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On the Vekua Pair in Spheroidal Geometry and its Role in Solving Boundary Value Problems

International Journal of Phytoremediation 2002年第1期21卷 85-113页

作者： Charalambopoulos, Antonios Dassios, George Division of Mathematics School of Engineering University of Thessaloniki Greece Division of Applied Mathematics Department of Chemical Engineering University of Patras Greece

The Vekua pair forms a transformation between the kernel of the Laplace's and the kernel of the Helmholtz's operator. In fact, it provides an interior solution of the Helmholtz's equation once an interior harmonic function is given, and conversely, given an interior solution of the Helmhotz's equation an interior harmonic function is constructed. Consequently, it seems that the Vekua connection offers the perfect ground to obtain solutions of boundary value problems connected with Helmholtz operator. Vekua expressed his transformation in spherical coordinates. Nevertheless, when a change of coordinates is applied, the transformation assumes a much more complicated form, but it still remains a very useful technique for dealing with solutions of the equations of Laplace and Helmholtz. Here we extend the Vekua theory to a new integral transformation pair concerning solutions of the aforementioned operators in exterior domains. In addition, the form of the Vekua transformation is analyzed in spheroidal coordinates and its implication to boundary value problems is investigated. © 2002, Copyright Taylor & Francis Group, LLC.

关键词： Helmholtz's Equation Laplace Equation Spheroidal Coordinates Vekua Pair

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Fluid-membrane tethers: Minimal surfaces and elastic boundary layers

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Physical Review E 2002年第4期65卷 041901-041901页

作者： Thomas R. Powers Greg Huber Raymond E. Goldstein Division of Engineering Brown University Providence Rhode Island 02912 Department of Physics University of Massachusetts at Boston Boston Massachusetts 02125 Department of Physics and Program in Applied Mathematics University of Arizona Tucson Arizona 85721

Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.

关键词： Fluid dynamics

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Aqueous humor and iris mechanics in synechial closure in primary angle-closure glaucoma

Aqueous humor and iris mechanics in synechial closure in pri...

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Annual International Conference of the IEEE engineering in Medicine and Biology Society (EMBC)

作者： E.C. Huang J.J. Heys V.H. Barocas Department of Chemical Engineering and Material Science University of Minnesota Minneapolis MN USA Department of Applied Mathematics University of Colorado Boulder CO USA Department of Biomedical Engineering University of Minnesota MN USA

Primary angle-closure glaucoma features a narrow anterior chamber angle in which the anteriorly positioned iris blocks aqueous humor outflow through the trabecular meshwork, subsequently increasing the intraocular pressure. A mathematical model is used to investigate the aqueous humor-iris interaction in synechial angle closure. The model predicted increased intraocular pressure as the anterior chamber angle decreased and a plateau iris configuration in synechial angle closure - consistent with clinical observations.

关键词： Iris Cornea Mathematical model Lenses Adhesives chemical engineering Materials science and technology mathematics Biomedical engineering Predictive models

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Fingering instability of thin evaporating liquid films

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Physical Review E 2002年第2期65卷 021602-021602页

作者： A. V. Lyushnin A. A. Golovin L. M. Pismen Department of Chemical Engineering Technion–Israel Institute of Technology Haifa 32000 Israel Department of Engineering Sciences and Applied Mathematics Northwestern University Evanston Illinois 60208-3100 Minerva Center for Nonlinear Physics of Complex Systems Technion–Israel Institute of Technology Haifa 32000 Israel

The fingering instability of growing dry patches in an evaporating film of a polar liquid placed on a solid substrate is investigated. The instability manifests itself as fingering of mobile fronts between growing “dry” (thin) and shrinking “wet” (thick) regions of the film corresponding to two stable states of the evaporating film in contact with its vapor. The boundaries of the fingering instability are found through linear stability analysis of numerical solutions of the nonlinear evolution equation defining the film profile, and the influence of the evaporation rate, polar intermolecular forces, and chemical heterogeneity of the substrate is investigated.

关键词： Thin films

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Spatiotemporal disturbance compensation for nonlinear transport processes via moving actuators

Spatiotemporal disturbance compensation for nonlinear transp...

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IEEE Conference on Decision and Control

作者： M.A. Demetriou N. Kazantzis B.B. King Department of Chemical Engineering Worcester Polytechnic Institute Worcester MA USA Interdisciplinary Center for Applied Mathematics Virginia Polytechnic Institute and State University Blacksburg VA USA

Deals with the development of a framework that allows an integrated actuator activation policy and controller synthesis method to be realized through a scheme of moving actuators for the performance enhancement of nonlinear transport processes in the presence of spatiotemporal disturbance variations. The transport processes of interest are modeled by nonlinear parabolic partial differential equations (PDEs) and are frequently encountered in a multitude of industrial applications. Standard state feedback controller synthesis methods based on linear matrix inequality-techniques (LMIs) are employed for a finite-dimensional Galerkin approximation of the original nonlinear distributed parameter system, and the value of an appropriately selected objective function is explicitly calculated by solving a location-parameterized Lyapunov matrix equation. A static optimization algorithm is developed that offers a guidance policy and optimal switching rules between the various actuator positions for process performance enhancement. An example with simulation results of a transport process modeled through Burger's equation is included, in order to evaluate the performance-enhancing capabilities of the proposed scheme.

