Solid and physical modeling with chain complexes

In this paper we present a complete formalization, using the ACL2 theorem prover, of the Normalization Theorem, a result in Algebraic Simplicial Topology stating that there exists a homotopy equivalence between the chain complex of a simplicial set, and a smaller chain complex for the same simplicial set, called the normalized chain complex. The interest of this work stems from three sources. First, the normalization theorem is the basis for some design decisions in the Kenzo computer algebra system, a program for computing in Algebraic Topology. Second, our proof of the theorem is new and shows the correctness of some formulas found experimentally, giving explicit expressions for the above-mentioned homotopy equivalence. And third, it demonstrates that the ACL2 theorem prover can be effectively used to formalize mathematics, even in areas where higher-order tools could be thought to be more appropriate.KeywordsChain ComplexAlgebraic TopologySimplicial IdentityNormalization TheoremPolynomial VersionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preface: Volume 81

Preface: Volume 52, Issue 2

Stone duality, topological algebra, and recognition

the University of Amsterdam, May 20-31, 1974.This Tract collects the lecture notes of five of the courses given.The sixth course, given by Dr. R. Kowalski on Predicate Logic as a Programming Language in Artificial Intelligence, is scheduled to appear elsewhere.We are very grateful to the Netherlands Organization for the Advancement of Pure Research (Z.W.O.)

The ACM Symposium on Solid and Physical Modeling and Applications is an annual international forum for the exchange of recent research results and applications of spatial modeling and computations in design, analysis and manufacturing, as well as in emerging biomedical, geophysical and other areas. Previous symposia in this series were held in Austin, Texas, 1991; Montreal, Canada, 1993; Salt Lake City, Utah, 1995; Atlanta, Georgia, 1997; Ann Arbor, Michigan in 1999 and 2001; Saarbrucken, Germany, 2002; Seattle, Washington, 2003; Genova, Italy, 2004, Cambridge, Massachusetts, 2005; Cardiff, Wales, United Kingdom, 2006; and Beijing, China, 2007. For additional information, please visit www.solidmodeling.org, the home page of The Solid Modeling Association that oversees this symposium series. The SPM symposium series started initially with the name "ACM Symposium on Solid Modeling and Applications." To emphasize the fact that solid modeling entails not only handling their geometric shapes, but also their physical properties, behaviors and simulations, the name of the symposium was expanded to The ACM Symposium on Solid and Physical Modeling and Applications (abbreviated as SPM) in 2005. SPM'08 was held at Suny, Stony Brook from June 2 to June 4, as part of Stony Brook Modeling Week that also featured international joint convention on shapes and solids. SPM'08 was held as a single track conference, which also included two mini-symposia. In response to SPM'08 call for papers, 79 technical papers were submitted and reviewed by an international program committee with 96 expert reviewers from around the world. At least three external reviewers and members of the program committee reviewed and discussed each submission. A total of 25 refereed papers have been selected for plenary presentation and publication in the proceedings as full papers. Moreover, a total of 18 refereed papers have been selected for poster presentation and publication in the proceedings as short papers. The symposium program also includes three invited presentations, by Helmut Pottmann (Vienna University of Technology), Hugues Hoppe (Microsoft Research) and Kokichi Sugihara (University of Tokyo), all leading researchers in their fields.

The ACM Symposium on Solid and Physical Modeling and Applications is an annual international forum for the exchange of recent research results and applications of spatial modeling and computations in design, analysis and manufacturing, as well as in emerging biomedical, geophysical and other areas. Previous symposia in this series were held in Austin, Texas, 1991; Montreal, Canada, 1993; Salt Lake City, Utah, 1995; Atlanta, Georgia, 1997; Ann Arbor, Michigan in 1999 and 2001; Saarbrucken, Germany, 2002; and Seattle, Washington, 2003, and Genova, Italy, 2004. For additional information, visit www.solidmodeling.org, the home page of the Solid Modeling Association that oversees this symposia series.Since its inception in 1991, the ACM Symposium on Solid Modeling and Applications has been the primary venue for disseminating research results in the design, representation, analysis, visualization, and use of digital models of real or planned solid objects and of their bounding surfaces. At the same time, modeling solids entails not only handling their geometric shape, but also their physical properties and behaviors. To emphasize this broader mission, we have expanded the name of the 2005 Symposium to Solid and Physical Modeling (abbreviated SPM). SPM-05 was held on the MIT campus, in Cambridge, Massachusetts, in plenary sessions (no parallel tracks) from Monday June 13 to Wednesday June 15, and was followed by the <u>Shape Modeling International</u> (SMI) conference. Both SPM and SMI events are part of the <u>2005 Joint Convention on Solids and Shapes</u>, (S&S'05) hosted at MIT and chaired by Nick Patrikalakis. The <u>2004 Joint Convention on Shapes and Solids</u> took place in Genoa Italy.Some sixty technical papers have been submitted and were reviewed by the international program committee and expert reviewers from around the world. At least three to four external reviewers and members of the program committee reviewed and discussed each submission. A total of 22 refereed papers have been selected for plenary presentation and full paper publication in the proceedings. In addition, 6 more papers have been selected as technical sketches for shorter publication and presentation at the conference. The symposium program also includes two keynote presentations invited from leading authorities in their fields: Bruce Donald and James O'Brien. Another new feature in the symposium program was that we had three panel session where recent trends and challenges are discussed. The panel sessions were organized by Dimitris Metaxas (Biomedical Modeling), Michael Wang (Physical Modeling and Simulation), and Jan Vandenbrande (Design, Analysis, and Manufacturing).

