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## Nonlinear Equations (nonlinear + equation)
## Selected Abstracts## Concentration dependency of biota-sediment accumulation factors for chlorinated dibenzo- p -dioxins and dibenzofurans in dungeness crab (Cancer magister) at marine pulp mill sites in British Columbia, Canada ENVIRONMENTAL TOXICOLOGY & CHEMISTRY, Issue 12 2000Walter J. CretneyAbstract Biota-sediment accumulation factors (BSAFs) for some chlorinated dibenzo- p -dioxin and dibenzofuran congeners (PCDD/Fs) in Dungeness crab (Cancer magister) hepatopancreas and associated sediments are concentration independent as required by equilibrium partition models. In particular 2, 3, 7, 8-tetrachlorodibenzo- p -dioxin (2, 3, 7, 8-TCDD), 2, 3, 7, 8-tetrachlorodibenzofuran, the 2, 3, 7, 8-substituted pentachlorodibenzofurans, and the non-2, 3, 7, 8-hexachlorodibenzofurans (HxCDFs) seem to fall into this group. The BSAFs for other isomers exhibit significant, nonlinear variations with sediment or crab PCDD/F concentrations. For some of these other isomers (e.g., the non-2, 3, 7, 8 TCDDs and possibility the 2, 3, 7, 8-substituted HxCDFs), association of a variable fraction of the total present with soot carbon may provide a satisfactory explanation for the concentration behavior. For the HxCDDs we propose that the nonlinear concentration behavior may arise from the thermodynamic properties of fluids confined in hydrophobic voids within particulate and colloidal material produced by the pulp mills. The nonlinear relationship between BSAFs and PCDD/F concentrations greatly complicates prediction of the potential for dioxin and furan bioaccumulation in crabs and the formulation of sediment quality criteria. We provide a nonlinear equation relating toxic equivalency and sediment concentrations. [source] ## Robustness improvement of a nonlinear H, controller for robot manipulators via saturation functions JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 8 2005Manuel G. OrtegaIn this paper, previous works on nonlinear H, control for robot manipulators are extended. In particular, integral terms are considered to cope with persistent disturbances, such as constant load at the end-effector. The extended controller may be understood as a computed-torque control with an external PID, whose gain matrices vary with the position and velocity of the robot joints. In addition, in order to increase the controller robustness, an extension of the algorithms with saturation functions has been carried out. This extension deals with the resulting nonlinear equation of the closed-loop error. A modified expression for the required increment in the control signal is provided, and the local closed-loop stability of this approach is discussed. Finally, simulation results for a two-link robot and experimental results for an industrial robot are presented. The results obtained with this technique have been compared with those attained with the original controllers to show the improvements achieved by means of the proposed method. © 2005 Wiley Periodicals, Inc. [source] ## Microbial Inactivation Kinetics during High-Pressure Carbon Dioxide Treatment: Nonlinear Model for the Combined Effect of Temperature and Pressure in Apple Juice JOURNAL OF FOOD SCIENCE, Issue 8 2008G. FerrentinoABSTRACT:, Isobaric and isothermal semi-logarithmic survival curves of natural microflora in apple juice treated with high-pressure carbon dioxide at 7, 13, and 16 MPa pressures and 35, 50, and 60 °C temperatures were fitted with a nonlinear equation to find the values of the coefficient b(P ), b(T ), n(P ), and n(T ). Profiles of the model parameters were obtained as a function of pressure and temperature. The model fitted with good agreement (R2 > 0.945), the survival curves. An empirical equation was proposed to describe the combined effects of pressure and temperature. The equation, derived from a power law model, was written in the form: . The proposed model fitted the experimental data well. At 7 MPa and 50 and 60 °C, 13 MPa and 35 and 60 °C, 16 MPa and 35 °C, the model provided log10 reduction residual values (observed value , fitted value) lower than 0.284 showing a good agreement between the experimental and the predicted survival levels. [source] ## Three transmission-line transformers for phase retrieval from scalar reflection coefficients MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 3 2004Ahmed M. AttiyaAbstract In this paper, a new approach to obtain the phase angle of an unknown complex load using scalar reflection coefficients is presented. This approach is based on measuring the scalar reflection coefficient using three different transmission-line transformers. The relation between the two scalar reflection coefficients is presented as a nonlinear equation of the unknown phase angle. The value of the unknown phase angle represents a common root of these nonlinear phase equations. