Step 1 Define the Problem

1 Reactions For this particular example, the system involves a parallel decomposition involving three components A, B, and C, in three reactions (two of the reactions are independent). 

In Equation 5.7a, component A decomposes to form component B. If B is present, then components A and B may combine, in an autocatalytic reaction, to form additional B by Equation 5.7b. Component A may also decompose in a parallel reaction to form C via Equation 5.7c. For this example, we shall assume that component B is the desired product and seek to determine the optimal reactor structure that maximizes the concentration of B, Cg. 

2 Kinetics and State Space The rate expression for this system is assumed to be a complex rate function involving the concentrations of components A and B only, which are given by 

Here K, a a2, and a3 are constants given by K = 40, ai =0.001 s , a2=10s , and a3 = 0.1s . Since the system may be expressed entirely in terms of the concentrations of components A and B alone, it is sensible to construct the AR in c -Cg space. Once the AR for the system has been determined, the concentration of component C, c, is easily determined by mass balance if desired. It follows that the concentration vector and rate vector for the system should be defined in the following way  

3 Feed and Equilibrium Points The feed stream is assumed to be pure in component A so that Cf = [1, 0] mol/L. It is good practice to locate any equilibrium points for the kinetics provided, if possible. This will assist with AR construction later on and will also provide insight into areas of the construction space (Ca-Cb space) where unexpected behavior might occur. Determination of the equilibrium points is performed by setting the component rate expressions to zero and then solving for the set of concentrations that satisfy the system of equations, hence 

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To summarize the steps, step 1 defined the problem you wished to solve, step 2 checked your programming, and step 3 instructed MATLAB to solve the problem. It is tempting to skip the second step - checking your programming - but remember If the programming is wrong, you will solve the wrong problem. 

Now amphfy step 1 (defining the problem) with more detail on replications, criteria, and schedule. 

The concept stage has four steps (1) define the problem, (2) brainstorm, (3) research and generate ideas, and (4) identify criteria and specify constraints. 

The basic steps that are taken to solve an analytical problem can be described using the scientific problem-solving approach shown in Figure 2.1. The first step in defining the problem is gaining an understanding of the context of the... 

Return now to the first part of the two-step procedure for characterizing an adsorption column. Our model represented by Equations 1, 2, 3, 4, and 5 shows that the following space and point rate coefficients define the problem ... 

The importance of modeling batch processing systems forces a review of the mathematical analysis needed to set up and solve the models. The mathematical definition of physical problems involves (1) identification, (2) expression of the problem in mathematical language, (3) finding a solution, and (4) evaluating the solution. The completion of these steps in the order established determines whether a solution can be attained. The problem must be identified before one spends time setting up equations these and the initial and boundary conditions that define the problem must be well established before a solution is attempted then a solution can be obtained and evaluated. 

However, such problem solving requires a carefully structured process to ensure that root causes are identified and proposed solutions are verified. Juran s project-by-project quality improvement process provides detailed guidelines that have been widely adopted and integrated into current team problem-solving methodology. The methodology outlines distinct steps for (1) carefully defining the problem,... 

Step 1 Insert the parameters for the viscosity under the Options/Constants and the equation for viscosity, using those parameters, in Options/Expressions/Subdomain Expressions. Then the shear rate is defined in terms of the parameters of the problem. Here the variables are u in the radial direction and v in the axial direction. Making the appropriate conversions to Eq. (10.7) gives Eq. (10.9), which you type as a subdomain expression. 

Defining a Problem Statement The first step in successfully implementing an automation project is to clearly define the problem that needs to be solved. Automation can solve a number of different problems. Each laboratory must ask itself which specific problems it wants to solve. The best place to start is in thinking about the needs of the laboratory. Is there a need to analyze more samples with fewer people or to shorten sample turnaround time Is there a need to increase the consistency of an assay or process Is there a need to reduce exposure to hazardous materials or to minimize operator fatigue or repetitive motion injuries Is there a need to reduce the cost per sample Is there a need for a process to run overnight or over the weekend ... 

The first major step toward managing any search system in so large a potential search space is the reduction of bulky molecular information to numbers. The numerical convention must retain the significant information, consolidate trivial distinctions such as minor functionality variants, and also serve to define the problem and its options sharply. This is the intent of Section 2. The tree, however, will still be very large and we must look further for criteria to apply... 

As mentioned in Chapter 1, the analytical process benefits when the analyst can be involved in defining the problem, that is, in making sure the proper questions are posed. When data requirements are poorly conceived or unrealistic, analytical measurements can be unnecessarily expensive if the method selected is more accurate than needed. Or, it may be inadequate if the method is less accurate than required, or of questionable value if the accuracy of the method is unknown. The first step in method development and validation is setting minimum requirements, which essentially are the specifications of the method for the intended purpose. How accurate and precise does it have to be W at is the target concentration ... 

Thus, in essence, eqs. 1.253 are surface analogs to the corresponding Maxwell s equations given in difTerential form in eq. 1.252. Therefore, starting from the system of differential equations (eq. 1.252) the problem of defining the field consists of the following steps ... 

System dynamics steps to solve the problem (Wu J.Z. et al. 1985) is (1) to identify the problem how the coal mine safety input influence factors of coal mine production, which in turn affect coal mine safety performance (2) to determine the system boundary safety production system in coal mine (3) to determine causal graph and define the variable draw causal graph of coal mine safety production system and define the model variable (4) to establish equations, models and analyze the simulation model. 

In step 1 you want to define the problem Make sure that you clearly understand all the words. Draw the system and label its parts. List all the known variables and constraints. Describe what you are asked to do. If you cannot define the problem clearly, you will probably be unable to solve it. 

The steps involved in the problem solving protocol are outlined in Table 7.1. They are rather simple and do not take much time to consider and such a protocol can save time in the long run. The protocol involves steps typical of scientific inquiry collect all the currently known facts, determine the nature of the problem, state the objective of the study, obtain the correct specimen, be sure to have experimental controls, look at the sample with the naked eye and then with a stereo microscope. These provide an aid to selection of the specific microscopy techniques and preparation methods needed to begin to address the objectives. The result should be that clearly defined analyses are conducted. 

As was said in the introduction (Section 2.1), chemical structures are the universal and the most natural language of chemists, but not for computers. Computers woi k with bits packed into words or bytes, and they perceive neither atoms noi bonds. On the other hand, human beings do not cope with bits very well. Instead of thinking in terms of 0 and 1, chemists try to build models of the world of molecules. The models ai e conceptually quite simple 2D plots of molecular sti uctures or projections of 3D structures onto a plane. The problem is how to transfer these models to computers and how to make computers understand them. This communication must somehow be handled by widely understood input and output processes. The chemists way of thinking about structures must be translated into computers internal, machine representation through one or more intermediate steps or representations (sec figure 2-23, The input/output processes defined... 

Step 1 Problem Formulation - here, the CAMD problem is defined in terms of target properties (both the identity of the property as well as their target values). 

Defining the risk assessment problem to be evaluated should precede entering the four-step process set out in Figure 7.1, Chapter 7. This means identifying the population that is to be the subject of the assessment, and specifying the conditions under which it is or may come to be exposed to a chemical or mixture of chemicals. Formulations of the problem might be similar to any of the five examples offered at the beginning of Chapter 7. 

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