Tutorial Example Research Articles

SLOW INVARIANT MANIFOLDS AS CURVATURE OF THE FLOW OF DYNAMICAL SYSTEMS

Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e. the curvature of the trajectory curves of any n-dimensional dynamical system directly provides its slow manifold analytical equation the invariance of which will be then proved according to Darboux theory. Thus, it will be stated that the flow curvature method, which uses neither eigenvectors nor asymptotic expansions but only involves time derivatives of the velocity vector field, constitutes a general method simplifying and improving the slow invariant manifold analytical equation determination of high-dimensional dynamical systems. Moreover, it will be shown that this method generalizes the Tangent Linear System Approximation and encompasses the so-called Geometric Singular Perturbation Theory. Then, slow invariant manifolds analytical equation of paradigmatic Chua's piecewise linear and cubic models of dimensions three, four and five will be provided as tutorial examples exemplifying this method as well as those of high-dimensional dynamical systems.

Coupled Quantum–Atomistic and Quantum–Continuum Mechanics Methods in Materials Research

AbstractThe interface of quantum mechanics methods with classical atomistic simulation techniques, such as molecular dynamics and Monte Carlo, continues to be an area of considerable promise and interest. Such coupled quantum–atomistic approaches have been developed and employed, for example, to gain a comprehensive understanding of the energetics, kinetics, and dynamics of chemical processes involving surfaces and interfaces of hard materials. More recently, it has become possible to directly couple first-principles electronic structure techniques to continuum solid mechanics, either on the fly with feedback between length scales or by information passing between length scales. We discuss, with tutorial examples, the merging of quantum mechanics with molecular dynamics and Monte Carlo simulations, as well as quantum–continuum coupled techniques. We illustrate the opportunities offered by incorporation of information from quantum mechanics (reducing assumptions in higher length-scale models) and outline the challenges associated with achieving full predictive capability for the behavior of materials.

Bond graph for dynamic modelling in chemical engineering

The bond graph representation is an energy-based graphical language that has been first developed for the dynamic modelling of finite dimensional mechanical, hydraulic and electrical systems. As such, this interdisciplinary modelling approach was a ‘mechatronic’ approach ‘avant-la-lettre’. It has been also applied to chemical engineering systems and, more recently, to infinite-dimensional systems models. Such an application is more directly related to the concepts of (irreversible) thermodynamics, even though all fields of applications implicitly satisfy the basic principles of thermodynamics. The aim of this paper is to present the bond graph language by using some rather simple dynamical systems as tutorial examples and to show the potentialities of this language to build dynamical models from reusable sub-models. Provided that software tools are available to manipulate this language, which is already the case for finite dimensional models at a commercial level and for infinite-dimensional models at a research level, it can be a solution to the problem of process model management during the process life that is encountered in the process industries.

Static checking of dynamically generated queries in database applications

Many data-intensive applications dynamically construct queries in response to client requests and execute them. Java servlets, for example, can create strings that represent SQL queries and then send the queries, using JDBC, to a database server for execution. The servlet programmer enjoys static checking via Java's strong type system. However, the Java type system does little to check for possible errors in the dynamically generated SQL query strings. Thus, a type error in a generated selection query (e.g., comparing a string attribute with an integer) can result in an SQL runtime exception. Currently, such defects must be rooted out through careful testing, or (worse) might be found by customers at runtime. In this article, we present a sound , static program analysis technique to verify that dynamically generated query strings do not contain type errors. We describe our analysis technique and provide soundness results for our static analysis algorithm. We also describe the details of a prototype tool based on the algorithm and present several illustrative defects found in senior software-engineering student-team projects, online tutorial examples, and a real-world purchase order system written by one of the authors.

Improved applicability of ray tracing in seismic acquisition, imaging, and interpretation

Ray-based seismic modeling methods can be applied at various stages of the exploration and production process. The standard ray method has several advantages, e.g., computational efficiency and the possibility of simulating propagation of elementary waves. As a high-frequency approximation, the method also has a number of limitations, particularly with respect to a lack of amplitude reliability in the presence of rapid changes of the model functions representing elastic parameters and interfaces. Given the objective of improving the applicability of the standard ray method, we present a strategy that does not require specific extension to finite frequencies. Instead, we define each ray-based process as an element of a system that, as a composite process, is able to obtain better results than the ray-based process applied alone. Other elements of the composite process can be finite-difference modeling or numerical solutions for surface and volume integrals, which are basic constituents of Kirchhoff modeling and imaging. We also include among the process elements recently developed techniques for simulating the migration amplitude on a target reflector and in a local volume, e.g., a reservoir zone. The model is decomposed according to its complexity into volume elements, surface elements, or a combination. The composite process consists of a specified interaction between process elements and model elements, which fits well with the philosophy of modern software design. Model elements that will be exposed to ray-tracing algorithms may need appropriate preparation, e.g., smoothing and resampling. We demonstrate specifically, in a tutorial example, that simulating the seismic response from a reflector by ray-based composite processes can yield better results than applying standard ray tracing alone.

