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Sun, H., and G. T. Schuster. "2‐D wavepath migration." GEOPHYSICS 66, no. 5 (September 2001): 1528–37. http://dx.doi.org/10.1190/1.1487099.
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Prestack Kirchhoff migration (KM) is computationally intensive for iterative velocity analysis. This is partly because each time sample in a trace must be smeared along a quasi‐ellipsoid in the model. As a less costly alternative, we use the stationary phase approximation to the KM integral so that the time sample is smeared along a small Fresnel zone portion of the quasi‐ellipsoid. This is equivalent to smearing the time samples in a trace over a 1.5‐D fat ray (i.e., wavepath), so we call this “wavepath migration” (WM). This compares to standard KM, which smears the energy in a trace along a 3‐D volume of quasi‐concentric ellipsoids. In principle, single trace migration with WM has a computational count of [Formula: see text] compared to KM, which has a computational count of [Formula: see text], where N is the number of grid points along one side of a cubic velocity model. Our results with poststack data show that WM produces an image that in some places contains fewer migration artifacts and is about as well resolved as the KM image. For a 2‐D poststack migration example, the computation time of WM is less than one‐third that of KM. Our results with prestack data show that WM images contain fewer migration artifacts and can define the complex structure more accurately. It is also shown that WM can be significantly faster than KM if a slant stack technique is used in the migration. The drawback with WM is that it is sometimes less robust than KM because of its sensitivity to errors in estimating the incidence angles of the reflections.
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Petrauskas, K., and R. Baronas. "Computational Modelling of Biosensors with an Outer Perforated Membrane." Nonlinear Analysis: Modelling and Control 14, no. 1 (January 20, 2009): 85–102. http://dx.doi.org/10.15388/na.2009.14.1.14532.
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This paper presents one-dimensional (1-D) and two-dimensional (2-D) in-space mathematical models for amperometric biosensors with an outer perforated membrane. The biosensor action was modelled by reaction-diffusion equations with a nonlinear term representing the Michaelis-Menten kinetics of an enzymatic reaction. The conditions at which the 1-D model can be applied to simulate the biosensor response accurately were investigated numerically. The accuracy of the biosensor response simulated by using 1-D model was evaluated by the response simulated with the corresponding 2-D model. A procedure for a numerical evaluation of the effective diffusion coefficient to be used in 1-D model was proposed. The numerically calculated effective diffusion coefficient was compared with the corresponding coefficients derived analytically. The numerical simulation was carried out using the finite difference technique.
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Blatter, Daniel, Anandaroop Ray, and Kerry Key. "Two-dimensional Bayesian inversion of magnetotelluric data using trans-dimensional Gaussian processes." Geophysical Journal International 226, no. 1 (March 25, 2021): 548–63. http://dx.doi.org/10.1093/gji/ggab110.
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SUMMARY Bayesian inversion of electromagnetic data produces crucial uncertainty information on inferred subsurface resistivity. Due to their high computational cost, however, Bayesian inverse methods have largely been restricted to computationally expedient 1-D resistivity models. In this study, we successfully demonstrate, for the first time, a fully 2-D, trans-dimensional Bayesian inversion of magnetotelluric (MT) data. We render this problem tractable from a computational standpoint by using a stochastic interpolation algorithm known as a Gaussian process (GP) to achieve a parsimonious parametrization of the model vis-a-vis the dense parameter grids used in numerical forward modelling codes. The GP links a trans-dimensional, parallel tempered Markov chain Monte Carlo sampler, which explores the parsimonious model space, to MARE2DEM, an adaptive finite element forward solver. MARE2DEM computes the model response using a dense parameter mesh with resistivity assigned via the GP model. We demonstrate the new trans-dimensional GP sampler by inverting both synthetic and field MT data for 2-D models of electrical resistivity, with the field data example converging within 10 d on 148 cores, a non-negligible but tractable computational cost. For a field data inversion, our algorithm achieves a parameter reduction of over 32× compared to the fixed parameter grid used for the MARE2DEM regularized inversion. Resistivity probability distributions computed from the ensemble of models produced by the inversion yield credible intervals and interquartile plots that quantitatively show the non-linear 2-D uncertainty in model structure. This uncertainty could then be propagated to other physical properties that impact resistivity including bulk composition, porosity and pore-fluid content.
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Salheddine, Mezbache, Paquier André, and Hasbaia Mahmoud. "A coupled 1-D/2-D model for simulating river sediment transport and bed evolution." Journal of Hydroinformatics 22, no. 5 (June 23, 2020): 1122–37. http://dx.doi.org/10.2166/hydro.2020.020.
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Abstract The paper details the method to couple a 1-D hydro-sedimentary model to a 2-D hydro-sedimentary model in order to represent the hydrodynamics and morphological processes during a flood event along a river. Tested on two field cases, the coupled model is stable even in the case of generalized overflow over the riverbanks or of levee breaching. For lateral coupling, the coupled model allows saving computational time compared to a full 2-D model and to provide valuable results concerning the flooding features as well as the evolution of the bed topography. However, despite a similar simplified representation of the sediment features in the 1-D and 2-D models, some discrepancies appear in the case of upstream/downstream coupling along a cross section perpendicular to the flow direction because the assumption of homogeneous velocity and concentration is not valid for estimating sediment transport. Further research is necessary to be able to define a suitable distribution of the sediments on the 1-D side of the boundary between the two models.
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Yang, Gang, Ai Feng Zhang, Hai Bin Wang, and Peng Niu. "Postbuckling Analysis of Laminate with Delamination Based on the Improved Damage Model of 2-D." Key Engineering Materials 385-387 (July 2008): 253–56. http://dx.doi.org/10.4028/www.scientific.net/kem.385-387.253.
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The paper presents the compatibility relation of displacement, strain energy expression, and the formulations of Finite Element Method in the transitional region for the improved damage model of 2-D delamination[1]. The postbuckling behaviors of composite laminated plate with a circular delamination are analyzed. Results show that the model mainly improves computational results of energy release rates in the delamination front. The model should only be used in a narrow region near the crack-tip and the normal Mindlin model in other regions. It leads to little increase in the amount of computation, but significant improvement in the results.
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Robertsson, Johan O. A., and Chris H. Chapman. "An efficient method for calculating finite‐difference seismograms after model alterations." GEOPHYSICS 65, no. 3 (May 2000): 907–18. http://dx.doi.org/10.1190/1.1444787.
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Seismic modeling, processing, and inversion often require the calculation of the seismic response resulting from a suite of closely related seismic models. Even though changes to the model may be restricted to a small subvolume, we need to perform simulations for the full model. We present a new finite‐difference method that circumvents the need to resimulate the complete model for local changes. By requiring only calculations in the subvolume and its neighborhood, our method makes possible significant reductions in computational cost and memory requirements. In general, each source/receiver location requires one full simulation on the complete model. Following these pre‐computations, recalculation of the altered wavefield can be limited to the region around the subvolume and its neighborhood. We apply our method to a 2-D time‐lapse seismic problem, thereby achieving a factor of 15 reduction in computational cost. Potential savings for 3-D are far greater.
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Suresh, Krishnan, and Murari Sinha. "A 2-D model that accounts for 3-D fringing in MEMS devices." Engineering Analysis with Boundary Elements 30, no. 11 (November 2006): 963–70. http://dx.doi.org/10.1016/j.enganabound.2006.07.007.