Chain complexes with a group of operators are a well known tool in algebraic topology, where they arise naturally as the chain complex of cellular chains of the universal cover of a reduced CW-complex X. The group of operators here is the fundamental group of X.

Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

Operads in the category of topological spaces Simplicial objects and homotopy theory Algebraic structures on chain complexes $A_\infty$-structures on chain complexes Operads and algebras over operads Homoloty of iterated loop spaces Homotopy theories and $E_\infty$-structures Operad methods in cobordism theory Description of the cohomology of groups and algebras Homology operations and differentials in the Adams spectral sequence Bibliography Index.

The authors of the article present the significance of cross-curriculum modules in Russia and abroad in obtaining a new quality of education: a holistic perception of the world, the assimilation of universal educational activities, meta-subject competencies. The possibilities of pedagogical integration in the formation of cross-curriculum modules of physics and computer science have been analyzed. The intercross-curriculum module as a didactic superstructure over the learning subjects necessary for the formation of meta-subject competencies is determined. The list of cross-curriculum modules of physics and computer science for general education, obtained on the basis of the method of inter-structural integration - the integration of methods and means of computer science with the content of the course of physics has been provided. The following cross-curriculum modules are shown: "Modeling in physics" and "Tabular information model of the domain" Dynamics", "Solving tasks on the laws of conservation and momentum of energy using the computer ","Creating algorithms and spreadsheets of oscillatory motion", "Creating a website layout on topic "Atomic and nuclear physics". The content of the cross-curriculum module "Graphical Information Models of Mechanical Motion" is revealed. Examples of graphic information models of mechanical motion and tasks necessary for their learning by students are provided. Methodical possibilities of inclusion of cross-curriculum modules in the system of teaching physics and computer science in general education are explained. It is shown how the study of these modules leads to the formation of meta-subject competencies in students, which proves the advantages of integrated modules over traditional teaching.

After the implementation of local mesh refinement (LMR) in solution of Euler equations and detonation simulation, the technique has been used to optimize the simulation of viscid flow. In this paper, LMR has been implemented in Navier-Stokes (NS) equations and LES turbulent model. In order to implement LMR in the simulation of viscid flow accurately and efficiently, hybrid interpolation and coarse flux limiter are established. At the same time, implementation of LMR maintains the temporal refinement in solution of NS equations. In practical application, 2D advection diffusion is used to show the advantages of LMR and verify the implementation.

