Computational tools MATLAB

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

There are numerous other examples of two-box models. For instance, a two-box epilimnion/hypolimnion model was discussed in Chapter 21, and additional examples are given as problems at the end of this chapter. We must remember that as long as these models are linear, their solutions can be constructed with the help of Box 21.6. They always consist of the sum of not more than two exponential functions and are thus fairly simple. This situation changes drastically if we allow the differential equations to become nonlinear. A system of two or more nonlinear differential equations rarely can be solved analytically, yet the available computer tools (such as MATLAB) make their solution easy. 

For large-scale problems, the most widely useful mathematical tool available is computational/numerical simulation. A great number of computer tools are available for simulation of ordinary differential equation (ODE) based models, such as Equations (3.27). Here we demonstrate how this system may be simulated using the ubiquitous Matlab software package. 

The DODS software package can be used to complete most of the examples and tutorials in this book. The package has been written in Matlab, but has been complied such that it may be used on a computer without Matlab installation. It is also useful as an independent design tool and, as shown in the examples in the book, the results obtained can be used as initialization to rigorous simulation packages such as Aspen Plus . The DODS package consists of five independent packages ... 

In Part Three of this book, we will introduce Microsoft Excel and MATLAB, two computational tools that are used commonly by engineers to solve engineering problems. These computational tools are used to record, organize, analyze data using formulas, and present the results of an analysis in chart forms. MATLAB is also versatile enough that you can use it to write your own program to solve complex problems. 

We have given up the pretense that we can cover controller design and still have time to do all the plots manually. We rely on MATLAB to construct the plots. For example, we take a unique approach to root locus plots. We do not ignore it like some texts do, but we also do not go into the hand sketching details. The same can be said with frequency response analysis. On the whole, we use root locus and Bode plots as computational and pedagogical tools in ways that can help to understand the choice of different controller designs. Exercises that may help such thinking are in the MATLAB tutorials and homework problems. 

With the advent of modern software tools, however, tools such as MATLAB and even the older language, APL, matrix operations can be coded directly from the matrix-math expressions, and then it becomes near-trivial to create and solve the matrix equations on-the-fly, so to speak, and calculate the coefficients for any derivative using any desired polynomial, and computed over any odd number of data points. 

There are several computer software packages that are quite helpful in applying some of the computationally intensive methods. The PC-MATLAB System Identification Toolbox (The Math Works, Inc., Sherborn, Mass.) is an easy-to-use, powerful software package that provides an array of alternative tools,... 

Overall, most of the requirements for a process spectrometer/analyzer are straightforward to implement, but they do require attention at the design level. Another important area, which is FTIR specific, is the user interface and the need to provide for industry standard data communications. Standard software packages do exist for process instrumentation. For prototype development, and even for the front-end interface in a stand-alone mode of operation, software products, such as National Instraments Lab View and the Mathworks MatLab, are also important instrumentation development tools. Note that National Instruments also provides important computer-based electronics and hardware that meet most of the computer interfacing, and system control and communications needs for modem instrumentation. For practical installations, a product known... 

With these five equations (Eqs. 23-42 to 23-46), two of them partial differential equations, the limits of the analytical approach and the goals of this book are clearly exceeded. However, at this point we take the occasion to look at how such equations are solved numerically. User-friendly computer programs, such as MAS AS (Modeling of Anthropogenic Substances in Aquatic Systems, Ulrich et al., 1995) or AQUASIM (Reichert, 1994), or just a general mathematical tool like MATLAB and MATHE-MATICA, can be used to solve these equations for arbitrary constant or variable parameters and boundary conditions. 

Root locus plots are easy to generate for first- and second-order systems since the roots can be found analytically as explicit functions of controller gain. For higher-order systems things become more difficult. Both numerical and graphical methods are available. Root-solving subroutines can be easily used on any computer to do the job. The easiest way is to utilize some user-friendly software tools. We illustrate the use of MATLAB for making root locus plots. 

They can be expressed either as functions of frequency, called frequency domain specifications, or as functions of time, called time domain specifications. To develop the specifications the mathematical equations have to be solved. Modern computer software, such as MATLAB (e.g., Kuo 1995), has provided convenient tools for solving the equations. 

EasySpin The tools for isotropic CW-ESR in EasySpin apply to 5 = V2 species with arbitrary number of nuclei. Resonance fields are calculated exactly (no perturbation formulae). The magnetic field range is automatically determined. A least-squares fitting to an experimental spectrum can be made. The program can be downloaded at http //www.easyspin.org/. MatLab must be installed on the computer and is not provided with EasySpin. EasySpin is written and maintained by Dr. S. Stoll at the University of California, Davis. 

As mentioned in Chapter 2 overlap of lines can make analysis difficult when several nuclei contribute in the one-dimensional (ID) ESEEM spectra. The HYSCORE method is at present the most commonly used two-dimensional (2D) ESEEM technique to simplify the analysis. Contour maps obtained after 2D Eourier transformation of the echo decay signal followed by projection on the frequency plane are mainly employed for visual or computer analysis to obtain the anisotropic hyperfine couplings. Software for the data processing to obtain the contour is often provided with commercial instruments. Tools for ID and 2D Eourier transforms are also available in commercial software like Matlab. 

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