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Jouzdani, Anahita, and Abdorreza Kabiri-Samani. "Investigations of the Difference in Dam Break Modeling Approaches between 1-D and 2-D Hydrodynamic Model." Applied Mechanics and Materials 90-93 (September 2011): 2423–26. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.2423.
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There are different numerical models performed on hydrodynamic behavior of dam break flood in canals and floodplains based on 1D and 2D modeling approaches. In recognition of increasing demand to precise modeling of dam break flood, and due to the limited instructions to choose the best computational model, this article appraises the difference between 1D and 2D modeling of the phenomenon based on the logical comparison of the results. For this purpose the Zayandeh-Rood dam in Iran was used as the case study and MIKE11 and MIKE21 are used for numerical exploration of the problem. The reliability of each approach is assessed and the applicability of each method for exact analyzing the dam break phenomena was demonstrated.
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Palm, Bruna G., Fábio M. Bayer, and Renato J. Cintra. "2-D Rayleigh autoregressive moving average model for SAR image modeling." Computational Statistics & Data Analysis 171 (July 2022): 107453. http://dx.doi.org/10.1016/j.csda.2022.107453.
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Vyas, Siddharth, Vladimir Genis, and Gary Friedman. "Computational Study of Kinematics of Capture of Magnetic Particles by Stent: 2-D Model." IEEE Transactions on Magnetics 52, no. 7 (July 2016): 1–4. http://dx.doi.org/10.1109/tmag.2015.2512537.
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Komeza, K., and S. Wiak. "ELECTROMAGNETIC FIELD CALCULATION OF A LEAKAGE TRANSFORMER BY MEANS OF FINITE ELEMENT METHOD WITH HERMITIAN ELEMENTS." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 13, no. 1 (January 1, 1994): 97–100. http://dx.doi.org/10.1108/eb051849.
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This paper deals with the field and leakage reactance calculations in the model leakage transformer. The approximate solution for 3‐D problem, made by composing 2‐D solutions for 3‐D solution, is applied. Hermitian hierarchical finite elements have been successfully applied to the field and reactance computation of the transformer. The computational results have been reported and compared with measurement giving the error not greater than 10%.
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Qin, Xinsheng, Michael Motley, Randall LeVeque, Frank Gonzalez, and Kaspar Mueller. "A comparison of a two-dimensional depth-averaged flow model and a three-dimensional RANS model for predicting tsunami inundation and fluid forces." Natural Hazards and Earth System Sciences 18, no. 9 (September 18, 2018): 2489–506. http://dx.doi.org/10.5194/nhess-18-2489-2018.
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Abstract. The numerical modeling of tsunami inundation that incorporates the built environment of coastal communities is challenging for both 2-D and 3-D depth-integrated models, not only in modeling the flow but also in predicting forces on coastal structures. For depth-integrated 2-D models, inundation and flooding in this region can be very complex with variation in the vertical direction caused by wave breaking on shore and interactions with the built environment, and the model may not be able to produce enough detail. For 3-D models, a very fine mesh is required to properly capture the physics, dramatically increasing the computational cost and rendering impractical the modeling of some problems. In this paper, comparisons are made between GeoClaw, a depth-integrated 2-D model based on the nonlinear shallow-water equations (NSWEs), and OpenFOAM, a 3-D model based on Reynolds-averaged Navier–Stokes (RANS) equation for tsunami inundation modeling. The two models were first validated against existing experimental data of a bore impinging onto a single square column. Then they were used to simulate tsunami inundation of a physical model of Seaside, Oregon. The resulting flow parameters from the models are compared and discussed, and these results are used to extrapolate tsunami-induced force predictions. It was found that the 2-D model did not accurately capture the important details of the flow near initial impact due to the transiency and large vertical variation of the flow. Tuning the drag coefficient of the 2-D model worked well to predict tsunami forces on structures in simple cases, but this approach was not always reliable in complicated cases. The 3-D model was able to capture transient characteristic of the flow, but at a much higher computational cost; it was found this cost can be alleviated by subdividing the region into reasonably sized subdomains without loss of accuracy in critical regions.
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Chunduru, Raghu K., Mrinal K. Sen, and Paul L. Stoffa. "2-D resistivity inversion using spline parameterization and simulated annealing." GEOPHYSICS 61, no. 1 (January 1996): 151–61. http://dx.doi.org/10.1190/1.1443935.
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Successful inversion of geophysical data depends on prior information, proper choice of inversion scheme, and on effective parameterization of the model space such that the model representation is appropriate and efficient. Inversion of resistivity data has long been recognized as a nonlinear or quasi‐linear problem. Traditionally, 2-D resistivity inversion has been performed by trial and error methods and with linear and iterative linear methods. The linear and iterative linear methods are limited because of the requirement of good prior knowledge of the subsurface. Unlike linear and iterative linear methods, most nonlinear inversion schemes do not depend strongly on the starting solution, but prior information helps to reduce the computational cost and to obtain geologically meaningful results. In the present study, we have applied a nonlinear optimization scheme called very fast simulated annealing (VFSA) in the inversion of 2-D dipole‐dipole resistivity data to image the subsurface. Unlike Metropolis simulated annealing (SA) in which each new model is drawn from a uniform distribution, VFSA draws a model from a Cauchy‐like distribution, which is also a function of a control parameter called temperature. The advantage of using such a scheme is that at high temperatures, the algorithm allows for searches far beyond the current position, while at low temperatures, it looks for improvement in the close vicinity of the current model. We have used the mean square error between the synthetics and original data as the error function to be minimized. The synthetic response for 2-D models was obtained by finite‐difference modeling, and cubic splines were used to parameterize the model space to get smooth images of the subsurface and to reduce computational cost. VFSA was used to estimate the conductivity at each spline node location. The inversion was applied to various synthetic data to study the influence of the starting solution and the location of the spline nodes. Finally, we applied it to real data collected over a disseminated sulfide zone at Safford, Arizona, and compared the results with those obtained from a linearized inversion and from a model based on geologic and well‐log data. The VFSA results are in good agreement with the previously published results.
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Ikhsani, Nur, Nasaruddin Salam, and Luther Sule. "Fluid Flow Through Serieal Parallel Circular Cylinder Arranged In Tandem." EPI International Journal of Engineering 4, no. 1 (September 15, 2021): 51–56. http://dx.doi.org/10.25042/epi-ije.022021.07.
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The Fluid flow through circular cylinders in serieal parallel positions arranged in tandem were analyzed computationally and experimentally at nine levels of Reynolds number, ReD 34,229; 47,921; 61,612; 75,304; 88,996; 102,688; 116,379; 130.071 and 143,763 The variation in the ratio of the distance between the front and rear cylinders is determined as M / D = 0.3, M / D = 0.5, M / D = 0.7, M / D = 0.9, and M / D = 1.1. While the distance between cylinder number 2 and 3 we set constantly and determined as N / D = 5 cm. The results displayed are flow velocity with computational approach validated by flow visualization, computational pressure contour, and drag coefficient through experimental testing. The results showed that the smallest boundary layer thickness was obtained in the model with a distance ratio of M / D = 2.5, using both computational and experimental approaches. The characteristics of the minimum pressure contour and the lowest drag coefficient (CD) = 0.7572 were also obtained at the ratio of the distance M / D = 0.25 and at upstream speed of 21 m / s
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Wu, Xiang, and Ling Feng Tang. "Review of Coupled Research for Mechanical Dynamics and Fluid Mechanics of Reciprocating Compressor." Applied Mechanics and Materials 327 (June 2013): 227–32. http://dx.doi.org/10.4028/www.scientific.net/amm.327.227.
