainly in terms of lateral spread and settlements, as documented during historical earthquakes. Liquefaction-potential (LP) estimation has become an important issue in seismic assessment, and this paper aims to propose a new methodology based on fragility curves. LP curves were developed and applied to two case studies performed with 3D numerical models applying Opensees. Nonlinear hysteretic materials and advanced plasticity models were used to reproduce the high nonlinear mechanisms of liquefaction, such as strong dilation tendency and cyclic shear behaviour. LP curves were applied to compare the results of the performed free field (FF) and soil–structure interaction (SSI) case studies.

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Areshi, Mounirah, Aly R. Seadawy, Asghar Ali, Abdulrahman F. AlJohani, Weam Alharbi, and Amal F. Alharbi. "Construction of Solitary Wave Solutions to the (3 + 1)-Dimensional Nonlinear Extended and Modified Quantum Zakharov–Kuznetsov Equations Arising in Quantum Plasma Physics." Symmetry 15, no. 1 (January 16, 2023): 248. http://dx.doi.org/10.3390/sym15010248.

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Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation of three mathematical methods. The concerned models have many fruitful applications to describe the waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in plasma. The derived results via the MEAEM method, ESE method, and modified F-expansion have been retrieved and will be expedient in the future to illuminate the collaboration between lower nonlinear ion-acoustic waves. For the physical behavior of the models, some solutions are plotted graphically in 2D and 3D by imparting particular values to the parameters under the given condition at each solution. Hence explored solutions have profitable rewards in the field of mathematical physics.

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Sohel Imtiaz, S. M., Samir M. El-Ghazaly, and Robert O. Grondin. "Advantages of Semiconductor Device Simulator Combining Electromagnetic and Electron Transport Models." VLSI Design 8, no. 1-4 (January 1, 1998): 495–500. http://dx.doi.org/10.1155/1998/85608.

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Physical simulation of semiconductor devices at high frequencies involves not only semiconductor transport issues but also electromagnetic wave propagation issues. In order to obtain the nonlinear and the large-signal characteristics of the semiconductor devices, an electromagnetic model should replace the traditional quasi-static model in the device simulator. In this paper, the advantages of a semiconductor device simulator combining an electromagnetic and an electron transport models are presented. This study is based on a semiconductor device simulator that couples a semiconductor model to the 3D time-domain solution of Maxwell's equations. The electromagnetic wave propagation effects on the millimeter-wave FETs are thoroughly analyzed. The use of the electromagnetic model over the conventional quasi-static model provides the actual device response at high frequencies. It also shows the nonlinear energy build-up along the device width whereas the quasi-static model provides a linear increase of energy. The combined model is capable of predicting the device nonlinearity and harmonic distortion of amplifier circuits at large signal.

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Journal articles on the topic '3d nonlinear models'

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