At the start of my Ph.D. in 1980, I caught a glimpse, purely by chance, of the emerging field of computer-aided design (CAD). It intrigued and fascinated me to such an extent that I ended up scrapping my original plans, switching schools and changing my research area. Even though my new school, Ohio State, was one of only a handful of schools with computing facilities dedicated to CAD, I ran into stiff resistance when I expressed my desire to get a Ph.D. in CAD. I was told that CAD was hardly an intellectually challenging field worthy of a Ph.D. dissertation. I was directed to consider mainstream mechanical engineering areas, such as solid mechanics, vibrations, kinematics, and dynamics. The closest I could get to CAD was to do my dissertation in FEA, which allowed me to do at least part of my work in computing and visualization.When I began my academic career at Arizona State, I thought I was finally free to pursue my true love. But I soon realized that we were still a fringe group; faculty in traditional fields, such as thermofluids and solid mechanics, took a dim view of computational research. The proposed thesis plan for my first graduate student (Expert System for Conceptual Synthesis of Frame Structures) was rejected by the Graduate Chair, who remarked “This is not mechanical engineering.” He viewed it as purely a computer program without any regard for the fact that we needed to explicate, structure, and represent experiential knowledge for structural synthesis not found in any textbook on the subject.Of course, I was not alone in facing this predicament. Fortunately, for misfits like us there was an ASME Division that welcomed us. Originally named the Computer Engineering Division (CED), and later known as Computer &amp; Information Engineering (CIE) Division, it was approved in 1979 and began operating in 1980. Unlike academia, industry was well aware of the potential of computing and information technologies to revolutionize product design and manufacturing. Visionaries from computer industry (CDC, IBM, DEC, Applicon), an infant software industry (SDRC, CV, Swanson), and a variety of OEMs (GM, GE, McDonnell-Douglas) led a grassroots effort to convince ASME of the importance of mechanical engineers active participation in these evolving areas through the creation of a new Division. The first CED newsletter in 1981 boldly heralds “…the dawn of an era that is certain to be dominated by computer technology. All projections indicate that mechanical engineers, more than any other professional group, will be more involved in the utilization of this (computer) technology.” They saw MEs playing as important a role in the IT revolution as their far predecessors had in the industrial revolution—a prediction that was to come true.Prof. Ali Seirig was appointed the first Chair of CED. I am in awe of the progress this new Division made in just the first two years. Twenty-four technical committees were set up and an annual conference was initiated in 1981. This conference was unique in that it was associated with an exhibition of the latest hardware and software from leading vendors. This element was critical in keeping the ASME community well informed about the current state of engineering computing. It is, therefore, not surprising to see that this Division was heavily industry dominated—21 out of 24 Technical Committee Chairs were from industry. Sadly, today industry participation in CIE has sagged. Did CIE change because industry participation diminished, or did industry reduce its participation because CIE became less relevant to their needs? We can only speculate about the reasons.CED soon became the fastest growing Division within ASME. The CED/CIE conference and exhibition attracted participants from a wide range of areas, not just CAD/CAM and FEA but kinematics, robotics, heat transfer, and fluid mechanics. This diverse community only had one thing in common, the application of computational methods to problems in their respective fields. As traditional conferences and journals gradually came around to seeing computational methods as valuable contributions in their own fields, they became more accepting of papers of this nature. Thus began the return of computational researchers back to their own discipline communities, shrinking the size of CIE conferences. Finally, in 1994, the CIE conference was colocated with Design Engineering Technical Conferences (DETC).The founders of CED debated the type of journal they needed to have. They felt that given the rapid evolution of computing technologies, an archival journal like an ASME Transactions was not appropriate. At the same time, they wanted their journal to be more technical than a trade magazine. They ended up creating a “hybrid” quarterly publication called CIME (Computers in Mechanical Engineering), with Ali Seirig as its editor. This magazine was produced in full color and was very informative about the latest developments in engineering software. In the words of the editor, CIME was “user-oriented” not “research oriented.” Unfortunately, this philosophy did not command much respect in academia and eventually CIME was merged into ASME’s monthly magazine Mechanical Engineering.And so it came to be that unlike all other ASME conferences and Divisions, CIE did not have any associated journal. Over the years, CIE leaders made several attempts at getting a Transactions journal approved, but to no avail. Reasons for rejection ranged from “computing technologies have no archival value” to the failure to sustain CIME magazine.In 2000, a small group of CIE Division “activists” decided to make another push for a journal. Yong Se Kim, David Lee, Simon Szykman, and David Rosen were the principals in this effort. They came up with a strategy based on lessons from past failures. That included building alliances with three other Divisions (Design, Manufacturing, and Systems &amp; Controls), and demonstrating that an editorial board could be formed with well known researchers who had extensive publication records. I became aware of this effort when I received a call out of the blue, asking me the intriguing question “How would you like to be the Chief Editor of an ASME Transactions?” Of course, the very next sentence brought me down to earth quickly “…the problem is that the journal doesn’t yet exist – will you help us get it approved by ASME?” Thus began my involvement with this journal. We put together an impressive editorial board that included two NAE members and research leaders in each of our targeted areas. Phil Divitero, ASME Director of Publications, immediately saw the marketing potential of this journal, and became a key ally. Bahram Ravani, DED Chair, gave valuable advice on writing our proposal to ASME. Art Erdman, himself a CIE pioneer, happened to be the Chair of ASME Publication Committee, which had authority of approving new journals, which gave us a much needed sympathetic ear on the committee to make our case. In a café in Chicago, before our presentation, we brainstormed various names for the journal and settled on Journal of Computing &amp; Information Science in Engineering (JCISE). The journal was approved and began publishing in the first year of the new millennium, 2001. The CIE Division finally had an archival journal of its own with three cosponsoring Divisions. In 2005, after much lobbying and deliberation, the Design Engineering Division became an equal partner with CIE—an important step in going mainstream.From the very beginning we decided to focus sharply on computational methods for mechanical product development. This set us apart from journals from private publishers that accepted everything and anything related to computing—from gaming to geology, from biology to every branch of engineering. We did not want to dilute our journal with such a wide and