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Research statuses of mechanical dynamics and fluid mechanics of a reciprocating compressor are reviewed respectively ,along with the presentation of coupled research for these two disciplines of a reciprocating compressor. Analyses for mechanical dynamics are focused on modal analysis and dynamic response analysis. Three methods can be adopted in dynamic response analysis,which are the combination of the formula derivation and finite element method, the combination of multi-rigid-body dynamics and finite element method , and thecombination of multi-flexible body dynamics and finite element method. Analytical models for fluid dynamics include 1-D computationalfluid dynamics model, 2-D computational fluid dynamics model and 3-D computational fluid dynamics model. In addition, limitations of researches for mechanical dynamics and fluid mechanics in a reciprocating compressor are also presented, as well as the prospect for the coupled research of two disciplines.
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Huang, S., J. Rauberg, H. Apel, and K. E. Lindenschmidt. "The effectiveness of polder systems on peak discharge capping of floods along the middle reaches of the Elbe River in Germany." Hydrology and Earth System Sciences Discussions 4, no. 1 (February 8, 2007): 211–41. http://dx.doi.org/10.5194/hessd-4-211-2007.
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Abstract. In flood modelling, many one-dimensional (1-D) hydrodynamic models are too restricted in capturing the spatial differentiation of processes within a polder or system of polders and two-dimensional (2-D) models are very demanding in data requirements and computational resources. The latter is an important consideration when uncertainty analyses using the Monte Carlo techniques are to complement the modelling exercises. This paper describes the development of a quasi-2-D modeling approach, which still calculates the dynamic wave in 1-D but the discretisation of the computational units is in 2-D, allowing a better spatial representation of the flow in polders and avoiding large additional expenditure on data pre-processing and computational time. The model DYNHYD (1-D hydrodynamics) from the WASP5 modeling package was used as a basis for the simulations and extended to incorporate the quasi-2-D approach. A local sensitive analysis shows the sensitivity of parameters and boundary conditions on the filling volume of polders and capping of the peak discharge in the main river system. Two flood events on the Elbe River, Germany were used to calibrate and test the model. The results show a good capping effect on the flood peak by the proposed systems. The effect of capping reduces as the flood wave propagates downstream from the polders (up to 0.5 cm of capping is lost for each additional kilometer from the polders).
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Huang, S., J. Rauberg, H. Apel, M. Disse, and K. E. Lindenschmidt. "The effectiveness of polder systems on peak discharge capping of floods along the middle reaches of the Elbe River in Germany." Hydrology and Earth System Sciences 11, no. 4 (July 3, 2007): 1391–401. http://dx.doi.org/10.5194/hess-11-1391-2007.
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Abstract. In flood modelling, many one-dimensional (1-D) hydrodynamic models are too restricted in capturing the spatial differentiation of processes within a polder or system of polders and two-dimensional (2-D) models are very demanding in data requirements and computational resources. The latter is an important consideration when uncertainty analyses using the Monte Carlo techniques are to complement the modelling exercises. This paper describes the development of a quasi-2-D modeling approach, which still calculates the dynamic wave in 1-D but the discretisation of the computational units are in 2-D, allowing a better spatial representation of the flow in polders and avoiding large additional expenditure on data pre-processing and computational time. The model DYNHYD (1-D hydrodynamics) from the WASP5 modeling package was used as a basis for the simulations and extended to incorporate the quasi-2-D approach. A local sensitivity analysis shows the sensitivity of parameters and boundary conditions on the filling volume of polders and capping of the peak discharge in the main river system. Two flood events on the Elbe River, Germany were used to calibrate and test the model. The results show a good capping effect on the flood peak by the proposed systems. The effect of capping reduces as the flood wave propagates down stream from the polders (up to 0.5 cm of capping is decreased for each additional kilometer from the polder).
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Oliveira, R., and B. M. Terhal. "The complexity of quantum spin systems on a two-dimensional square lattice." Quantum Information and Computation 8, no. 10 (November 2008): 900–924. http://dx.doi.org/10.26421/qic8.10-2.
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The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA. In this paper we show that this important problem remains QMA-complete when the interactions of the 2-local Hamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to manipulate k-local interactions. As a side result, we obtain that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuit model of quantum computation. Our perturbation method also shows how any stabilizer space associated with a k-local stabilizer (for constant k) can be generated as an approximate ground-space of a 2-local Hamiltonian.
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Córdoba, G., M. F. Sheridan, and E. B. Pitman. "TITAN2F: a pseudo-3-D model of 2-phase debris flows." Natural Hazards and Earth System Sciences Discussions 3, no. 6 (June 12, 2015): 3789–822. http://dx.doi.org/10.5194/nhessd-3-3789-2015.
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Abstract. Debris flows, avalanches, landslides, and other geophysical mass flows can contain O(106–1010) m3 or more of material. These flows commonly consist of mixture of soil and rocks with a significant quantity of interstitial fluid. They can be tens of meters deep, and their runouts can extend many kilometers. The complicated rheology of such a mixture challenges every constitutive model that can reasonably be applied; the range of length and timescales involved in such mass flows challenges the computational capabilities of existing systems.This paper extends recent efforts to develop a depth averaged "thin layer" model for geophysical mass flows that contain a mixture of solid material and fluid. Concepts from the engineering community are integrated with phenomenological findings in geo-science, resulting in a theory that accounts for the principal solid and fluid forces as well as interactions between the phases, across a wide range of solid volume fraction. A principal contribution here is to present drag and phase interaction terms that comport with the literature in geo-sciences. The program predicts the evolution of the concentration and dynamic pressure. The theory is validated with with data from one dimensional dam break solutions and it is verified with data from artificial channel experiments.
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Tennyson, J., M. J. Barber, and R. E. A. Kelly. "An adiabatic model for calculating overtone spectra of dimers such as (H 2 O) 2." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1968 (June 13, 2012): 2656–74. http://dx.doi.org/10.1098/rsta.2011.0243.
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The near-infrared and visible wavelength spectrum of the water dimer is considered to be the major contributor to the so-called water continuum at these wavelengths. However, theoretical models of this spectrum require the simultaneous treatment of both monomer and dimer excitations. A model for treating this problem is proposed which is based upon a Franck–Condon-like separation between the monomer and dimer vibrational motions. In this model, one of the monomers is treated as the chromophore and its absorption is assumed to be given by its, possibly perturbed, vibrational band intensity. The main computational issue is the treatment of separate monomer and dimer motions. Various approaches for obtaining dimer vibration–rotation tunnelling spectra that allow for monomer motion are explored. These approaches include ways of treating the adiabatic separation of dimer vibrational modes from monomer vibrational modes. We classify the adiabatic separation methods under four main approaches: namely fixed-geometry , free-monomer , perturbed-monomer and coupled-monomer methods. The latter being the most computationally expensive as the monomer wave functions are dependent on the dimer coordinates. For each of these approaches, expectation values over the full potential are calculated for the given monomer vibrational wave functions. Various full (named VAP 2 p D in the text) and partial (VAP (+ p )D) averaging techniques are outlined to calculate the vibrationally averaged, monomer state-dependent, dimer interaction potentials. The computational costs associated with application of these techniques to the water dimer are estimated and the prospects for full calculations based on this approach are assessed.
