Nonlinear Iterative Method Research Articles

Nonlinear analysis on constraint forces and space configuration of flexible pipe

The nonlinear iteration method of compelling displacement of boundary support was presented, combined with the nonlinear element method of space beam and Newton-Raphson nonlinear iteration, which can succeed flexibly in finding equilibrium configuration under complicated external loads. The relationship between space configuration of flexible pipe, constraint forces and active load by mining machine was studied. The result shows that the computing method is important to engineering.

Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration

Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first self-consistent-field (SCF) iteration. The method may be viewed as an approach to solve the original nonlinear Kohn-Sham equation by a nonlinear subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problems. It reaches self-consistency within a similar number of SCF iterations as eigensolver-based approaches. However, replacing the standard diagonalization at each SCF iteration by a Chebyshev subspace filtering step results in a significant speedup over methods based on standard diagonalization. Here, we discuss an approach for implementing this method in multi-processor, parallel environment. Numerical results are presented to show that the method enables to perform a class of highly challenging DFT calculations that were not feasible before.

Corrected Uzawa methods for solving large nonsymmetric saddle point problems

In this paper we consider the solution of linear systems of large nonsymmetric saddle point problems by two nonlinear iterative methods, which are similar in some respects to the Uzawa-type methods and are called corrected Uzawa methods. Their convergence rates are analyzed. The results of numerical experiments are presented when we apply them to Navier–Stokes equations discretized by mixed finite elements.

Identification of Proteomic Signatures of Exposure to Marine Pollutants in Mussels (Mytilus edulis)

Bivalves and especially mussels are very good indicators of marine and estuarine pollution, and so they have been widely used in biomonitoring programs all around the world. However, traditional single parameter biomarkers face the problem of high sensitivity to biotic and abiotic factors. In our study, digestive gland peroxisome-enriched fractions of Mytilus edulis (L., 1758) were analyzed by DIGE and MS. We identified several proteomic signatures associated with the exposure to several marine pollutants (diallyl phthalate, PBDE-47, and bisphenol-A). Animals collected from North Atlantic Sea were exposed to the contaminants independently under controlled laboratory conditions. One hundred and eleven spots showed a significant increase or decrease in protein abundance in the two-dimensional electrophoresis maps from the groups exposed to pollutants. We obtained a unique protein expression signature of exposure to each of those chemical compounds. Moreover a set of proteins composed a proteomic signature in common to the three independent exposures. It is remarkable that the principal component analysis of these spots showed a discernible separation between groups, and so did the hierarchical clustering into four classes. The 14 proteins identified by MS participate in alpha- and beta-oxidation pathways, xenobiotic and amino acid metabolism, cell signaling, oxyradical metabolism, peroxisomal assembly, respiration, and the cytoskeleton. Our results suggest that proteomic signatures could become a valuable tool to monitor the presence of pollutants in field experiments where a mixture of pollutants is often present. Further studies on the identified proteins could provide crucial information to understand possible mechanisms of toxicity of single xenobiotics or mixtures of them in marine ecosystems.

Self-calibration from turn-table sequences in presence of zoom and focus

This paper proposes a novel method, using constant inter-frame motion, for self-calibration from an image sequence of an object rotating around a single axis with varying camera internal parameters. Our approach makes use of the facts that in many commercial systems rotation angles are often controlled by an electromechanical system, and that the inter-frame essential matrices are invariant if the rotation angles are constant but not necessary known. Therefore, recovering camera internal parameters is possible by making use of the equivalence of essential matrices which relate the unknown calibration matrices to the fundamental matrices computed from the point correspondences. We also describe a linear method that works under restrictive conditions on camera internal parameters, the solution of which can be used as the starting point of the iterative non-linear method with looser constraints. The results are refined by enforcing the global constraints that the projected trajectory of any 3D point should be a conic after compensating for the focusing and zooming effects. Finally, using the bundle adjustment method tailored to the special case, i.e., static camera and constant object rotation, the 3D structure of the object is recovered and the camera parameters are further refined simultaneously. To determine the accuracy and the robustness of the proposed algorithm, we present the results on both synthetic and real sequences.

Nonlinear iterative methods for linear ill-posed problems in Banach spaces

We introduce and discuss nonlinear iterative methods to recover the minimum-norm solution of the operator equation Ax = y in Banach spaces X, Y, where A is a continuous linear operator from X to Y. The methods are nonlinear due to the use of duality mappings which reflect the geometrical aspects of the underlying spaces. The space X is required to be smooth and uniformly convex, whereas Y can be an arbitrary Banach space. The case of exact as well as approximate and disturbed data and operator are taken into consideration and we prove the strong convergence of the sequence of the iterates.