On choosing governance structures

Two main paradigms split the core of the debate on governance structures: the maxi-minimizing and the satisficing paradigms. Some differences between the two has been hidden by the (only apparently) similarity of the “maximum” and “maximal” concepts. If the maximizing behavior refers to the maximum of the utility function and not to the maximal of a binary preference relation, then satisficing does not correspond to maximizing behavior. Besides such differences, from an empirically grounded point of view the maxi-minimizing approach to choose and to evaluate governance structures has relevant limitations. The remarkable limitations of the maxi-minimizing approach become further evident and crucial when one acknowledges that the comparison between alternative governance structures is – like almost any other human choice – unavoidably multicriteria. The absence of tradeoffs among the different criteria prevents the generalized use of a single real-valued function (utility, profit, cost, etc.) to represent decision maker's goals. However, multicriteria problems can be solved when properly dealt with outranking methods. These are heuristic choice algorithms fully consistent with the satisficing paradigm and with the behavioral economic theory. In order to show its effectiveness, a tutorial example is discussed in detail comparing the three main forms of governance structures: market, hierarchy and network. They are scrutinized by four evaluation criteria: profitability, effectiveness, accountability and organizational capability. It will be demonstrated that the outranking algorithm can solve multicriteria decision making problems under conflicting criteria of evaluation. Outranking solutions are at the same time satisficing solutions, that take into account and operationalize the Simonian “levels of aspiration” through concrete parameters.

MTCLAB: A MATLAB ®-based program for traveltime quality analysis and pre-inversion velocity tuning in 2D transmission tomography

A MATLAB ®-based computer code that analyses the traveltime distribution and performs quality analysis at the pre-inversion stage for 2D transmission experiments is presented. The core tools of this approach are the so-called mean traveltime curves. For any general recording geometry, the user may select any pair of subsets of contiguous sources and receivers. The portion of the domain swept by the implied rays defines a zone of analysis, and for each source (receiver) the outcoming (incoming) ray fan is named a source (receiver) gather. The empirical mean traveltime curves are constructed, for each zone, by assigning the average and the standard deviation of the traveltimes in the gathers to the positions of the sources (receivers). The theoretical expressions assume isotropic homogeneous velocity inside each zone. The empirical counterparts use the observed traveltimes and make no assumptions. Isotropic velocity in each zone is inferred by least-squares fitting of the empirical mean traveltime curves. The user may refine the analysis considering different zones (multi-zone analysis). Initially the whole domain is modelled as a single zone. The procedure compares empirical versus theoretical curves. In addition, residuals can be plotted using source–receiver positions as plane coordinates. The results are used to unravel the possible presence of anomalous gathers, heterogeneities, anisotropies, etc. Depending on the kind of anomalies, velocity estimation and mean time residuals are different in the source and receiver gather curves. This software helps to grasp a better understanding of the data variability before the inversion and provides to the geophysicist an approximate zonal isotropic model and a range of velocity variation that can be used in the inverse problem as a priori information (regularization term). Its use is described through tutorial examples. A guided user interface leads the user through the algorithm steps.

Designing Platforms for Customizable Products and Processes in Markets of Non-Uniform Demand

The foremost difficulty in making the transition to mass customization is how to offer product variety affordably. The answer to this quandary lies in the successful management of modularity and commonality in the development of products and their production processes. While several platform design techniques have emerged as a means to offer modularity and commonality, they are limited by an inability to handle multiple modes of offering variety for multiple design specifications. The Product Platform Constructal Theory Method (PPCTM) is a technique that enables a designer to develop platforms for customizable products while handling issues of multiple levels of commonality, multiple product specifications, and the inherent tradeoffs between platform extent and performance. The method is limited, however, by its inability to handle multiple design objectives and its reliance on the assumption that demand in the market is uniform for each product variant. The authors address these limitations in this study by infusing the utility-based compromise decision support problem and demand modeling techniques. The authors further augment the PPCTM by extending its use to a new domain: the design of process parameter platforms. The augmented approach is illustrated through a tutorial example: the design of a product and a process parameter platform for the realization of a line of customizable cantilever beams.