关键词： Spatiotemporal phenomena Actuators Linear matrix inequalities Partial differential equations Electrical equipment industry State feedback Linear feedback control systems Nonlinear control systems Control system synthesis Moment methods

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Nonuniversality of invasion percolation in two-dimensional systems

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Physical Review E 2002年第3期65卷 035101(R)-035101(R)页

作者： Mark A. Knackstedt Muhammad Sahimi Adrian P. Sheppard Department of Applied Mathematics Research School of Physical Sciences and Engineering Australian National University Canberra ACT 0200 Australia Australian Petroleum Cooperative Research Centre University of New South Wales Sydney NSW 2052 Australia Department of Chemical Engineering University of Southern California Los Angeles California 90089-1211 Institute for Advanced Studies in Basic Sciences Gava Zang Zanjan 45195-159 Iran

Employing highly efficient algorithms for simulating invasion percolation (IP) with trapping, we obtain precise estimates for the fractal dimensions of the sample-spanning cluster, the backbone, and the minimal path in a variety of two-dimensional lattices. The results indicate that these quantities are nonuniversal and vary with the coordination number Z of the lattices. In particular, while the fractal dimension Df of the sample-spanning cluster in lattices with low Z has the generally accepted value of about 1.82, it crosses over to the value of random percolation, Df≃1.896, if Z is large enough. Since optimal paths in strongly disordered media and minimum spanning trees on random graphs are related to IP, the implication is that these problems do not also possess universal scaling properties.

关键词： Percolation (fluids)

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mathematics and chemical engineering education

Mathematics and chemical engineering education

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2001 ASEE Annual Conference and Exposition: Peppers, Papers, Pueblos and Professors

作者： Carpenter, Jenna P. Cutlip, Michael B. Graham, Michael D. Pintar, Anton J. Puszynski, Jan A. Louisiana Tech University University of Connecticut University of Wisconsin-Madison Michigan Technological University S. Dakota Sch. of Mines and Technol. Department of Mathematics Elect. Eng. Elect. Eng. T. C.S. Louisiana Tech University Department of Chemical Engineering University Honors Program University of Connecticut Department of Chemical Engineering University of Wisconsin Madison Department of Chemical Engineering Michigan Technological University Department of Chemistry Engineering Coll. of Mat. Sci. and Engineering S. Dakota Sch. of Mines and Technol.

This paper is based on the report developed by the authors at the mathematics Association of America (MAA) Curriculum Foundations engineering Workshop held at Clemson University in May 2000. The objectives of this paper are to identify the mathematics needed by chemical engineering undergraduates, to stimulate a dialog between mathematics and chemical engineering educators on this topic, and to determine the most effective way of providing the necessary mathematics. The focus is on subject matter and not on pedagogy. The broad categories of mathematics essential to chemical engineering are pre-calculus foundations (provided by the K-12 school system or the by first-year university mathematics program), linear algebra, calculus, differential equations, and probability/statistics. Important topics within each area can be identified. The best place and time to teach this body of knowledge is open to discussion i.e.. what topics are best taught by the mathematics department, what topics should be incorporated into chemical engineering courses, what topics should be covered in the first and second years, and to what extent should the mathematics be spread out over four years? The effective use of "mathematics technology" in mathematics and chemical engineering courses is discussed. Also, various ways are presented for exposing students to chemical engineering applications in the mathematics courses.

关键词： engineering education

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Towards automatic verification of embedded control software

Towards automatic verification of embedded control software

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Asia-Pacific Conference on Quality Software

作者： N. Bauer R. Huuck Department of Chemical Engineering University of Dortmund Dortmund Germany Institute of Computer Science and Applied Mathematics University of Kiel Kiel Germany

ISBN: (纸本)0769512879

The language: sequential function charts (SFC), is a programming and structuring language for programmable logic controllers (PLC). It is defined in the IEC 61131-3 standard and includes various interesting concepts such as parallelism, hierarchy, priorities, and activity manipulation. Although SFCs are perpetually used in the engineering community for programming and the design of embedded control systems, there are hardly any specific verification approaches for them. Existing approaches for Petri nets, Grafcets, or (UML-)Statecharts do not really apply to SFCs, whose structures are similar but include distinct features. We present a method to model-check SFCs. This is done by defining a translation of SFCs into the native language of the Cadence Symbolic Model Verifier (CaSMV). This translation is specifically tailored to cover all the concepts of SFCs and can be performed automatically. Moreover, we demonstrate our approach by an application to a control process in chemical engineering.