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Ghalenoei, Emad, Jan Dettmer, Mohammed Y. Ali, and Jeong Woo Kim. "Trans-dimensional gravity and magnetic joint inversion for 3-D earth models." Geophysical Journal International 230, no. 1 (February 25, 2022): 363–76. http://dx.doi.org/10.1093/gji/ggac083.
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SUMMARY Studying 3-D subsurface structure based on spatial data is an important application for geophysical inversions. However, major limitations exist for conventional regularized inversion when applied to potential-field data. For example, global regularization parameters can mask model features that may be important for interpretation. In addition, 3-D inversions are typically based on data acquired in 2-D at the Earth’s surface. Such data may contain significant spatial error correlations in 2-D due to the choice of spatial sampling, acquisition geometry, ambient noise and model assumptions. These correlations can cause trade-offs with spatial resolution and should be accounted for. However, correlations are often ignored, particularly 2-D correlations in spatial data, such as potential field data recorded on the Earth’s surface. Non-linear Bayesian methods can address these shortcomings and we present a new hierarchical model for 2-D correlated errors. Nonetheless, limitations also exist. For example, non-linear Bayesian estimation requires numerical integration with a considerable computational burden to collect a posterior ensemble of models. For 3-D applications, this cost can be prohibitive. This paper presents a non-linear Bayesian inversion with trans-dimensional (trans-D) partitioning of space by a hierarchy of Voronoi nodes and planes (VP), and trans-D estimation of the data noise covariance matrix. The addition of planes permits the introduction of prior information which reduces non-uniqueness. The covariance matrix estimation uses a trans-D autoregressive (AR) noise model to quantify correlated noise on 2-D potential-field data. We address computational cost by wavelet compression in the forward problem and by basing susceptibility on an empirical relationship with density contrast. The method is applied to simulated data and field data from off-shore Abu Dhabi. With simulated data, we demonstrate that subsurface structures are well-resolved with the trans-D model that applies hierarchical VP partitioning. In addition, the model locally adapts based on data information without requiring regularization. The method is also successful in reducing 2-D error correlation via trans-D AR models in 2-D. From field data, the inversion efficiently resolves basement topography and two distinct salt diapirs with a parsimonious and data-driven parametrization. Results show a considerable reduction in 2-D spatial correlations of field data using the proposed trans-D AR model.
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Michelena, R. J., and J. M. Harris. "Tomographic traveltime inversion using natural pixels." GEOPHYSICS 56, no. 5 (May 1991): 635–44. http://dx.doi.org/10.1190/1.1443080.
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Traditionally in the problem of tomographic traveltime inversion, the model is divided into a number of rectangular cells of constant slowness. Inversion consists of finding these constant values using the measured traveltimes. The inversion process can demand a large computational effort if a high‐resolution result is desired. We show how to use a different kind of parameterization of the model based on beam propagation paths. This parameterization is obtained within the framework of reconstruction in Hilbert spaces by minimizing the error between the true model and the estimated model. The traveltimes are interpreted as the projections of the slowness along the beampaths. Although the actual beampaths are described by complicated spatial functions, we simplify the computations by approximating these functions with functions of constant width and height, i.e., “fat” rays, which collectively form a basis set of natural pixels. With a simple numerical example we demonstrate that the main advantage of this parameterization, compared with the traditional decomposition of the model in rectangular pixels, is that 2-D reconstructed images of similar quality can be obtained with considerably less computational effort. This result suggests that the natural pixels can provide considerable computational advantage for 3-D problems.
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Wahab, M. M. Abdel, and G. De Roeck. "A 2-D five-noded finite element to model power singularity." International Journal of Fracture 74, no. 1 (August 1996): 89–97. http://dx.doi.org/10.1007/bf00018577.
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Nguyen, Thao Danh, and Duy The Nguyen. "SIMULATION OF WAVE PRESSURE ON A VERTICAL WALL BASED ON 2-D NAVIER-STOKES EQUATIONS." Science and Technology Development Journal 12, no. 18 (December 15, 2009): 59–68. http://dx.doi.org/10.32508/stdj.v12i18.2384.
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This paper applies and develops a numerical model based on the two-dimensional vertical Navier-Stokes equations to simulate the temporal and spatial variations of wave parameters in front of vertical walls. A non-uniform grids system is performed in the numerical solution of the model by transforming a variable physical domain to a fixed computational domain. Through present model, beside some basic hydrodynamic problems of water waves such as wave profile and water particle velocities, standing wave pressures at the wall are examined. Numerical results of the present model are compared with laboratory data and with existing empirical and theoretical models. The comparisons show that the model can simulate reasonably the wave processes of the waves in front of vertical walls as well as the wave pressures on the wall.
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Shakeel, Muhammad. "2-D coupled computational model of biological cell proliferation and nutrient delivery in a perfusion bioreactor." Mathematical Biosciences 242, no. 1 (March 2013): 86–94. http://dx.doi.org/10.1016/j.mbs.2012.12.004.
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PRIOLO, ENRICO. "EARTHQUAKE GROUND MOTION SIMULATION THROUGH THE 2-D SPECTRAL ELEMENT METHOD." Journal of Computational Acoustics 09, no. 04 (December 2001): 1561–81. http://dx.doi.org/10.1142/s0218396x01001522.
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The application of the 2-D Chebyshev spectral element method (SPEM) to engineering seismology problems is reviewed in this paper. The SPEM is a high-order finite element technique which solves the variational formulation of the seismic wave propagation equations. The computational domain is discretised into an unstructured grid composed by irregular quadrilateral elements. This property makes the SPEM particularly suitable to compute numerically accurate solutions of the full wave equations in complex media. The earthquake is simulated following an approach that can be considered "global", that is all the factors influencing the wave propagation — source, crustal heterogeneity, fine details of the near-surface structure, and topography — are taken into account and solved simultaneously. The basic earthquake source is represented by a 2-D point double couple model. Ruptures propagating along fault segments placed on the model plane are simulated as a finite summation of elementary point sources. After a general introduction, the paper first gives an overview of the method; then it concentrates on some methodological topics of interest for practical applications, such as quadrangular mesh generation, source definition and scaling, numerical accuracy and computational efficiency. Limitations and advantages of using a 2-D approach, although sophisticated such as the SPEM, are addressed, as well. The effectiveness of the method is illustrated through two case histories, i.e. the ground shaking prediction in Catania (Sicily, Italy) for a catastrophic earthquake, and the analysis of the ground motion in the presence of a massive structure.
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Benmessaoud, Youcef, Frédéric Dubas, and Mickael Hilairet. "Combining the Magnetic Equivalent Circuit and Maxwell–Fourier Method for Eddy-Current Loss Calculation." Mathematical and Computational Applications 24, no. 2 (June 4, 2019): 60. http://dx.doi.org/10.3390/mca24020060.
