Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.

Stability of the Iteration Method for non Expansive Mappings

The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.

Reversibility Iteration Method to Understand Reaction Networks and to Solve Micro-Kinetics in Heterogeneous Catalysis

Solving microkinetics of catalytic systems, which bridges microscopic processes and macroscopic reaction rates, is currently vital for understanding catalysis in silico. However, traditional microkinetic solvers possess several drawbacks that make the process slow and unreliable for complicated catalytic systems. In this paper, a new approach, the so-called reversibility iteration method (RIM), is developed to solve microkinetics for catalytic systems. Using the chemical potential notation we previously proposed to simplify the kinetic framework, the catalytic systems can be analytically illustrated to be logically equivalent to the electric circuit, and the reaction rate and coverage can be calculated by updating the values of reversibilities. Compared to the traditional modified Newton iteration method (NIM), our method is not sensitive to the initial guess of the solution and typically requires fewer iteration steps. Moreover, the method does not require arbitrary-precision arithmetic and has a higher probability of successfully solving the system. These features make it ∼1000 times faster than the modified Newton iteration method for the systems we tested. Moreover, the derived concept and the mathematical framework presented in this work may provide new insight into catalytic reaction networks.

An effortless hybrid method to solve economic load dispatch problem in power systems

This paper proposes a new approach and coding scheme for solving economic dispatch problems (ED) in power systems through an effortless hybrid method (EHM). This novel coding scheme can effectively prevent futile searching and also prevents obtaining infeasible solutions through the application of stochastic search methods, consequently dramatically improves search efficiency and solution quality. The dominant constraint of an economic dispatch problem is power balance. The operational constraints, such as generation limitations, ramp rate limits, prohibited operating zones (POZ), network loss are considered for practical operation. Firstly, in the EHM procedure, the output of generator is obtained with a lambda iteration method and without considering POZ and later in a genetic based algorithm this constraint is satisfied. To demonstrate its efficiency, feasibility and fastness, the EHM algorithm was applied to solve constrained ED problems of power systems with 6 and 15 units. The simulation results obtained from the EHM were compared to those achieved from previous literature in terms of solution quality and computational efficiency. Results reveal that the superiority of this method in both aspects of financial and CPU time. (C) 2011 Elsevier Ltd. All rights reserved.

Coletores de distribuição e sua otimização hidráulica, aplicados a uma instalação de produção de água arrefecida em sistemas de AVAC ( Fórum Picoas)

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

SSPBE: um programa para solução numérica da equação de Poisson-Boltzmann em simetria esférica com modelo de adsorção

A Fortran77 program, SSPBE, designed to solve the spherically symmetric Poisson-Boltzmann equation using cell model for ionic macromolecular aggregates or macroions is presented. The program includes an adsorption model for ions at the aggregate surface. The working algorithm solves the Poisson-Boltzmann equation in the integral representation using the Picard iteration method. Input parameters are introduced via an ASCII file, sspbe.txt. Output files yield the radial distances versus mean field potentials and average molar ion concentrations, the molar concentration of ions at the cell boundary, the self-consistent degree of ion adsorption from the surface and other related data. Ion binding to ionic, zwitterionic and reverse micelles are presented as representative examples of the applications of the SSPBE program.

TitGer: uma planilha eletrônica para simulação de titulação de mistura de compostos polipróticos

The aim of this paper is to present a simple way of treating the general equation for acid-base titrations based on the concept of degree of dissociation, and to propose a new spreadsheet approach for simulating the titration of mixtures of polyprotic compounds. The general expression, without any approximation, is calculated a simple iteration method, making number manipulation easy and painless. The user-friendly spreadsheet was developed by using MS-Excel and Visual-Basic-for-Excel. Several graphs are drawn for helping visualizing the titration behavior. A Monte Carlo function for error simulation was also implemented. Two examples for titration of alkalinity and McIlvaine buffer are presented.