general scope. We stipulated that every paper submitted to JCISE must demonstrate applications of its techniques to mechanical design, mechanical analysis, product manufacturing, or quality assurance. Through several iterations we settled on eight major categories to include within the scope of our journal: solid modeling (including parametrics), computational geometry (including reverse engineering), computational metrology (including CMM and tolerance modeling), haptics and virtual reality, engineering informatics, simulation (including FEA, meshing, and optimization), AI/Knowledge based systems, and computer aided manufacturing. Given the practical nature of our field, we also decided to publish papers along two tracks: Research and Application. The latter has subcategories of Software Reviews, Technology Reviews, Tech Notes, and Industry Pilot Projects. The idea was to keep the journal relevant to industry as well as academia. We instituted a three-level rigorous review process for appointment of Associate Editors. We owe it to the founding editorial board for setting sound policies that resulted in quick recognition of JCISE as an archival publication of high quality. That group consisted of Paul Wright, David Rosen, Nick Patrikalakis, Deba Dutta, Susan Urban, Martti Mantyla, Dana Nau, S. Jayaram, Pradeep Khosla, Harry Cheng, and Ravi Rangan. Since we see ourselves as being at the intersection of computer science and mechanical engineering, it was appropriate to have about half of the AEs from each field, and we managed to do so.ACM (Association for Computing Machinery) approached us in 2001 to become an official cosponsor—an offer we gladly accepted in order to strengthen the linkage with our computer science colleagues. From 2001 to 2004, we published a special issue annually drawn from the best papers of the ACM Solid Modeling conferences. Unfortunately, this conference series became too broad, and it was difficult to accommodate their best papers in JCISE without violating our objective of serving the engineering community; this annual tradition of ACM special issues had to be discontinued.ISI included JCISE in its data collection in 2004; after 3 years of this process, the first Impact Factors for JCISE became available in 2007 (for the 2004–2006 period). With respect to ISI Impact Factors, JCISE ranks in the top third of all ASME Transactions; it is better than many long established journals in CAD/CAM and AI areas. Our Impact Factor has continued to improve each year. How meaningful are such statistics in gauging the quality of a journal is debatable. More meaningful metrics are in the offing and we hope they will supplant bean counters of today.When we opened shop in 2000, ASME did not have any web based tool for paper submission and review management. Being the journal focused on computing and information science, we refused to conduct paper reviews the old fashioned way and began developing eLane. With the help of one of our associate editors, Susan Urban, a database expert, and one of her brilliant students, Anish Shah (no relation), we designed and implemented eLane over a period of 3 years. For the past 10 years, we have hosted, maintained, and continuously improved eLane to support not only JCISE but also other journals, such as Research in Engineering Design, and CIE, DTM, and NSF Grantees conferences. eLane blazed a new trail and guided ASME to develop its own “Journal Tool.” Data security and confidentiality is a critical issue in online systems. I am particularly indebted to one of our founding associate editors, Simon Szykman, who provided valuable advice on security aspects of the system by constantly trying to enter the system through unintended holes. It is no surprise that Simon went on to become the first Director of the Cyber-Security group at US Department of Homeland Security and is now the CIO of the Department of Commerce.With Bahram Ravani taking over as the new chief editor of JCISE, we have begun the process of gradually migrating from eLane to ASME’s Journal Tool. Although the Journal Tool still lacks some functionality available in eLane, the reasons for migration are that this will provide greater visibility to JCISE through ASME websites, set JCISE at par with other Transactions, make it easier to transfer papers between ASME journals and, most importantly, have 24/7 support from ASME’s IT professionals.My tenure as chief editor is ending as it started, with a special issue providing snapshots of each of the technology areas within our scope. In both cases, I put together a wish list of papers and expert groups to co-author the state of art reviews. I had hoped to have every area covered, but some papers did not materialize this time around. Nevertheless, this special issue will be a good reference for most, if not all of the areas JCISE covers. For V1 N1, I invited each of our founding Associate Editors to write state-of-the-art surveys of their fields in collaboration with other experts in their respective areas. This special issue contains survey papers not only in some well-established CIE areas but also in a few emerging fields.Computational methods and information technologies related to engineering product development have come a long way. CAD, CAM, FEA, CFD, VR, Reverse Engineering, Computational Metrology, Optimization, and many other simulation techniques are now pervasive in industry. Even traditional fields, such as thermal science, fluid mechanics, and solid mechanics, have embraced numerical methods and computer visualization. What started on the fringes is now the mainstream. We owe it to the founders of the CED/CIE Division who saw this potential more than 30 years ago. Let us recognize Ali Seireg (Wisconsin), J. Callahan (McDonnell Douglas), V. Tipnis, T. Shoup (Santa Clara), D. Dietrich (Swanson), L. Hulbert (Battelle), E. Heer (NASA), S. Rhode (GM), R. Fulton (Georgia Tech), J.Cokonis (GE), R. Arvikar (Bell Labs), J. Lemon (SDRC), D. Riley (U. Minnesota), and R. Raghavan (Foster Wheeler).A high quality archival journal is extremely important to any research community. A conference alone cannot be sufficient. Conferences, at least in engineering, serve the purpose of quick dissemination of work in progress. Having an archival journal aids the maturation of a research community. Not all conference papers are suitable for archival in a journal. An additional complication in computing and IT is the rapid rate of development and consequent obsolescence of ideas and methods. What then should we archive? There certainly are many techniques in our field that have withstood the test of time. B-Rep solid models, B-splines, and NURBS, regularized Boolean algorithms, Attributed Adjacency Graph based feature recognition, and bipartite graphs for constraint solving are but a few examples. But most research is incremental, and it is important to archive snapshots of major milestones in each area. NURBS did not just come about suddenly. There were B-splines, rational B-splines before the idea of nonuniform knot spacing.JCISE associate editors serve 3 year terms, renewable for an additional 3. In addition to the founding group of AEs, I want to take this opportunity to thank all our current and past AEs. They are the ones that do the bulk of the work and get the credit for maintaining our high quality. I am very grateful to the following individuals: J. Michopoulos, K. Saitou, A. Goel, I. Grosse, K. Law, X. Qian, J. Oliver, S. McMains, S. Gao, A. Fischer, J. Vandenbrande, C. Geiger, Y. Kitamura, C. McMahon, A. Joneja, S. K. Gupta, R. Crawford, K. Lee, J. Corney, N. Dorighi, L. Joskowicz, and S. Callahan.I am sure that our new chief editor, Bahram Ravani, will take JCISE to new heights. My very best wishes to JCISE readers, authors, and reviewers. For me, this has been a labor of love.