A Nonlinear Iterative Method for Retrieving Land Surface Temperature by Using MODIS Data

Land surface temperature(LST) is an important parameter in meteorology,hydrology,ecology and so on.This paper has proposed a nonlinear iterative method for retrieving land surface temperature(LST) from MODIS data which needs two parameters(land surface emissivity and atmosphere transmittance).At first,two radiance transfer equations for MODIS band 31 and 32 had been built,which involves two unknowns(land surface temperature and average atmosphere temperature).Because of complexity,a numerical algorithm has been developed to solve the equations using iterative approach.Then,the estimation of the two essential parameters of the nonlinear iterative method has been extensively discussed.The atmospheric transmittance can be estimated on the basis of the relationship between atmospheric transmittance and water content which can be retrieved from the visible and infrared bans of MODIS data.As MODIS image has the lower resolution,the pixels of MODIS for most natural surfaces can be viewed as composed of three land cover patterns: vegetation,bare soil and water.The composition ration of vegetation and bare soil can be estimated from NDVI,and the land surface emissivity of MODIS31 and MODIS32 can be estimated by using the land surface thermal radiation equations of composed pixel and the known emissivity of land cover patterns.Finally,the sensitivity of parameters is analyzed and the results indicate that the parameters are not sensitive to the LST retrieval method we have proposed.The retrieved LST in Jiangsu province indicated the space difference,urban heat island effect and different ground object types.

Error estimation in multicanonical Monte Carlo Simulations with applications to polarization-mode-dispersion emulators

This paper shows how to estimate errors in multicanonical Monte Carlo (MMC) simulations using a transition-matrix method. MMC is a biasing Monte Carlo technique that allows one to compute the probability of rare events, such as the outage probability in optical-fiber communication systems. Since MMC is a Monte Carlo technique, it is subject to statistical errors, and it is essential to determine their magnitude. Since MMC is a highly nonlinear iterative method, linearized error-propagation techniques and standard error analyses do not work, and a more sophisticated method is needed. The proposed method is based on bootstrap techniques. This method was applied to efficiently estimate the error in the probability density function (pdf) of the differential group delay (DGD) of polarization-mode-dispersion (PMD) emulators that has been calculated using MMC. The method was validated by comparison to the results obtained using a large ensemble of MMC simulations.

An iterative method for single and vertically stacked semiconductor quantum dots simulation

We present in this paper a computational effective nonlinear iterative method for calculating the electron energy spectra in single and vertically stacked InAs/GaAs semiconductor quantum dots. The physical model problem is formulated with the effective one electronic band Hamiltonian, the energy- and position-dependent electron effective mass approximation, and the Ben Daniel-Duke boundary conditions. The multishift QR algorithm is implemented in the nonlinear iterative method for solving the corresponding nonlinear eigenvalue problem. This method converges monotonically when solving the nonlinear Schrödinger equation for all quantum dot simulations. Numerical results show that the electron energy spectra are significantly dependent on the number of coupled layers. For the excited states, the layer dependence effect has been found to be weaker than that for the ground state.

Solutions of the full- and quasi-vector wave equations based on H-field for optical waveguides by using mapped Galerkin method

The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x–y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method.

Magnetization and Magnetic Susceptibility in Nanoscale Vertically Coupled Semiconductor Quantum Rings

In this paper we computationally examine the magnetization and the magnetic susceptibility for vertically coupled quantum rings (VCQRs) under applied magnetic fields. The theoretical model of VCQRs considers a three-dimensional (3D) effective one-electronic-band Hamiltonian with the position- and energy-dependent effective mass, the finite hard-wall confinement potential, and the Ben Daniel-Duke boundary condition. The nonlinear iterative method is applied to solve the problem in the structure of VCQRs. For the structure formed with nanoscale disk-shaped InAs/GaAs quantum rings, the the tunable states of structure as well as the electron transition energy is dominated by the radius of ring (R) and the inter-distance (d) between quantum rings. The electron energy oscillates non-periodically among the lowest electron states as a function of external magnetic fields due to the penetration of magnetic fields into the inter-regions of VCQRs. The magnetization of VCQRs at zero temperature is non-periodical oscillation and the period of jump is governed by R. Therefore, the differential susceptibility of VCQRs has delta-like paramagnetic peaks. When d is increased, the peak is decreased which is contrary to conventional mesoscopic arguments. Our investigation is constructive for studying the magneto-optical phenomena of the nanoscale semiconductor artificial molecules.