Two derivations of the master equation of quantum Brownian motion

Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the ‘preferred basis’ for decoherence in this model.

On the Linear Analysis of Synchronous Switching Networks

An exposition of an earlier seminal paper on the linear analysis of synchronous switching networks is presented. This analysis, based on the use of the finite or Galois field GF(2), resembles the linear analysis of continuous systems and has important applications in genetics and biochemistry. A synchronous switching network is represented by a function matrix or by a transition matrix, which are related by a similarity transformation in terms of a state matrix. Our use of a novel recursive ordering for the keys or indices of these matrices reveals several new and interesting features and properties. The state matrix is observed to depend not on the particular network but merely on its number of nodes, and is further given a novel interpretation via the modern concept of subsumption of a logical product by another. This reveals a recursive structure of the state matrix and leads to a proof that it is involutory (self- inverse). The autonomous behavior of synchronous switching networks is studied via the characteristic equations and eigenvectors of the aforementioned matrices. In general, the classical ideas are enriched with modern concepts and terminology, supported with correct proofs, and clarified with detailed tutorial examples.

Inferring operating rules for reservoir operations using fuzzy regression and ANFIS

The methods of ordinary least-squares regression (OLSR), fuzzy regression (FR), and adaptive network-based fuzzy inference system (ANFIS) are compared in inferring operating rules for a reservoir operations optimization problem. Dynamic programming (DP) is used as an example optimization tool to provide the input–output data set to be used by OLSR, FR, and ANFIS models. The coefficients of an FR model are found by solving a linear programming (LP) problem. The objective function of the LP is to minimize the total fuzziness of the FR model, which is related to the width of fuzzy coefficients in the regression model. Before applying FR to the reservoir operations problem, two FR formulations and interval regression (IR) are first examined in a simple tutorial example. ANFIS is also used to derive the reservoir operating rules as fuzzy IF-THEN rules. The OLSR, FR, and ANFIS based rules are then simulated and compared based on their performance in simulation. The methods are applied to a long-term planning problem as well as to a medium-term implicit stochastic optimization model. The results indicate that FR is useful to derive operating rules for a long-term planning model, where imperfect and partial information is available. ANFIS is beneficial in medium-term implicit stochastic optimization as it is able to extract important features of the system from the generated input–output set and represent those features as general operating rules.

The use of stochastic analytic center for yield maximization of systems with general distributions of component values

This paper presents a new method for maximizing manufacturing yield when the realizations of system components are dependent random variables with general distributions. The method uses a new concept of stochastic analytic center introduced herein to design the unknown parameters of component values. Design specifications define a feasible region which, in the nonlinear case, is linearized using a first-order approximation. The resulting problem becomes a convex optimization problem. Monte Carlo simulation is used to evaluate the actual yield of the optimal designs of a tutorial example.

Approximate robust dynamic programming and robustly stable MPC

We present a technique for approximate robust dynamic programming that is suitable for linearly constrained polytopic systems with piecewise affine cost functions. The approximation method uses polyhedral representations of the cost-to-go function and feasible set, and can considerably reduce the computational burden compared to recently proposed methods for exact robust dynamic programming [Bemporad, A., Borrelli, F., & Morari, M. (2003). Min–max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control, 48(9), 1600–1606; Diehl, M., & Björnberg, J. (2004). Robust dynamic programming for min–max model predictive control of constrained uncertain systems. IEEE Transactions on Automatic Control, 49(12), 2253–2257]. We show how to apply the method to robust MPC, and give conditions that guarantee closed-loop stability. We finish by applying the method to a state constrained tutorial example, a parking car with uncertain mass.

Some remarks on conflict analysis

Study of conflicts is of greatest importance both practically and theoretically. Conflict analysis and resolution play an important role in business, governmental, political and lawsuits disputes, labor-management negotiations, military operations and others. Many formal models of conflict situations have been proposed and studied. In this paper we outline a new approach to conflict analysis, which will be illustrated by a simple tutorial example of voting analysis in conflict situations.

Online Tutorials as Instruction for Distance Students

SUMMARY Many academic libraries offer an array of library services to their off-campus and distance students, but library instruction for these populations is still a challenge. Librarians and teaching faculty struggle with how to effectively reach students that are truly distant, offering them the same library instruction and information literacy training that is possible in the classroom. The online tutorial has gained popularity in recent years and this article will address Web-based interactive tutorials as a means of providing library instruction to distance learners. Examples of tutorials aimed at distance students are examined, along with studies assessing the effectiveness of online tutorials.