The research investigates and advances strategies how to bridge the scale discrepancies between local, regional and global phenomena in climate models without the prohibitive computational costs of global cloud-resolving simulations. In particular, the research explores new frontiers in computational geoscience by introducing high-order Adaptive Mesh Refinement (AMR) techniques into climate research. AMR and statically-adapted variable-resolution approaches represent an emerging trend for atmospheric models and are likely to become the new norm in future-generation weather and climate models. The research advances the understanding of multi-scale interactions in the climate system and showcases a pathway how to model these interactions effectively with advanced computational tools, like the Chombo AMR library developed at the Lawrence Berkeley National Laboratory. The research is interdisciplinary and combines applied mathematics, scientific computing and the atmospheric sciences. In this research project, a hierarchy of high-order atmospheric models on cubed-sphere computational grids have been developed that serve as an algorithmic prototype for the finite-volume solution-adaptive Chombo-AMR approach. The foci of the investigations have lied on the characteristics of both static mesh adaptations and dynamically-adaptive grids that can capture flow fields of interest like tropical cyclones. Six research themes have been chosen. These are (1) the introduction of adaptive mesh refinement techniques into the climate sciences, (2) advanced algorithms for nonhydrostatic atmospheric dynamical cores, (3) an assessment of the interplay between resolved-scale dynamical motions and subgrid-scale physical parameterizations, (4) evaluation techniques for atmospheric model hierarchies, (5) the comparison of AMR refinement strategies and (6) tropical cyclone studies with a focus on multi-scale interactions and variable-resolution modeling. The results of this research project demonstrate significant advances in all six research areas. The major conclusions are that statically-adaptive variable-resolution modeling is currently becoming mature in the climate sciences, and that AMR holds outstanding promise for future-generation weather and climate models on high-performance computing architectures.

Topological rewriting and the geometrization of programming