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In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series) is developed. This model coupling has been applied to a U-cored static electromagnetic device. The main objective is to compute the magnetic field behavior in massive conductive parts (e.g., aluminum, magnets, copper, iron) considering the skin effect (i.e., with the eddy-current reaction field) and to predict the eddy-current losses. The magnetic field distribution for various models is validated with 2-D and three-dimensional (3-D) finite-element analysis (FEA). The study is also focused on the discretization influence of 2-D generic MEC on the eddy-current loss calculation in conductive regions. Experimental tests and 3-D FEA have been compared with the proposed approach on massive conductive parts in aluminum. For an operating point, the computation time is divided by ~4.6 with respect to 3-D FEA.
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Seydgar, Majid, Amin Alizadeh Naeini, Mengmeng Zhang, Wei Li, and Mehran Satari. "3-D Convolution-Recurrent Networks for Spectral-Spatial Classification of Hyperspectral Images." Remote Sensing 11, no. 7 (April 11, 2019): 883. http://dx.doi.org/10.3390/rs11070883.
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Nowadays, 3-D convolutional neural networks (3-D CNN) have attracted lots of attention in the spectral-spatial classification of hyperspectral imageries (HSI). In this model, the feed-forward processing structure reduces the computational burden of 3-D structural processing. However, this model as a vector-based methodology cannot analyze the full content of the HSI information, and as a result, its features are not quite discriminative. On the other hand, convolutional long short-term memory (CLSTM) can recurrently analyze the 3-D structural data to extract more discriminative and abstract features. However, the computational burden of this model as a sequence-based methodology is extremely high. In the meanwhile, the robust spectral-spatial feature extraction with a reasonable computational burden is of great interest in HSI classification. For this purpose, a two-stage method based on the integration of CNN and CLSTM is proposed. In the first stage, 3-D CNN is applied to extract low-dimensional shallow spectral-spatial features from HSI, where information on the spatial features are less than that of the spectral information; consequently, in the second stage, the CLSTM, for the first time, is applied to recurrently analyze the spatial information while considering the spectral one. The experimental results obtained from three widely used HSI datasets indicate that the application of the recurrent analysis for spatial feature extractions makes the proposed model robust against different spatial sizes of the extracted patches. Moreover, applying the 3-D CNN prior to the CLSTM efficiently reduces the model’s computational burden. The experimental results also indicated that the proposed model led to a 1% to 2% improvement compared to its counterpart models.
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MIKHAEL, WASFY B., and HAOPING YU. "ADAPTIVE, FREQUENCY DOMAIN, 2-D MODELING USING SPATIOTEMPORAL SIGNALS." Journal of Circuits, Systems and Computers 06, no. 04 (August 1996): 351–58. http://dx.doi.org/10.1142/s0218126696000236.
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In this paper, an adaptive, frequency domain, steepest descent algorithm for two-dimensional (2-D) system modeling is presented. Based on the equation error model, the algorithm, which characterizes the 2-D spatially linear and invariant unknown system by a 2-D auto-regressive, moving-average (ARMA) process, is derived and implemented in the 3-D spatiotemporal domain. At each iteration, corresponding to a given pair of input and output 2-D signals, the algorithm is formulated to minimize the error-function’s energy in the frequency domain by adjusting the 2-D ARMA model parameters. A signal dependent, optimal convergence factor, referred to as the homogeneous convergence factor, is developed. It is the same for all the coefficients but is updated once per iteration. The resulting algorithm is called the Two-Dimensional, Frequency Domain, with Homogeneous µ*, Adaptive Algorithm (2D-FD-HAA). In addition, the algorithm is implemented using the 2-D Fast Fourier Transform (FFT) to enhance the computational efficiency. Computer simulations demonstrate the algorithm’s excellent adaptation accuracy and convergence speed. For illustration, the proposed algorithm is successfully applied to modeling a time varying 2-D system.
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Arunkumar, H. S., Chidanand Mangrulkar, and Trushar Gohil. "Vortex dynamics and elliptical structure wake interaction in the proximity of wall using 2-D RANS simulation." MATEC Web of Conferences 144 (2018): 04018. http://dx.doi.org/10.1051/matecconf/201814404018.
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The 2-D numerical study is performed to analyses the flow characteristic behind the elliptical structure placed near the wall for three different gap ratios as 0.25, 0.5, and 1.0. Computational domain and model is initially validated with the unbounded flow over a cylinder without considering wall effect for Reynolds number of 3900. For flow over the cylinder with near wall, computational domain is modelled as Blasius profile is the input to the area of interest. At different gap ratios the effect of boundary layer on vortex shedding is studied with Reynolds number of 1440. By applying different turbulent model for analysis, study the variation in the results and suggest the suitable model for the present type of study. It has been observed that the wall effect is predominant in case of the gap ratio of 0.25 as compared to other gap ratios.
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Zadeh, Saman Naghib, Matin Komeili, and Marius Paraschivoiu. "MESH CONVERGENCE STUDY FOR 2-D STRAIGHT-BLADE VERTICAL AXIS WIND TURBINE SIMULATIONS AND ESTIMATION FOR 3-D SIMULATIONS." Transactions of the Canadian Society for Mechanical Engineering 38, no. 4 (December 2014): 487–504. http://dx.doi.org/10.1139/tcsme-2014-0032.
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Mesh resolution requirements are investigated for 2-D and 3-D simulations of the complex flow around a straight-blade vertical axis wind turbine (VAWT). The resulting flow, which may include large separation flows over the blades, dynamic stall, and wake-blade interaction, is simulated by an Unsteady Reynolds-Averaged Navier–Stokes analysis, based on the Spalart-Allmaras (S–A) turbulence model. A grid resolution study is conducted on 2-D grids to examine the convergence of the CFD model. Hence, an averaged-grid residual of y+ > 30 is employed, along with a wall treatment, to capture the near-wall region’s flow structures. Furthermore a 3-D simulation on a coarse grid of the VAWT model is performed in order to explore the influence of the 3-D effects on the aerodynamic performance of the turbine. Finally, based on the 2-D grid convergence study and the 3-D results, the required computational time and mesh to simulate 3-D VAWT accurately is proposed.
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Tanveer, N. K. Mohamad, Chandran Mohanraj, K. Jegadeesan, and S. Maruthupandiyan. "Comparative Studies on Various Turbulent Models with Liquid Rocket Nozzle through Computational Tool." Advanced Materials Research 984-985 (July 2014): 1204–9. http://dx.doi.org/10.4028/www.scientific.net/amr.984-985.1204.
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Supersonic flows associated with missiles, aircraft, missile engine intake and rocket nozzles are often steady. In this present work, the computational analysis was conducted on C-D (convergent –divergent) nozzle for understanding the flow regime with various flow properties such as velocity and various turbulent models (spalert almaras, K-ε and K-ω). The Scale down model of C-D nozzle was chosen for this study and it was modelled computationally with Gambit software package. In this integrated component model, the inlet flow is assumed a two-dimensional, steady, compressible, turbulent and supersonic. The physics based mathematical model of the considered flow consists of conservation of mass, momentum and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The system of the governing equations with turbulent effects is solved numerically using different turbulence models to demonstrate their numerical accuracy in predicting the characteristics of turbulent gas flow in such complex geometry. Fluent software package was used for solving gas flow equations with turbulence models. The Mach number was chosen for different cases of analyses were 1.2, 1.5 and 2. For each case, different turbulence were engaged and solved and all the results were compared finally.