Robust Dynamic Programming for Min–Max Model Predictive Control of Constrained Uncertain Systems

We address min-max model predictive control (MPC) for uncertain discrete-time systems by a robust dynamic programming approach, and develop an algorithm that is suitable for linearly constrained polytopic systems with piecewise affine cost functions. The method uses polyhedral representations of the cost-to-go functions and feasible sets, and performs multiparametric programming by a duality based approach in each recursion step. We show how to apply the method to robust MPC, and give conditions guaranteeing closed loop stability. Finally, we apply the method to a tutorial example, a parking car with uncertain mass.

W3MCSim: an online and reconfigurable Monte Carlo simulator for interactive probabilistic/statistical modeling

We have implemented a Monte Carlo simulator (W3MCSim) as an Internet software tool, primarily for interactive use by students, educators, life and other physical scientists, as well as other practitioners of probabilistic and statistical modeling. Interested users download, install and run W3MCSim by visiting the application website. This application incorporates three freely available Microsoft web technologies, namely the Internet Explorer web browser, the Component Object Model software framework and the JScript web page script interpreter. We define the software architecture here, as a web application model, and show how incorporation of these technologies provides an efficient solution to W3MCSim software deployment. We demonstrate the usability and versatility of this simulator with three distinct tutorial examples: simulating the sum of six-sided dice, estimating intersection frequency in "Buffon's needle problem", and testing an animal experiment design model a priori. We also show how the program components can be reconfigured into other programs.

A recipe to detect the error in discretization schemes

AbstractThe necessity for a reliable measure of the discretization error arises in adaptive mesh refinement and in moving mesh adaptation. The present work discusses a detector of the discretization error based on the interpolation reconstruction of the operators. The technique presented here is named operator recovery error source detector (ORESD). Its main features are: First, the technique is based on the operators being discretized and does not require any user intervention or any a priori knowledge of the solution or its properties. Second, the ORESD is an a posteriori error indicator, but it is shown to be consistent with the a priori error provided by the modified equation approach. Third, the technique is based on the operators being solved and is tailored to the specific problem at hand. Four, the technique is simple and is based on a small stencil, resulting in a very inexpensive error detection.In the present work, the ORESD is derived and applied to two tutorial examples: divergence and gradient. With the aid of the two examples and using the general derivation, the ORESD is then applied to the gas dynamics equations. Two benchmarks are used to test the performance. First, a shock tube problem is solved (Sod's benchmark) in a Lagrangian and in a Eulerian frame. Second, the Colella's wedge problem is solved using CLAWPACK. Finally, the ORESD is applied to the 2D Poisson equation on a uniform and on a non‐uniform grid to test the application to elliptic problems. In all examples the operator recovery error source detector succeeds in detecting the real sources of error. Copyright © 2004 John Wiley & Sons, Ltd.

IMe: 4-Term Formula Method for the Symbolic Analysis of Linear Circuits

This paper is intended to show a general method (inhibition method) that relies on the superposition principle to analyze linear systems and electric circuits, based on hierarchical sequences of more simple topologies with some inhibited elements and on a simple recollecting logic to calculate the final solution from the previous partial and more elementary solutions. The result of the analysis is represented by and stored into a table (called the inhibition sequence table), which thus consists in a kind of database for the system or electric circuit being analyzed. The method follows a hierarchical structuration that is halfway physical (the hierarchical blocks have a nonabstract meaning) and halfway logical (the relationships among the blocks carry out information richer than the hierarchy itself). Once the table is calculated for a particular system, then a little calculation overhead allows some other interesting features, like the possibility to analyze an old circuit with some new branches added by analyzing the new elements only, or like the calculation of exact sensitivities without using derivatives, or like the calculation of the inverse matrix avoiding the usual matrix inversion procedure. A proof of the Inhibition Theorem is given and also some tutorial circuit examples.

Comparing and choosing organizational structures: A multicriteria methodology

To the extent an organizational structure is the outcome of an intentional and rational choice, such a choice is complex. A relevant aspect of such a complexity is the number of different and usually conflicting criteria employed by the decision maker. The application of traditional and pragmatic approaches implies the choice of one type of organizational structure through multiple assessing criteria. A multicriteria choice is involved even in a purely scientific approach: different organization theories suggest different criteria. The standard decision theory, based on the maxi-minimization of some utility function, cannot deal with multicriteriality. The task can be fulfilled in a rigorous and formal way by outranking methods, which are a branch of operations research. With an application to the problem of choosing the organizational structure, a tutorial example of outranking methods is discussed, addressing the larger theoretical framework where they can be placed and developed in management science.