Transition Energies of Vertically Coupled Multilayer Nanoscale InAs/GaAs Semiconductor Quantum Dots of Different Shapes

The energy spectra of vertically coupled multilayer nanoscale semiconductor quantum dots (QDs) are theoretically studied using a unified three-dimensional (3D) model. The model formulation includes (1) the position-dependent effective mass Hamiltonian in a nonparabolic approximation for electrons, (2) the position-dependent effective mass Hamiltonian in a parabolic approximation for holes, (3) the finite hard wall confinement potential, and (4) Ben Daniel-Duke boundary conditions. To solve a nonlinear problem, a nonlinear iterative method is further improved in our developed 3D QD simulator. At an applied magnetic field (B), we explore the transition energy and the energy band gap of disk (DI)-, ellipsoid (EL)- and cone (CO)-shaped vertically coupled multilayer nanoscale semiconductor quantum dots. We find that the electron transition energy of vertically coupled multilayer InAs/GaAs QDs depends on their shape and is strongly dominated by the number of stacked layers (N). The interdistance (d) among InAs QDs plays a crucial role in the tunable states of these QDs. In DI-shaped vertically coupled 10-layer QDs at B=0 T and d=1.0 nm, we find approximately 40% variation in electron ground state energy, which is larger than that (∼20% variation) in CO-shaped QDs. In QDs at a nonzero magnetic field, the electron transition energy decreases with increasing N. In QDs with d=1 nm, the rate of decrease is low when N>6. This results in QDs with energy band gaps having similar dependences on N. This study implies different applications in magnetooptical phenomena and quantum optical structures.

05/00876 Entropy generation due to non-Newtonian flow around a spherical particle at low Reynolds number

In this paper, performances of spatial homogenization methods for fuel or non-fuel cells are compared in slab geometry in order to facilitate pin-by-pin core calculations. Since the spatial homogenization methods were mainly developed for fuel assemblies, systematic study of their performance for the cell-level homogenization has not been carried out. Importance of cell-level homogenization is recently increasing since the pin-by-pin mesh core calculation in actual three-dimensional geometry, which is less approximate approach than current advanced nodal method, is getting feasible. Four homogenization methods were investigated in this paper; the flux-volume weighting, the generalized equivalence theory, the superhomogenization (SPH) method and the nonlinear iteration method. The last one, the nonlinear iteration method, was tested as the homogenization method for the first time. The calculations were carried out in simplified colorset assembly configurations of PWR, which are simulated by slab geometries, and homogenization performances were evaluated through comparison with the reference cell-heterogeneous calculations. The calculation results revealed that the generalized equivalence theory showed best performance. Though the nonlinear iteration method can significantly reduce homogenization error, its performance was not as good as that of the generalized equivalence theory. Through comparison of the results obtained by the generalized equivalence theory and the superhomogenization method, important byproduct was obtained; deficiency of the current superhomogenization method, which could be improved by incorporating the “cell-level discontinuity factor between assemblies”, was clarified.

A comparison between one‐way and two‐way wave‐equation migration

Results for wave‐equation migration in the frequency domain using the constant‐density acoustic two‐way wave equation have been compared to images obtained by its one‐way approximation. The two‐way approach produces more accurate reflector amplitudes and provides superior imaging of steep flanks. However, migration with the two‐way wave equation is sensitive to diving waves, leading to low‐frequency artifacts in the images. These can be removed by surgical muting of the input data or iterative migration or high‐pass spatial filtering. The last is the most effective.Iterative migration based on a least‐squares approximation of the seismic data can improve the amplitudes and resolution of the imaged reflectors. Two approaches are considered, one based on the linearized constant‐density acoustic wave equation and one on the full acoustic wave equation with variable density. The first converges quickly. However, with our choice of migration weights and high‐pass spatial filtering for the linearized case, a real‐data migration result shows little improvement after the first iteration. The second, nonlinear iterative migration method is considerably more difficult to apply. A real‐data example shows only marginal improvement over the linearized case.In two dimensions, the computational cost of the two‐way approach has the same order of magnitude as that for the one‐way method. With our implementation, the two‐way method requires about twice the computer time needed for one‐way wave‐equation migration.

Adaptive control through optimized trajectory tracking

New methods are proposed in the paper to design adaptive control for discrete time lumped parameter systems. Model reference adaptive control is treated as adaptive tracking control on infinite horizon. The self-tuning and gain scheduling adaptive control problem is regarded as iterative parameter optimization problem in the closed and open loop, respectively. Finite horizon optimum adaptive control is solved through a sequence of two-stage optimizations and iteration. For nonlinear parameter estimation iterative solution and linear model based solution, for nonlinear observation and state estimation iterative method is shown. The presentation is made for general nonlinear systems with time varying parameters.