Power semiconductor nonlinearities in active du/dt output filtering

This doctoral thesis introduces an improved control principle for active du/dt output filtering in variable-speed AC drives, together with performance comparisons with previous filtering methods. The effects of power semiconductor nonlinearities on the output filtering performance are investigated. The nonlinearities include the timing deviation and the voltage pulse waveform distortion in the variable-speed AC drive output bridge. Active du/dt output filtering (ADUDT) is a method to mitigate motor overvoltages in variable-speed AC drives with long motor cables. It is a quite recent addition to the du/dt reduction methods available. This thesis improves on the existing control method for the filter, and concentrates on the lowvoltage (below 1 kV AC) two-level voltage-source inverter implementation of the method. The ADUDT uses narrow voltage pulses having a duration in the order of a microsecond from an IGBT (insulated gate bipolar transistor) inverter to control the output voltage of a tuned LC filter circuit. The filter output voltage has thus increased slope transition times at the rising and falling edges, with an opportunity of no overshoot. The effect of the longer slope transition times is a reduction in the du/dt of the voltage fed to the motor cable. Lower du/dt values result in a reduction in the overvoltage effects on the motor terminals. Compared with traditional output filtering methods to accomplish this task, the active du/dt filtering provides lower inductance values and a smaller physical size of the filter itself. The filter circuit weight can also be reduced. However, the power semiconductor nonlinearities skew the filter control pulse pattern, resulting in control deviation. This deviation introduces unwanted overshoot and resonance in the filter. The controlmethod proposed in this thesis is able to directly compensate for the dead time-induced zero-current clamping (ZCC) effect in the pulse pattern. It gives more flexibility to the pattern structure, which could help in the timing deviation compensation design. Previous studies have shown that when a motor load current flows in the filter circuit and the inverter, the phase leg blanking times distort the voltage pulse sequence fed to the filter input. These blanking times are caused by excessively large dead time values between the IGBT control pulses. Moreover, the various switching timing distortions, present in realworld electronics when operating with a microsecond timescale, bring additional skew to the control. Left uncompensated, this results in distortion of the filter input voltage and a filter self-induced overvoltage in the form of an overshoot. This overshoot adds to the voltage appearing at the motor terminals, thus increasing the transient voltage amplitude at the motor. This doctoral thesis investigates the magnitude of such timing deviation effects. If the motor load current is left uncompensated in the control, the filter output voltage can overshoot up to double the input voltage amplitude. IGBT nonlinearities were observed to cause a smaller overshoot, in the order of 30%. This thesis introduces an improved ADUDT control method that is able to compensate for phase leg blanking times, giving flexibility to the pulse pattern structure and dead times. The control method is still sensitive to timing deviations, and their effect is investigated. A simple approach of using a fixed delay compensation value was tried in the test setup measurements. The ADUDT method with the new control algorithm was found to work in an actual motor drive application. Judging by the simulation results, with the delay compensation, the method should ultimately enable an output voltage performance and a du/dt reduction that are free from residual overshoot effects. The proposed control algorithm is not strictly required for successful ADUDT operation: It is possible to precalculate the pulse patterns by iteration and then for instance store them into a look-up table inside the control electronics. Rather, the newly developed control method is a mathematical tool for solving the ADUDT control pulses. It does not contain the timing deviation compensation (from the logic-level command to the phase leg output voltage), and as such is not able to remove the timing deviation effects that cause error and overshoot in the filter. When the timing deviation compensation has to be tuned-in in the control pattern, the precalculated iteration method could prove simpler and equally good (or even better) compared with the mathematical solution with a separate timing compensation module. One of the key findings in this thesis is the conclusion that the correctness of the pulse pattern structure, in the sense of ZCC and predicted pulse timings, cannot be separated from the timing deviations. The usefulness of the correctly calculated pattern is reduced by the voltage edge timing errors. The doctoral thesis provides an introductory background chapter on variable-speed AC drives and the problem of motor overvoltages and takes a look at traditional solutions for overvoltage mitigation. Previous results related to the active du/dt filtering are discussed. The basic operation principle and design of the filter have been studied previously. The effect of load current in the filter and the basic idea of compensation have been presented in the past. However, there was no direct way of including the dead time in the control (except for solving the pulse pattern manually by iteration), and the magnitude of nonlinearity effects had not been investigated. The enhanced control principle with the dead time handling capability and a case study of the test setup timing deviations are the main contributions of this doctoral thesis. The simulation and experimental setup results show that the proposed control method can be used in an actual drive. Loss measurements and a comparison of active du/dt output filtering with traditional output filtering methods are also presented in the work. Two different ADUDT filter designs are included, with ferrite core and air core inductors. Other filters included in the tests were a passive du/dtfilter and a passive sine filter. The loss measurements incorporated a silicon carbide diode-equipped IGBT module, and the results show lower losses with these new device technologies. The new control principle was measured in a 43 A load current motor drive system and was able to bring the filter output peak voltage from 980 V (the previous control principle) down to 680 V in a 540 V average DC link voltage variable-speed drive. A 200 m motor cable was used, and the filter losses for the active du/dt methods were 111W–126 W versus 184 W for the passive du/dt. In terms of inverter and filter losses, the active du/dt filtering method had a 1.82-fold increase in losses compared with an all-passive traditional du/dt output filter. The filter mass with the active du/dt method was 17% (2.4 kg, air-core inductors) compared with 14 kg of the passive du/dt method filter. Silicon carbide freewheeling diodes were found to reduce the inverter losses in the active du/dt filtering by 18% compared with the same IGBT module with silicon diodes. For a 200 m cable length, the average peak voltage at the motor terminals was 1050 V with no filter, 960 V for the all-passive du/dt filter, and 700 V for the active du/dt filtering applying the new control principle.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