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Fiorina, Carlo, Alessandro Scolaro, Daniel Siefman, Mathieu Hursin, and Andreas Pautz. "Artificial Neural Networks as Surrogate Models for Uncertainty Quantification and Data Assimilation in 2-D/3-D Fuel Performance Studies." Journal of Nuclear Engineering 1, no. 1 (November 10, 2020): 54–62. http://dx.doi.org/10.3390/jne1010005.
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This paper preliminarily investigates the use of data-driven surrogates for fuel performance codes. The objective is to develop fast-running models that can be used in the frame of uncertainty quantification and data assimilation studies. In particular, data assimilation techniques based on Monte Carlo sampling often require running several thousand, or tens of thousands of calculations. In these cases, the computational requirements can quickly become prohibitive, notably for 2-D and 3-D codes. The paper analyses the capability of artificial neural networks to model the steady-state thermal-mechanics of the nuclear fuel, assuming given released fission gases, swelling, densification and creep. An optimized and trained neural network is then employed on a data assimilation case based on the end of the first ramp of the IFPE Instrumented Fuel Assemblies 432.
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Munzir, S., L. S. Jennings, and M. T. Koh. "Computational models satisfying relative angle constraints for 2-dimensional segmented bodies." ANZIAM Journal 47, no. 4 (April 2006): 541–54. http://dx.doi.org/10.1017/s1446181100010129.
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AbstractPlanar hinged segmented bodies have been used to represent models of biomechanical systems. One characteristic of a segmented body moving under gravitational acceleration and torques between segments is the possibility that the body's segments spin through more than a revolution or past a natural limit, and a computational mechanism to stop such behaviour should be provided. This could be done by introducing angle constraints between segments, and computational models utilising optimal control are studied here. Three models to maintain angle constraints between segments are proposed and compared. These models are: all-time angle constraints, a restoring torque in the state equations and an exponential penalty model. The models are applied to a 2-D three-segment body to test the behaviour of each model when optimising torques to minimise an objective. The optimisation is run to find torques so that the end effector of the body follows the trajectory of a half-circle. The result shows the behaviour of each model in maintaining the angle constraints. The all-time constraints case exhibits a behaviour of not allowing torques (at a solution) which makes segments move past the constraints, while the other two show a flexibility in handling the angle constraints which is more similar to what occurs in a real biomechanical system.
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Roussel-Dupre, R. "HYDROFLASH: A 2-D Nuclear EMP Code Founded on Finite Volume Techniques." Advanced Electromagnetics 6, no. 2 (March 23, 2017): 14. http://dx.doi.org/10.7716/aem.v6i2.472.
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The basic mechanisms that govern the generation of an electromagnetic pulse (EMP) following a nuclear detonation in the atmosphere, including heights of burst (HOB) relevant to surface bursts (0 km), near surface bursts (0-2 km), air bursts (2-20 km) and high-altitude bursts (> 20 km), are reviewed. Previous computational codes developed to treat the source region and predict the EMP are discussed. A new 2-D hydrodynamic code (HYDROFLASH) that solves the fluid equations for electron and ion transport in the atmosphere and the coupled Maxwell equations using algorithms extracted from the Conservation Law (CLAW) package for solving multi-dimensional hyperbolic equations with finite volume techniques has been formulated. Simulations include the ground, atmospheric gradient, and an azimuthal applied magnetic field as a first approximation to the geomagnetic field. HYDROFLASH takes advantage of multiprocessor systems by using domain decomposition together with the Message Passing Interface (MPI) protocol for parallel processing. A detailed description of the model is presented along with computational results for a generic 10 kiloton (kT) burst detonated at 0 and 10 km altitude.
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Milosevic, Miljan, Dusica Stojanovic, Vladimir Simic, Bogdan Milicevic, Andjela Radisavljevic, Petar Uskokovic, and Milos Kojic. "A Computational Model for Drug Release from PLGA Implant." Materials 11, no. 12 (November 29, 2018): 2416. http://dx.doi.org/10.3390/ma11122416.
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Due to the relative ease of producing nanofibers with a core–shell structure, emulsion electrospinning has been investigated intensively in making nanofibrous drug delivery systems for controlled and sustained release. Predictions of drug release rates from the poly (d,l-lactic-co-glycolic acid) (PLGA) produced via emulsion electrospinning can be a very difficult task due to the complexity of the system. A computational finite element methodology was used to calculate the diffusion mass transport of Rhodamine B (fluorescent drug model). Degradation effects and hydrophobicity (partitioning phenomenon) at the fiber/surrounding interface were included in the models. The results are validated by experiments where electrospun PLGA nanofiber mats with different contents were used. A new approach to three-dimensional (3D) modeling of nanofibers is presented in this work. The authors have introduced two original models for diffusive drug release from nanofibers to the 3D surrounding medium discretized by continuum 3D finite elements: (1) A model with simple radial one-dimensional (1D) finite elements, and (2) a model consisting of composite smeared finite elements (CSFEs). Numerical solutions, compared to experiments, demonstrate that both computational models provide accurate predictions of the diffusion process and can therefore serve as efficient tools for describing transport inside a polymer fiber network and drug release to the surrounding porous medium.
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Kang, Yuchi, Meihong Liu, Sharon Kao-Walter, Wureguli Reheman, and Jinbin Liu. "Predicting aerodynamic resistance of brush seals using computational fluid dynamics and a 2-D tube banks model." Tribology International 126 (October 2018): 9–15. http://dx.doi.org/10.1016/j.triboint.2018.04.023.
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KÄRKKÄINEN, LEO, and KARI RUMMUKAINEN. "CRITICAL SURFACE EXPONENTS IN 2-D 10-STATE POTTS MODEL." International Journal of Modern Physics C 03, no. 05 (October 1992): 1125–36. http://dx.doi.org/10.1142/s0129183192000750.
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At low temperature, the Potts models can have interfaces between domains ordered to different directions. We use the difference of periodic and twisted boundary conditions to study planar order-order interfaces. We show that the interface tension, energy and width display critical properties as one approaches the critical point. We measure the critical exponents connected to their power like singular behaviour at the critical point.
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Shen, D., J. Wang, X. Cheng, Y. Rui, and S. Ye. "Integration of 2-D hydraulic model and high-resolution LiDAR-derived DEM for floodplain flow modeling." Hydrology and Earth System Sciences Discussions 12, no. 2 (February 13, 2015): 2011–46. http://dx.doi.org/10.5194/hessd-12-2011-2015.