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 231,235, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11338 [source] ## Manifestly covariant classical correlation dynamics I. General theory ANNALEN DER PHYSIK, Issue 10-11 2009C. TianAbstract In this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Based on the action-at-a-distance formalism we obtain a single-time Liouville equation. This equation describes the manifestly covariant evolution of the distribution function of full classical many-body systems. For such global evolution the Bogoliubov functional assumption is justified. In particular, using the Balescu-Wallenborn projection operator approach we find that the distribution function of full many-body systems is completely determined by the reduced one-body distribution function. A manifestly covariant closed nonlinear equation satisfied by the reduced one-body distribution function is rigorously derived. We also discuss extensively the generalization to general relativity especially an application to self-gravitating systems. [source] ## Manifestly covariant classical correlation dynamics I. General theory ANNALEN DER PHYSIK, Issue 10-11 2009C. TianAbstract In this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Based on the action-at-a-distance formalism we obtain a single-time Liouville equation. This equation describes the manifestly covariant evolution of the distribution function of full classical many-body systems. For such global evolution the Bogoliubov functional assumption is justified. In particular, using the Balescu-Wallenborn projection operator approach we find that the distribution function of full many-body systems is completely determined by the reduced one-body distribution function. A manifestly covariant closed nonlinear equation satisfied by the reduced one-body distribution function is rigorously derived. We also discuss extensively the generalization to general relativity especially an application to self-gravitating systems. [source] ## Multidimensional second order systems with controls, ASIAN JOURNAL OF CONTROL, Issue 2 2010D. BorsAbstract In the paper, a nonlinear equation with decreasing mass is considered. Sufficient conditions for the existence of solutions on the interval [t1, t2] are proved. Moreover, theorem on the stability of system and the existence of optimal control are presented. The proofs of the main results are based on variational method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] ## Kinematic transformations for planar multi-directional pseudodynamic testing EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2009Oya MercanAbstract The pseudodynamic (PSD) test method imposes command displacements to a test structure for a given time step. The measured restoring forces and displaced position achieved in the test structure are then used to integrate the equations of motion to determine the command displacements for the next time step. Multi-directional displacements of the test structure can introduce error in the measured restoring forces and displaced position. The subsequently determined command displacements will not be correct unless the effects of the multi-directional displacements are considered. This paper presents two approaches for correcting kinematic errors in planar multi-directional PSD testing, where the test structure is loaded through a rigid loading block. The first approach, referred to as the incremental kinematic transformation method, employs linear displacement transformations within each time step. The second method, referred to as the total kinematic transformation method, is based on accurate nonlinear displacement transformations. Using three displacement sensors and the trigonometric law of cosines, this second method enables the simultaneous nonlinear equations that express the motion of the loading block to be solved without using iteration. The formulation and example applications for each method are given. Results from numerical simulations and laboratory experiments show that the total transformation method maintains accuracy, while the incremental transformation method may accumulate error if the incremental rotation of the loading block is not small over the time step. A procedure for estimating the incremental error in the incremental kinematic transformation method is presented as a means to predict and possibly control the error. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Equivalent force control method for generalized real-time substructure testing with implicit integration EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2007Bin WuAbstract This paper presents a new method, called the equivalent force control method, for solving the nonlinear equations of motion in a real-time substructure test using an implicit time integration algorithm. The method replaces the numerical iteration in implicit integration with a force-feedback control loop, while displacement control is retained to control the motion of an actuator. The method is formulated in such a way that it represents a unified approach that also encompasses the effective force test method. The accuracy and effectiveness of the method have been demonstrated with numerical simulations of real-time substructure tests with physical substructures represented by spring and damper elements, respectively. The method has also been validated with actual tests in which a Magnetorheological damper was used as the physical substructure. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Formal and Informal Risk Sharing in LDCs: Theory and Empirical Evidence ECONOMETRICA, Issue 4 2008Pierre DuboisWe develop and estimate a model of dynamic interactions in which commitment is limited and contracts are incomplete to explain the patterns of income and consumption growth in village economies of less developed countries. Households can insure each other through both formal contracts and informal agreements, that is, self-enforcing agreements specifying voluntary transfers. This theoretical setting nests the case of complete markets and the case where only informal agreements are available. We derive a system of nonlinear equations for income and consumption growth. A key prediction of our model is that both variables are affected by lagged consumption as a consequence of the interplay of formal and informal contracting possibilities. In a semiparametric setting, we prove identification, derive testable restrictions, and estimate the model with the use of data from Pakistani villages. Empirical results are consistent with the economic arguments. Incentive constraints due to self-enforcement bind with positive probability and formal contracts are used to reduce this probability. [source] ## A perturbation analysis of harmonic generation from saturated elements in power systems ELECTRICAL ENGINEERING IN JAPAN, Issue 4 2010Teruhisa KumanoAbstract Nonlinear phenomena such as saturation of magnetic flux have considerable effects in power systems analysis. It is reported that a failure in a real 500-kV system triggered islanding operation, where resultant even harmonics caused malfunctions in protective relays. It is also reported that the major origin of this wave distortion is nothing but unidirectional magnetization of the transformer iron core. Time simulation is widely used today to analyze phenomena of this type, but it has basically two shortcomings. One is that the time simulation takes too much computing time in the vicinity of inflection points in the saturation characteristic curve because certain iterative procedures such as N-R (Newton,Raphson) must be used and such methods tend to be caught in an ill-conditioned numerical hunting. The other is that such simulation methods sometimes do not aid an intuitive understanding of the studied phenomenon because all of the nonlinear equations are treated in matrix form and are not properly divided into understandable parts, as is done in linear systems. This paper proposes a new computation scheme that is based on the so-called perturbation method. Magnetic saturation of iron cores in a generator and a transformer are taken into account. The proposed method has a special feature to deal with the first shortcoming of the N-R-based time simulation method stated above. The proposed method does not use an iterative process to reduce the equation residue, but uses perturbation series, so that it is free of the ill-conditioning problem. The user need only calculate the perturbation terms one by one until the necessary accuracy is attained. In a numerical example treated in the present paper, first-order perturbation can achieve reasonably high accuracy, which means very fast computing time. In a numerical study, three nonlinear elements are considered. The calculation results are almost identical to the conventional N-R-based time simulation, which shows the validity of the method. The proposed method can be effectively used in screening where many case studies are needed. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 170(4): 35,42, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20895 [source] ## Fast multipole boundary element analysis of two-dimensional elastoplastic problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007P. B. WangAbstract This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix,vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Analysis of velocity equation of steady flow of a viscous incompressible fluid in channel with porous walls INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010M. BabaelahiAbstract Steady flow of a viscous incompressible fluid in a channel, driven by suction or injection of the fluid through the channel walls, is investigated. The velocity equation of this problem is reduced to nonlinear ordinary differential equation with two boundary conditions by appropriate transformation and convert the two-point boundary-value problem for the similarity function into an initial-value problem in which the position of the upper channel. Then obtained differential equation is solved analytically using differential transformation method and compare with He's variational iteration method and numerical solution. These methods can be easily extended to other linear and nonlinear equations and so can be found widely applicable in engineering and sciences. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A comparative study of GLS finite elements with velocity and pressure equally interpolated for solving incompressible viscous flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2009Yongtao WeiAbstract A comparative study of the bi-linear and bi-quadratic quadrilateral elements and the quadratic triangular element for solving incompressible viscous flows is presented. These elements make use of the stabilized finite element formulation of the Galerkin/least-squares method to simulate the flows, with the pressure and velocity fields interpolated with equal orders. The tangent matrices are explicitly derived and the Newton,Raphson algorithm is employed to solve the resulting nonlinear equations. The numerical solutions of the classical lid-driven cavity flow problem are obtained for Reynolds numbers between 1000 and 20 000 and the accuracy and converging rate of the different elements are compared. The influence on the numerical solution of the least square of incompressible condition is also studied. The numerical example shows that the quadratic triangular element exhibits a better compromise between accuracy and converging rate than the other two elements. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Time-linearized time-harmonic 3-D Navier,Stokes shock-capturing schemes INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2008J.-C. ChassaingAbstract In the present paper, a numerical method for the computation of time-harmonic flows, using the time-linearized compressible Reynolds-averaged Navier,Stokes equations is developed and validated. The method is based on the linearization of the discretized nonlinear equations. The convective fluxes are discretized using an O(,x) MUSCL scheme with van Leer flux-vector-splitting. Unsteady perturbations of the turbulent stresses are linearized using a frozen-turbulence-Reynolds-number hypothesis, to approximate eddy-viscosity perturbations. The resulting linear system is solved using a pseudo-time-marching implicit ADI-AF (alternating-directions-implicit approximate-factorization) procedure with local pseudo-time-steps, corresponding to a matrix-successive-underrelaxation procedure. The stability issues associated with the pseudo-time-marching solution of the time-linearized Navier,Stokes equations are discussed. Comparison of computations with measurements and with time-nonlinear computations for 3-D shock-wave oscillation in a square duct, for various back-pressure fluctuation frequencies (180, 80, 20 and 10,Hz), assesses the shock-capturing capability of the time-linearized scheme. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Phptotophysics and kinetics of naphthopyran derivatives, part 4: Investigation of [3H]-naphthopyran kinetics considered as an ABC(2k, 6,) system yielding a monoexponential trace INTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 7 2006M. MaafiThe elucidation of [3H]-naphthopyran photochromic kinetics has been dealt with in this investigation by approximating the photocoloring traces as monoexponential. The experimental data have been analyzed, and 13 defining equations of the reactive dynamics have been established. These have been solved simultaneously as a system of nonlinear equations depending on the extinction coefficients and the six possible quantum yields of this ABC type system. The results of this new approach predict that both colored species are directly photochemically produced from the starting material. The most photochemically reactive photoisomer is the most thermally stable and is also the one characterized by the lowest extinction coefficient of the visible absorption band. The mechanism predicted for 3,3-diphenyl-3H -naphtho[2,1- b]pyran in toluene at 30°C obeys ABC(1k,6,) kinetics. © 2006 Wiley Periodicals, Inc. J Chem Kinet 38: 431,438, 2006 [source] ## An application of dynamic positioning control using wave feed forward INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2001A. B. AalbersAbstract The paper presents the results of model tests for a large tanker in which wave drift force feed forward was applied in the dynamic positioning control system. The estimation method of the nonlinear (second order) wave drift forces from the measurement of relative water motions at the side of a ship hull is presented. The estimated wave drift forces are used in the DP control system, to enhance the filter process of the extended Kalman filter, and in the required thruster set-points. The EKF uses the nonlinear equations of low-frequency ship motions on the horizontal plane, which are also presented. The results of the model tests show that the use of wave drift force feed forward significantly improves the positioning accuracy in sea states with 3.5 m significant wave height or higher. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Biodegradation kinetics of benzene, methyl tert -butyl ether, and toluene as a substrate under various substrate concentrations JOURNAL OF CHEMICAL TECHNOLOGY & BIOTECHNOLOGY, Issue 1 2007Chi-Wen LinAbstract Owing to the complexity of conventional methods and shortcomings in determining kinetic parameters, a convenient approach using the nonlinear regression analysis of Monod or Haldane type nonlinear equations is presented. This method has been proven to provide accurate estimates of kinetic parameters. The major work in this study consisted of the testing of aromatic compound-degrading cultures in batch experiments for the biodegradation of benzene, methyl tert -butyl ether (MTBE), and toluene. Additionally, batch growth data of three pure cultures (i.e., Pseudomonas aeruginosa YAMT421, Ralstonia sp. YABE411 and Pseudomonas sp. YATO411) isolated from an industrial petrochemical wastewater treatment plant under aerobic conditions were assessed with the nonlinear regression technique and with a trial-and-error procedure to determine the kinetic parameters. The growth rates of MTBE-, benzene-, and toluene-degrading cultures on MTBE, benzene, and toluene were significant. Monod's model was a good fit for MTBE, benzene and toluene at low substrate concentrations. In contrast, Haldane's equation fitted well in substrate inhibition concentration. Monod and Haldane's expressions were found to describe the results of these experiments well, with fitting values higher than 98%. The kinetic parameters, including a maximum specific growth rate (µm), a half-saturation constant (Ks), and an inhibition constant (Ki), were given. Copyright © 2007 Society of Chemical Industry [source] ## Globally convergent computation of chemical equilibrium composition JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 7 2008Sunil PatilAbstract We report the Newton,Raphson based globally convergent computational method for determination of chemical equilibrium composition. In the computation of chemical equilibrium composition, an appearance of nonpositive value of number of moles of any component leads to discrepancy. The process of conditional backtracking and adaptive set of refining factors for Newton,Raphson steps are employed to resolve the problem. The mathematical formulation proposed by Heuze et al. (J Chem Phys 1985, 83, 4734) has been solved using proposed computational method, instead of empirical iterative formulation, as proposed by them. Results for the same numerical example, used by Heuze et al. (J Chem Phys 1985, 83, 4734) and White et al. (J Chem Phys 1958, 28, 751) are presented in addition to decomposition of Cyclotrimethylenetrinitramine for fixed temperature and pressure. It is observed that the proposed method is efficient and globally convergent. An even noteworthy finding is that the set of refining factors can be chosen from the range 0.1 to ,, where , may be greater than one depending on how smoothly system of nonlinear equations is dependant on corresponding variable. Related analysis and results are discussed. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] ## Computation of an extractive distillation column with affine arithmetic AICHE JOURNAL, Issue 7 2009Ali BaharevAbstract The need of reliably solving systems of nonlinear equations often arises in the everyday practice of chemical engineering. In general, standard methods cannot provide theoretical guarantee for convergence to a solution, cannot reliably find multiple solutions, and cannot prove nonexistence of solutions. Interval methods provide tools to overcome these problems, thus achieving reliability. To the authors' best knowledge, computation of distillation columns with interval methods have not yet been considered in the literature. This article presents significant enhancements compared with a previously published interval method of the authors. The proposed branch-and-prune algorithm is guaranteed to converge, and is fairly general at the same time. If no solution exists then this information is provided by the method as a result. Power of the suggested method is demonstrated by solving, with guaranteed convergence, even the MESH equations of a 22 stage extractive distillation column with a ternary mixture. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] ## Draw ratio enhancement in nonisothermal melt spinning AICHE JOURNAL, Issue 3 2009Balram SumanAbstract Nonisothermal melt spinning of materials having a step-like viscosity variation with temperature is studied in this work. A set of nonlinear equations is used to describe the fiber behavior and to obtain the draw ratio, the square of the ratio of the fiber diameter at the entrance to that at the exit of the fiber-spinning device. The fluid-flow equation is based on a slender-jet approximation, and external heating and cooling have been accounted for with a one-dimensional model in order to obtain the fiber temperature and viscosity along the fiber length. The model is similar to that used by Wylie et al. (J Fluid Mech. 2007;570:1,16) but accounts for inertia, shear stress at the fiber surface, surface tension, gravity, cooling, and larger heating rates. Steady-state analysis reveals that the draw ratio increases with an increase in the pulling force, passes through a maximum, and then starts increasing again, resulting in three possible pulling forces for the same draw ratio. However, linear stability analysis reveals that depending on the strength of heating and/or cooling, at most two of the steady states are stable. The stability analysis also predicts complicated oscillatory and nonoscillatory dynamical behavior as the pulling force varies. Nonlinear simulations reveal that an unstable system always tends to limit-cycle behavior. Systems predicted as stable by the linear stability analysis are also stable for large-amplitude perturbations. External heating is found to dramatically enhance the draw ratio of the melt-spinning process. The addition of a cooling section suppresses the draw ratio, but this can be compensated for with a higher heating strength. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] ## Systematic estimation of state noise statistics for extended Kalman filters AICHE JOURNAL, Issue 2 2000Jaleel ValappilThe successful application of model-based control depends on the information about the states of the dynamic system. State-estimation methods, like extended Kalman filters (EKF), are useful for obtaining reliable estimates of the states from a limited number of measurements. They also can handle the model uncertainties and the effect of unmeasured disturbances. The main issue in applying EKF remains that one needs to specify the confidence in the model in terms of process noise covariance matrix. The information about the model uncertainties can effectively and systematically calculate the process noise covariance matrix for an EKF. Two systematic approaches are used for this calculation. The first is based on a Taylor series expansion of the nonlinear equations around the nominal parameter values, while the second accounts for the nonlinear dependence of the system on the fitted parameters by Monte Carlo simulations that can easily be performed on-line. The value of the process noise covariance matrix obtained is not limited to a diagonal form and depends on the current state of the dynamic system. Thus the a-priori information regarding the uncertainty in the model is utilized and the need for extensive tuning of the EKF is eliminated. The application of these techniques to example processes is also discussed. The accuracy of this methodology is compared very favorably with the traditional methods of trial-and-error tuning of EKF. [source] ## Non-perturbative solution of three-dimensional Navier,Stokes equations for the flow near an infinite rotating disk MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2010Ahmet YAbstract In this paper, we present Homotopy perturbation method (HPM) and Padé technique, for finding non-perturbative solution of three-dimensional viscous flow near an infinite rotating disk. We compared our solution with the numerical solution (fourth-order Runge,Kutta). The results show that the HPM,Padé technique is an appropriate method in solving the systems of nonlinear equations. The mathematical technique employed in this paper is significant in studying some other problems of engineering. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2009M. EfendievAbstract We consider the following doubly nonlinear parabolic equation in a bounded domain ,,,3: where the nonlinearity f is allowed to have a degeneracy with respect to ,tu of the form ,tu|,tu|p at some points x,,. Under some natural assumptions on the nonlinearities f and g, we prove the existence and uniqueness of a solution of that problem and establish the finite-dimensionality of global and exponential attractors of the semigroup associated with this equation in the appropriate phase space. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Ishikawa iterative process with errors for nonlinear equations of generalized monotone type in Banach spaces MATHEMATISCHE NACHRICHTEN, Issue 10 2005Ljubomir B.Abstract The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D , X , 2D be a multi-valued operator of generalized monotone type with fixed points. A new general lemma on the convergence of real sequences is proved and used to show that {xn} converges strongly to a unique fixed point of T in D. This result is applied to the iterative approximation method for solutions of nonlinear equations with generalized strongly accretive operators. Our results generalize many of know results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Two classes of multisecant methods for nonlinear acceleration NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 3 2009Haw-ren FangAbstract Many applications in science and engineering lead to models that require solving large-scale fixed point problems, or equivalently, systems of nonlinear equations. Several successful techniques for handling such problems are based on quasi-Newton methods that implicitly update the approximate Jacobian or inverse Jacobian to satisfy a certain secant condition. We present two classes of multisecant methods which allow to take into account a variable number of secant equations at each iteration. The first is the Broyden-like class, of which Broyden's family is a subclass, and Anderson mixing is a particular member. The second class is that of the nonlinear Eirola,Nevanlinna-type methods. This work was motivated by a problem in electronic structure calculations, whereby a fixed point iteration, known as the self-consistent field (SCF) iteration, is accelerated by various strategies termed ,mixing'. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Homotopy perturbation method for numerical solutions of KdV-Burgers' and Lax's seventh-order KdV equations NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2010Ahmet YildirimAbstract In this article, we applied homotopy perturbation method to obtain the solution of the Korteweg-de Vries Burgers (for short, KdVB) and Lax's seventh-order KdV (for short, LsKdV) equations. The numerical results show that homotopy perturbation method can be readily implemented to this type of nonlinear equations and excellent accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] ## Numerical solution of the free-surface viscous flow on a horizontal rotating elliptical cylinder NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2008Roland HuntAbstract The numerical solution of the free-surface fluid flow on a rotating elliptical cylinder is presented. Up to the present, research has concentrated on the circular cylinder for which steady solutions are the main interest. However, for noncircular cylinders, such as the ellipse, steady solutions are no longer possible, but there will be periodic solutions in which the solution is repeated after one full revolution of the cylinder. It is this new aspect that makes the investigation of noncircular cylinders novel. Here we consider both the time-dependent and periodic solutions for zero Reynolds number fluid flow. The numerical solution is expedited by first mapping the fluid film domain onto a rectangle such that the position of the free-surface is determined as part of the solution. For the time-dependent case a simple time-marching method of lines approach is adopted. For the periodic solution the discretised nonlinear equations have to be solved simultaneously over a time period. The resulting large system of equations is solved using Newton's method in which the form of the Jacobian enables a straightforward decomposition to be implemented, which makes matrix inversion manageable. In the periodic case all derivatives have been approximated pseudospectrally with the time derivative approximated by a differentiation matrix which has been specially derived so that the weight of fluid is algebraically conserved. Of interest is the solution for which the weight of fluid is at its maximum possible value, and this has been obtained by increasing the weight until a consistency break-down occurs. Time-dependent solutions do not produce the periodic solution after a long time-scale but have protuberances which are constantly appearing and disappearing. Periodic solutions exhibit spectral accuracy solutions and maximum supportable weight solutions have been obtained for ranges of eccentricity and angular velocity. The maximum weights are less than and approximately proportional to those obtained for the circular case. The shapes of maximum weight solutions is distinctly different from sub-maximum weight solutions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] ## Photoluminescence and in-plane diffusion of indirect excitons PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 11 2005L. E. SmallwoodAbstract In-plane spatial diffusion of indirect excitons in GaAs/AlGaAs coupled quantum wells (QWs) is studied theoretically. In spatial photoluminescence (PL) diagrams obtained from experiments, two rings of PL appear around the excitation spot, and their size and intensity depend upon the lattice temperature Tb and the optical pump intensity. We explain and model numerically the first PL ring, by using coupled nonlinear equations for the diffusion, thermalization and optical decay of the excitons. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Verbund-Simulation , Strategic Planning and Optimization of Integrated Production Networks CHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 4 2010T. ViereAbstract Strategic analysis and optimization of highly integrated production networks is an essential requirement for cost-effective and resource-efficient production. This paper presents a comprehensive software-based concept for modeling, simulation, optimization, and visualization of an integrated silicone production network of Wacker Chemie AG. A Verbund-Model was implemented in a step-by-step approach, starting with primary material streams in one business unit up to the modeling of all energy, waste, and cost streams in several business units. The system's flexibility enables different levels of detail for modeling processes and parts of the network: from simple input-output relations to complex, nonlinear equations and specifications. The proactive implementation of technical measures and projects based on the assessment of future scenarios is an important outcome of the Verbund-simulation. [source] |