In this thesis, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the Explicitly-Restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of Boiling Water Reactors. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

Physical properties of sediment cores of the Bengal Fan

We examined geophysical data from a Multi-Sensor Core Logger (MSCL), a logging device providing continuous measurements of gamma-ray attenuation, p-wave travel time, and magnetic susceptibility on marine sediment cores. In the first part we focused on the gamma-ray system and compared two different calibration methods. From the gamma-ray attenuation, we calculated densities and porosities by incorporating mass weighted attenuation coefficients. The application of an iteration method reduces the error of the density and porosity estimates compared to GRAPE data. In addition, we derived equations to calculate water content and dry bulk density from gamma-ray attenuation measurements. Comparison with physical properties determined on discrete samples revealed a very good correlation of both data sets (r = 0.99). This correlation is valid for sediments from substantially different geological settings (e.g., turbidites, hemipelagic muds, and opal-rich sediments). In the second part we applied our data to marine geological questions. For sediments from the Antarctic Polar Frontal Zone, there is indication that the content of biogenic opal can be assessed using a correlation of density and p-wave velocity. For sediments from the Bengal Fan, the relationship between the MSCL acoustic impedance (the product of density and p-wave velocity) and the grain-size distribution in discrete samples can be used to predict clay and sand/silt ratios for sediment cores from the shelf and upper continental slope.

Single diode model parameters analysis of photovoltaic cell

In this paper it is proposed to obtain enhanced and more efficient parameters model from generalized five parameters (single diode) model of PV cells. The paper also introduces, describes and implements a seven parameter model for photovoltaic cell (PV cell) which includes two internal parameters and five external parameters. To obtain the model the mathematical equations and an equivalent circuit consisting of a photo generated current source, a series resistor, a shunt resistor and a diode is used. The fundamental equation of PV cell is used to analyse and best fit the observation data. Especially bisection iteration method is used to obtain the expected result and to understand the deviation of changes in different parameters situation at various conditions respectively. The produced model can be used of measuring and understanding the actions of photovoltaic cells for certain changes and parameters extraction. The effect is also studied with I-V and P-V characteristics of PV cells though it is a challenge to optimize the output with real time simulation. The working procedure is also discussed and an experiment presented to get the closure and insight about the produced model and to decide upon the model validity. At the end, we observed that the result of the simulation is very close to the produced model.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.