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Abstract. The rapid progress of Light Detection And Ranging (LiDAR) technology has made acquirement and application of high-resolution digital elevation model (DEM) data increasingly popular, especially with regards to the study of floodplain flow modeling. High-resolution DEM data include many redundant interpolation points, needs a high amount of calculation, and does not match the size of computational mesh. These disadvantages are a common problem for floodplain flow modeling studies. Two-dimensional (2-D) hydraulic modeling, a popular method of analyzing floodplain flow, offers high precision of elevation parameterization for computational mesh while ignoring much micro-topographic information of the DEM data itself. We offer a flood simulation method that integrates 2-D hydraulic model results and high-resolution DEM data, enabling the calculation of flood water levels in DEM grid cells through local inverse distance weighted interpolation. To get rid of the false inundation areas during interpolation, it employs the run-length encoding method to mark the inundated DEM grid cells and determine the real inundation areas through the run-length boundary tracing technique, which solves the complicated problem of the connectivity between DEM grid cells. We constructed a 2-D hydraulic model for the Gongshuangcha polder, a flood storage area of Dongting Lake, using our integrated method to simulate the floodplain flow. The results demonstrate that this method can solve DEM associated problems efficiently and simulate flooding processes with greater accuracy than DEM only simulations.
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Rahman, Md Siddiqur, and Jafar A. Khan. "Building a Robust Linear Model with Backward Elimination Procedure." Dhaka University Journal of Science 62, no. 2 (February 8, 2015): 87–93. http://dx.doi.org/10.3329/dujs.v62i2.21971.
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For building a linear prediction model, Backward Elimination (BE) is a computationally suitable stepwise procedure for sequencing the candidate predictors. This method yields poor results when data contain outliers and other contaminations. Robust model selection procedures, on the other hand, are not computationally efficient or scalable to large dimensions, because they require the fitting of a large number of submodels. Robust version of BE is proposed in this study, which is computationally very suitable and scalable to large high-dimensional data sets. Since BE can be expressed in terms of sample correlations, simple robustifications are obtained by replacing these correlations by their robust counterparts. A pairwise approach is used to construct the robust correlation matrix -- not only because of its computational advantages over the d-dimensional approach, but also because the pairwise approach is more consistent with the idea of step-by-step algorithms. The performance of the proposed robust method is much better than standard BE. DOI: http://dx.doi.org/10.3329/dujs.v62i2.21971 Dhaka Univ. J. Sci. 62(2): 87-93, 2014 (July)
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Shen, D., J. Wang, X. Cheng, Y. Rui, and S. Ye. "Integration of 2-D hydraulic model and high-resolution lidar-derived DEM for floodplain flow modeling." Hydrology and Earth System Sciences 19, no. 8 (August 18, 2015): 3605–16. http://dx.doi.org/10.5194/hess-19-3605-2015.
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Abstract. The rapid progress of lidar technology has made the acquirement and application of high-resolution digital elevation model (DEM) data increasingly popular, especially in regards to the study of floodplain flow. However, high-resolution DEM data pose several disadvantages for floodplain modeling studies; e.g., the data sets contain many redundant interpolation points, large numbers of calculations are required to work with data, and the data do not match the size of the computational mesh. Two-dimensional (2-D) hydraulic modeling, which is a popular method for analyzing floodplain flow, offers highly precise elevation parameterization for computational mesh while ignoring much of the micro-topographic information of the DEM data itself. We offer a flood simulation method that integrates 2-D hydraulic model results and high-resolution DEM data, thus enabling the calculation of flood water levels in DEM grid cells through local inverse distance-weighted interpolation. To get rid of the false inundation areas during interpolation, it employs the run-length encoding method to mark the inundated DEM grid cells and determine the real inundation areas through the run-length boundary tracing technique, which solves the complicated problem of connectivity between DEM grid cells. We constructed a 2-D hydraulic model for the Gongshuangcha detention basin, which is a flood storage area of Dongting Lake in China, by using our integrated method to simulate the floodplain flow. The results demonstrate that this method can solve DEM associated problems efficiently and simulate flooding processes with greater accuracy than simulations only with DEM.
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Woronowicz, Konrad, Majd Abdelqader, Ryszard Palka, and Jordan Morelli. "2-D quasi-static Fourier series solution for a linear induction motor." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 3 (May 8, 2018): 1099–109. http://dx.doi.org/10.1108/compel-06-2017-0247.
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Purpose This paper aims to present a method for calculating electromagnetic fields, eddy currents and forces for a quasi-static two-dimensional (2-D) model of linear induction motors (LIMs) where the primary side is modeled as a collection of individual coils. Design/methodology/approach An analytical solution using Fourier series is derived for a general source with current excitations residing in an airgap and moving relative to a conducting plate and back iron. Ideal magnetic material with infinite permeability is used to model the primary iron above the primary source and the back iron below the conducting plate. Findings The analytical solution is compared to a commercial 2-D finite element analysis (FEA) simulation for validation and then compared to a 2-D FEA model with a more detailed geometry of the LIM. The analytical model accurately predicts LIM thrust even though the geometry of the primary core is simplified as an infinitely long flat slab. 2-D frequency FEA can be used successfully to predict in motion LIM performance. Originality/value The analytical solution presented here models the primary excitations as individual discrete coils instead of current sheets, which all existing models are based on. The discrete coils approach provides a more intuitive and realistic model of the LIM.
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Li, Rui, David Soper, Jianlin Xu, Yongxing Jia, Jiqiang Niu, and Hassan Hemida. "A Separated-Flow Model for 2-D Viscous Flows around Bluff Bodies Using the Panel Method." Applied Sciences 12, no. 19 (September 26, 2022): 9652. http://dx.doi.org/10.3390/app12199652.
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Panel methods have been applied to many fields of fluid owing to their computational efficiency. However, their applications are limited in simulating highly turbulent flow with separations due to the inviscid flow assumptions, such as those associated with train aerodynamics. Some researchers employed the wake models to simulate large vortices in the wake of trains with predetermined separation locations according to experimental results. In this paper, a modified 2-D constant source/vortex panel method for modelling the separated flow around 2-D bluff bodies is presented. The proposed separated-flow model includes the prediction of separation locations based on the integral boundary-layer method and the shear layer, and large vortices in the wake of the bluff bodies are modelled by the wake model. The proposed method is validated by comparing the calculated pressure distribution on a 2-D circular cylinder with the experimental results. The method is then applied to simulate the flow around a 2-D generic train and calculate the pressure distribution on the train. Since trains run very close to the ground, the effect of the ground configuration on the pressure distribution of the 2-D train is also investigated in this paper using the proposed method. The main contribution of the work is to present a 2-D separated-flow model with wake modelling and separation prediction. The proposed model can be used in the rapid evaluation of bluff-body aerodynamics.
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Siripunvaraporn, Weerachai, and Gary Egbert. "An efficient data‐subspace inversion method for 2-D magnetotelluric data." GEOPHYSICS 65, no. 3 (May 2000): 791–803. http://dx.doi.org/10.1190/1.1444778.