Vertical coupling effects and transition energies in multilayer InAs/GaAs quantum dots

Abstract We investigate the transition energy of vertically stacked semiconductor quantum dots with a complete three-dimensional (3D) model in an external magnetic field. In this study, the model formulation includes: (1) the position-dependent effective mass Hamiltonian in non-parabolic approximation for electrons, (2) the position-dependent effective mass Hamiltonian in parabolic approximation for holes, (3) the finite hard-wall confinement potential, and (4) the Ben Daniel–Duke boundary conditions. To solve the nonlinear problem, a nonlinear iterative method is implemented in our 3D nanostructure simulator. For multilayer small InAs/GaAs quantum dots, we find that the electron–hole transition energy is dominated by the number of stacked layers. The inter-distance d plays a crucial role in the tunable states of the quantum dots. Under zero magnetic field for a 10-layer QDs structure with d =1.0 nm, there is about 30% variation in the electron ground state energy. Dependence of the magnetic field on the electron–hole transition energy is weakened when the number of stacked layers is increased. Our investigation is constructive in studying the magneto-optical phenomena and quantum optical structures.

Cell homogenization methods for pin-by-pin core calculations tested in slab geometry

In this paper, performances of spatial homogenization methods for fuel or non-fuel cells are compared in slab geometry in order to facilitate pin-by-pin core calculations. Since the spatial homogenization methods were mainly developed for fuel assemblies, systematic study of their performance for the cell-level homogenization has not been carried out. Importance of cell-level homogenization is recently increasing since the pin-by-pin mesh core calculation in actual three-dimensional geometry, which is less approximate approach than current advanced nodal method, is getting feasible. Four homogenization methods were investigated in this paper; the flux-volume weighting, the generalized equivalence theory, the superhomogenization (SPH) method and the nonlinear iteration method. The last one, the nonlinear iteration method, was tested as the homogenization method for the first time. The calculations were carried out in simplified colorset assembly configurations of PWR, which are simulated by slab geometries, and homogenization performances were evaluated through comparison with the reference cell-heterogeneous calculations. The calculation results revealed that the generalized equivalence theory showed best performance. Though the nonlinear iteration method can significantly reduce homogenization error, its performance was not as good as that of the generalized equivalence theory. Through comparison of the results obtained by the generalized equivalence theory and the superhomogenization method, important byproduct was obtained; deficiency of the current superhomogenization method, which could be improved by incorporating the “cell-level discontinuity factor between assemblies”, was clarified.

Lax–Friedrichs sweeping scheme for static Hamilton–Jacobi equations

We propose a simple, fast sweeping method based on the Lax–Friedrichs monotone numerical Hamiltonian to approximate viscosity solutions of arbitrary static Hamilton–Jacobi equations in any number of spatial dimensions. By using the Lax–Friedrichs numerical Hamiltonian, we can easily obtain the solution at a specific grid point in terms of its neighbors, so that a Gauss–Seidel type nonlinear iterative method can be utilized. Furthermore, by incorporating a group-wise causality principle into the Gauss–Seidel iteration by following a finite group of characteristics, we have an easy-to-implement, sweeping-type, and fast convergent numerical method. However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation. We give a simple recipe which enforces a version of discrete min–max principle. Some convergence analysis is done for the one-dimensional eikonal equation. Extensive 2-D and 3-D numerical examples illustrate the efficiency and accuracy of the new approach. To our knowledge, this is the first fast numerical method based on discretizing the Hamilton–Jacobi equation directly without assuming convexity and/or homogeneity of the Hamiltonian.

NUMERICAL CALCULATION OF ELECTRON ENERGY STATES FOR NANOSCOPIC InAs/GaAs QUANTUM RINGS

In this paper we study the electron energy states for nanoscopic semiconductor quantum rings. The effective one-band Hamiltonian approximation and the Ben Daniel–Duke boundary conditions are simultaneously considered in our three-dimensional (3D) model. The rectangular and ellipsoidal torus-shaped rings have been investigated with the 3D model. The proposed model is numerically solved with nonlinear iterative method. This computational method calculates the solution without any fitting parameters and is robust for all simulation cases. For InAs/GaAs quantum rings, it is found that (1) there is a significant energy difference between the 2D and 3D models; (2) the electron energy state depends strongly on the ring shape and size; and (3) the dependency of the energy state on an external magnetic field is different from conventional 1D/2D periodical result. We find the electron energy state nonperiodically oscillates versus the applied magnetic field which is in agreement with the experimental observation.

Mean value iterations for nonlinear elliptic Cauchy problems

We investigate the Cauchy problem for a class of nonlinear elliptic operators with $C^\infty$-coefficients at a regular set $\Omega \subset R^n$. The Cauchy data are given at a manifold $\Gamma \subset \partial\Omega$ and our goal is to reconstruct the trace of the $H^1(\Omega)$ solution of a nonlinear elliptic equation at $\partial \Omega / \Gamma$. We propose two iterative methods based on the segmenting Mann iteration applied to fixed point equations, which are closely related to the original problem. The first approach consists in obtaining a corresponding linear Cauchy problem and analyzing a linear fixed point equation; a convergence proof is given and convergence rates are obtained. On the second approach a nonlinear fixed point equation is considered and a fully nonlinear iterative method is investigated; some preliminary convergence results are proven and a numerical analysis is provided.