关键词： Automatic control Embedded software programmable control IEC standards Functional programming Logic programming Design engineering Control systems Petri nets Process control

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MODELING A SIMPLE CHOICE TASK: STOCHASTIC DYNAMICS OF MUTUALLY INHIBITORY NEURAL GROUPS

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Stochastics and Dynamics 2001年第2期1卷 159-191页

作者： ERIC BROWN PHILIP HOLMES Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA Also at Department of Mechanical and Aerospace Engineering Princeton University Princeton NJ 08544 USA.

We describe the dynamical and bifurcational behavior of two mutually inhibitory, leaky, neural units subject to external stimulus, random noise, and "priming biases". The model describes a simple forced choice experiment and accounts for varying levels of expectation and control. By projecting the model's dynamics onto slow manifolds, using judicious linear approximations, and solving for one-dimensional (reduced) probability densities, analytical estimates are developed for reaction time distributions and shown to compare satisfactorily with "full" numerical data. A sensitivity analysis is performed and the effects of parameters assessed. The predictions are also compared with behavioral data. These results may help correlate low-dimensional models of stochastic neural networks with cognitive test data, and hence assist in parameter choices and model building.

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Survey of reduced workload and crewing strategies for ocean patrol vessels

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NAVAL ENGINEERS JOURNAL 2001年第2期113卷 29-44页

作者： Baker, C Krull, R Snyder, G Lincoln, W Malone, TB Clifford C. Baker CIE CHFEP is a senior staff scientist at Carlow International Incorporated. He has applied most of his 24 years of experience in the application of human engineering technology to maritime systems. Mr. Baker has directed much of Carlow's efforts to reduce ship workload and to improve human performance and maritime safety through application of human factors methods and data. He is a Certified Industrial Ergonomist (CIE) as well as a Certified Human Factors Engineering Professional (CHFEP). Both certifications were granted by Oxford Research where Mr. Baker also serves as an Advisory Board member. Russell D. Krull P.E. is a senior engineer with A&T/Proteus Engineering with more than 18 years of experi-ence in marine engineering naval architecture and program management including 16 years of active duty in the U.S. Coast Guard. Recent experience includes advanced ship design studies engineering software development technical support for the USMC Advanced Amphibious Assault Vehicle propulsion systems analyses ship structural engineering and cargo handling systems engineering. Mr. Krull has an M.S.E. in naval architecture and marine engineering and an M.S.E. in industrial and operations engineering from University of Michigan and a B.S. in ocean engineering from the U.S. Coast Guard Academy. Capt. Glenn L. Snyder USCG. Regrettably since this paper was originally written Capt. Snyder has passed away. At the time of his death he was an operations specialist assigned to the Coast Guard's Deepwater Capabilities Replacement Project as Chief of Human Systems Integration. He served as commanding officer of the patrol boat Cape George (WPB-95306) the icebreaking tug Biscayne Bay (WTGB-104) and the cutter Legare (WMEC-911). A 1975 graduate of the U.S. Coast Guard Academy Capt. Snyder held an M.A. in national security and strategic studies from the U.S. Naval War College and an M.A. in international relations from Salve Regina College. In addition he was a 1998 fellow of the Foreign Service

The U.S. Coast Guard is in the concept exploration phase of its Integrated Deepwater System (IDS) acquisition project. This project will define the next generation of surface, air and command, control, communications, computers, intelligence, surveillance, and reconnaissance (C4ISR) assets used to perform the Coast Guard's missions in the IDS environment (>50 NM off the U. S. coastline). As part of early technology investigations, the needs exist to: (1) analyze the workload requirements of the IDS, (2) identify alternative means to perform ship's work, and (3) optimize ship manning consistent with ship workload, performance criteria, and the available tools and equipment aboard. To reduce shipboard work requires an understanding of the mission and support requirements placed on the vessel and crew, how these requirements are currently met, and how requirements might otherwise be met to reduce workload and crew size. This study examined currently implemented workload and manpower reducing approaches of commercial maritime fleets, U.S. and foreign navies, and foreign coastguards. These approaches were analyzed according to evaluation criteria approved by the IDS acquisition project team. From this, strategies for shipboard work reduction that may be considered for adoption by the IDS were identified and analyzed according to performance and costs factors. Ten workload-reducing strategies were identified: damage control, bridge, multiple crewing, engineering, risk acceptance, modularity, deck, enabling technologies, ship/personnel readiness, and operability and maintainability.

关键词： Naval vessels

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