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There are currently three types of algorithms in use for regularized 2-D inversion of magnetotelluric (MT) data. All seek to minimize some functional which penalizes data misfit and model structure. With the most straight‐forward approach (exemplified by OCCAM), the minimization is accomplished using some variant on a linearized Gauss‐Newton approach. A second approach is to use a descent method [e.g., nonlinear conjugate gradients (NLCG)] to avoid the expense of constructing large matrices (e.g., the sensitivity matrix). Finally, approximate methods [e.g., rapid relaxation inversion (RRI)] have been developed which use cheaply computed approximations to the sensitivity matrix to search for a minimum of the penalty functional. Approximate approaches can be very fast, but in practice often fail to converge without significant expert user intervention. On the other hand, the more straightforward methods can be prohibitively expensive to use for even moderate‐size data sets. Here, we present a new and much more efficient variant on the OCCAM scheme. By expressing the solution as a linear combination of rows of the sensitivity matrix smoothed by the model covariance (the “representers”), we transform the linearized inverse problem from the M-dimensional model space to the N-dimensional data space. This method is referred to as DASOCC, the data space OCCAM’s inversion. Since generally N ≪ M, this transformation by itself can result in significant computational saving. More importantly the data space formulation suggests a simple approximate method for constructing the inverse solution. Since MT data are smooth and “redundant,” a subset of the representers is typically sufficient to form the model without significant loss of detail. Computations required for constructing sensitivities and the size of matrices to be inverted can be significantly reduced by this approximation. We refer to this inversion as REBOCC, the reduced basis OCCAM’s inversion. Numerical experiments on synthetic and real data sets with REBOCC, DASOCC, NLCG, RRI, and OCCAM show that REBOCC is faster than both DASOCC and NLCG, which are comparable in speed. All of these methods are significantly faster than OCCAM, but are not competitive with RRI. However, even with a simple synthetic data set, we could not always get RRI to converge to a reasonable solution. The basic idea behind REBOCC should be more broadly applicable, in particular to 3-D MT inversion.
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Thierry, Philippe, Stéphane Operto, and Gilles Lambaré. "Fast 2-D ray+Born migration/inversion in complex media." GEOPHYSICS 64, no. 1 (January 1999): 162–81. http://dx.doi.org/10.1190/1.1444513.
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In this paper, we evaluate the capacity of a fast 2-D ray+Born migration/inversion algorithm to recover the true amplitude of the model parameters in 2-D complex media. The method is based on a quasi‐Newtonian linearized inversion of the scattered wavefield. Asymptotic Green’s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method. The model is described by velocity perturbations associated with diffractor points. Both the first traveltime and the strongest arrivals can be inverted. The algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm. Both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2-D Marmousi example. Comparison between logs extracted from the exact Marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations are recovered accurately in the regions of the model where the ray field is single valued. In the presence of caustics, neither the first traveltime nor the most energetic arrival inversion allow for a full recovery of the amplitudes although the latter improves the results. We conclude that all the arrivals associated with multipathing through transmission caustics must be taken into account if the true amplitude of the perturbations is to be found. Only 22 minutes of CPU time is required to migrate the full 2-D Marmousi data set on a Sun SPARC 20 workstation. The amplitude loss induced by the numerical approximations on the first traveltime and the most energetic migrated images are evaluated quantitatively and do not exceed 8% of the energy of the image computed without numerical approximation. Computational evaluation shows that extension to a 3-D ray+Born migration/inversion algorithm is realistic.
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Ferrari, Alessia, Marco D'Oria, Renato Vacondio, Alessandro Dal Palù, Paolo Mignosa, and Maria Giovanna Tanda. "Discharge hydrograph estimation at upstream-ungauged sections by coupling a Bayesian methodology and a 2-D GPU shallow water model." Hydrology and Earth System Sciences 22, no. 10 (October 16, 2018): 5299–316. http://dx.doi.org/10.5194/hess-22-5299-2018.
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Abstract. This paper presents a novel methodology for estimating the unknown discharge hydrograph at the entrance of a river reach when no information is available. The methodology couples an optimization procedure based on the Bayesian geostatistical approach (BGA) with a forward self-developed 2-D hydraulic model. In order to accurately describe the flow propagation in real rivers characterized by large floodable areas, the forward model solves the 2-D shallow water equations (SWEs) by means of a finite volume explicit shock-capturing algorithm. The two-dimensional SWE code exploits the computational power of graphics processing units (GPUs), achieving a ratio of physical to computational time of up to 1000. With the aim of enhancing the computational efficiency of the inverse estimation, the Bayesian technique is parallelized, developing a procedure based on the Secure Shell (SSH) protocol that allows one to take advantage of remote high-performance computing clusters (including those available on the Cloud) equipped with GPUs. The capability of the methodology is assessed by estimating irregular and synthetic inflow hydrographs in real river reaches, also taking into account the presence of downstream corrupted observations. Finally, the procedure is applied to reconstruct a real flood wave in a river reach located in northern Italy.
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CAIAFA, C. F., and A. N. PROTO. "TEMPERATURE ESTIMATION IN THE TWO-DIMENSIONAL ISING MODEL." International Journal of Modern Physics C 17, no. 01 (January 2006): 29–38. http://dx.doi.org/10.1142/s0129183106008856.
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We present two new algorithms for the estimation of the temperature from a realization of a 2-D Ising model. The methods here introduced are based in the maximization of pseudo likelihood and on the minimum mean squared error (MSE) fit of the conditional probability function. We derive the analytical expressions of these estimators and also we include computational results comparing these new techniques with the traditional method. A very good performance in terms of the average absolute error and the average standard deviation is demonstrated through simulations in a 100 × 100 lattice in the ferromagnetic and antiferromagnetic cases. Summarizing, we have provided two new useful computational tools that allow us to measure the "virtual" temperature of an Ising like system.
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Iuchi, Satoru, and Nobuaki Koga. "A model electronic Hamiltonian to describe low‐lying d–d and metal‐to‐ligand charge‐transfer excited states of [Fe(bpy) 3 ] 2+." Journal of Computational Chemistry 42, no. 3 (November 4, 2020): 166–79. http://dx.doi.org/10.1002/jcc.26444.
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Jiang, Wei, Jiancheng Xu, Li Kunpeng, Ye Ouyang, and Jinzhou Yan. "Coupling Heat Conduction and Radiation by an Isogeometric Boundary Element Method in 2-D Structures." Mathematical Problems in Engineering 2022 (September 7, 2022): 1–14. http://dx.doi.org/10.1155/2022/4209720.
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We propose an efficient isogeometric boundary element method to address the coupling of heat conduction and radiation in homogeneous or inhomogeneous materials. The isogeometric boundary element method is used to construct irregular 2D models, which eliminate errors in model construction. The physical unknowns in the governing equations for heat conduction and radiation are discretized using an interpolation approximation, and the integral equations are finally solved by Newton–Raphson iteration; it is noteworthy that we use the radial integration method to convert the domain integrals to boundary integrals, and we combine the numerical schemes for heat conduction and radiation. The results of the three numerical cases show that the adopted algorithm can improve the computational accuracy and efficiency.
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Li, Shengfeng, and Yi Dong. "Parametric Estimation in the Vasicek-Type Model Driven by Sub-Fractional Brownian Motion." Algorithms 11, no. 12 (December 4, 2018): 197. http://dx.doi.org/10.3390/a11120197.
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In the paper, we tackle the least squares estimators of the Vasicek-type model driven by sub-fractional Brownian motion: d X t = ( μ + θ X t ) d t + d S t H , t ≥ 0 with X 0 = 0 , where S H is a sub-fractional Brownian motion whose Hurst index H is greater than 1 2 , and μ ∈ R , θ ∈ R + are two unknown parameters. Based on the so-called continuous observations, we suggest the least square estimators of μ and θ and discuss the consistency and asymptotic distributions of the two estimators.