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Differential Form (differential + form)
Selected AbstractsSurface wavelets: a multiresolution signal processing tool for 3D computational modellingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001Kevin Amaratunga Abstract In this paper, we provide an introduction to wavelet representations for complex surfaces (surface wavelets), with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modelling. This motivates the study of surface wavelets as an efficient representation for the modelling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, stated either in integral form or in differential form. We analyse and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties. We show both theoretically and experimentally that an O(h) convergence rate, hn being the mesh size, can be obtained by retaining only O((logN) 7/2N) entries in the discrete operator matrix, where N is the number of unknowns. The principles described here may also be extended to volumetric discretizations. Copyright © 2001 John Wiley & Sons, Ltd. [source] High-resolution, monotone solution of the adjoint shallow-water equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002Brett F. Sanders Abstract A monotone, second-order accurate numerical scheme is presented for solving the differential form of the adjoint shallow-water equations in generalized two-dimensional coordinates. Fluctuation-splitting is utilized to achieve a high-resolution solution of the equations in primitive form. One-step and two-step schemes are presented and shown to achieve solutions of similarly high accuracy in one dimension. However, the two-step method is shown to yield more accurate solutions to problems in which unsteady wave speeds are present. In two dimensions, the two-step scheme is tested in the context of two parameter identification problems, and it is shown to accurately transmit the information needed to identify unknown forcing parameters based on measurements of the system response. The first problem involves the identification of an upstream flood hydrograph based on downstream depth measurements. The second problem involves the identification of a long wave state in the far-field based on near-field depth measurements. Copyright © 2002 John Wiley & Sons, Ltd. [source] Simplified solution of developing laminar forced flow between parallel platesINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 5 2002Esmail M. A. Mokheimer Abstract A simplified simulation for developing laminar forced flow in the entrance region between two parallel plates is presented. This simulation is based on an implicit finite difference numerical representation of a boundary layer model describing the flow in the entry region. This boundary layer model comprises the two conservation equations of mass and momentum. A non-iterative implicit numerical scheme is developed to convert the partial differential form of these governing equations into algebraic equations. The resultant algebraic equations have been solved simultaneously via a simplified simulation using spreadsheet programs as well as a Fortran code for the sake of comparison. The numerically obtained developing axial velocity profile at large distance downstream of the entrance shows excellent agreement with the available fully developed analytical profile. Comparison between the abilities of the spreadsheet simulation with other high-level programming languages is outlined. Copyright © 2002 John Wiley & Sons, Ltd. [source] Kinematic modeling of mobile robots by transfer method of augmented generalized coordinatesJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2004Wheekuk Kim A kinematic modeling method, which is directly applicable to any type of planar mobile robots, is proposed in this work. Since holonomic constraints have the same differential form as nonholonomic constraints, the instantaneous motion of the mobile robot at current configuration can be modeled as that of a parallel manipulator. A pseudo joint model denoting the interface between the wheel and the ground (i.e., the position of base of the mobile robot) enables the derivation of this equivalent kinematic model. The instantaneous kinematic structures of four different wheels are modeled as multiple pseudo joints. Then, the transfer method of augmented generalized coordinates, which has been popularly employed in modeling of parallel manipulators, is applied to obtain the instantaneous kinematic models of mobile robots. The kinematic models of six different types of planar mobile robots are derived to show the effectiveness of the proposed modeling method. Lastly, for the mobile robot equipped with four conventional wheels, an algorithm estimating a sensed forward solution for the given information of the rotational velocities of the four wheels is discussed. © 2004 Wiley Periodicals, Inc. [source] Global weak solution to the flow of liquid crystals systemMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2009Fei Jiang Abstract In this paper, we study a simplified system for the flow of nematic liquid crystals in a bounded domain in the three-dimensional space. We derive the basic energy law which enables us to prove the global existence of the weak solutions under the condition that the initial density belongs to L,(,) for any . Especially, we also obtain that the weak solutions satisfy the energy inequality in integral or differential form. Copyright © 2009 John Wiley & Sons, Ltd. [source] Gazing at the Hand: A Foucaultian View of the Teaching of Manipulative Skills to Introductory Chemistry Students in the United States and the Potential for Transforming Laboratory InstructionCURRICULUM INQUIRY, Issue 3 2005STEPHEN DEMEO ABSTRACT Many studies of chemistry have described the rise of the academic chemical laboratory and laboratory skills in the United States as a result of famous men, important discoveries, and international influences. What is lacking is a perspective of the manifestations of the balances of power and knowledge between teacher and student. A Foucaultian analysis of the teaching of manipulative skills to the introductory student in high school and college in the United States during the later half of the 19th and into the 20th century has provided such a perspective. The analysis focuses on the body, specifically students' hands, and how this body has been redescribed in terms of time, space, activity, and their combinations. It is argued in the first part of this article that the teaching of manipulative skills in the chemistry laboratory can be characterized by effects of differential forms of power and knowledge, such as those provided by Foucault's ideas of hierarchical observation, normalization, and the examination. Moreover, it is evident that disciplinary techniques primarily focused on the physical hands of the student have been recast to include a new cognitive-physiological space in which the teaching of manipulative skills currently takes place. In the second part of this article, the author describes his own professional development as a laboratory instructor through a series of reflective statements that are critiqued from a Foucaultian perspective. The personal narratives are presented in order to pro- vide science educators with an alternative way for their students to think about the relationship between one's manipulative skills and the quality of their data. The pedagogical approach is related to the maturation process of the chemist and contextualized in the current paradigm of laboratory practice, inquiry-based science education. [source] Dissipativity and stability of interconnectionsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5-6 2007Jan C. Willems Abstract A new definition of dissipativity is proposed. It is purely in terms of the rate of supply that goes in and out of a dynamical system. It is proven that dissipativity is equivalent to the existence of a non-negative storage. Several results regarding the dissipativity of systems defined by quadratic differential forms are given, and some open questions are mentioned. These ideas are applied to the question of stability of interconnected systems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Antecedents for aggression and the function analytic approach to the assessment of aggression and violence in personality disordered patients within secure settingsPERSONALITY AND MENTAL HEALTH, Issue 2 2007Michael Daffern The aim of this paper is to explore the validity and clinical utility of a function analytic approach to the assessment of aggression and violence in patients with personality disorder. This paper begins with a review of the factors that are associated with aggression in personality disordered patients, and focuses in particular upon those patients whose aggressive and violent behaviour has been the reason for their admission to a secure facility, and who may continue to engage in aggression. Two approaches that may explain such aggression are discussed and evaluated: (1) the identification of personality traits that may influence aggression and (2) the differentiation of hostile and instrumental aggression. Some limitations with these two approaches are identified, and an argument is made for function analytic assessment methods. An overview of one form of functional assessment, the Assessment and Classification of Function method, which assists in the classification of differential forms of aggression, is provided. Finally, the clinical and treatment implications of the function analytic approach are discussed. Copyright © 2007 John Wiley & Sons, Ltd. [source] | ||||||||||