3,683 research outputs found
Interval modeling of dynamics for multibody systems
AbstractModeling of multibody systems is an important though demanding field of application for interval arithmetic. Interval modeling of dynamics is particularly challenging, not least because of the differential equations which have to be solved in the process. Most modeling tools transform these equations into a (non-autonomous) initial value problem, interval algorithms for solving of which are known. The challenge then consists in finding interfaces between these algorithms and the modeling tools. This includes choosing between “symbolic” and “numerical” modeling environments, transforming the usually non-autonomous resulting system into an autonomous one, ensuring conformity of the new interval version to the old numerical, etc. In this paper, we focus on modeling multibody systems’ dynamics with the interval extension of the “numerical” environment MOBILE, discuss the techniques which make the uniform treatment of interval and non-interval modeling easier, comment on the wrapping effect, and give reasons for our choice of MOBILE by comparing the results achieved with its help with those obtained by analogous symbolic tools
BioSimulator.jl: Stochastic simulation in Julia
Biological systems with intertwined feedback loops pose a challenge to
mathematical modeling efforts. Moreover, rare events, such as mutation and
extinction, complicate system dynamics. Stochastic simulation algorithms are
useful in generating time-evolution trajectories for these systems because they
can adequately capture the influence of random fluctuations and quantify rare
events. We present a simple and flexible package, BioSimulator.jl, for
implementing the Gillespie algorithm, -leaping, and related stochastic
simulation algorithms. The objective of this work is to provide scientists
across domains with fast, user-friendly simulation tools. We used the
high-performance programming language Julia because of its emphasis on
scientific computing. Our software package implements a suite of stochastic
simulation algorithms based on Markov chain theory. We provide the ability to
(a) diagram Petri Nets describing interactions, (b) plot average trajectories
and attached standard deviations of each participating species over time, and
(c) generate frequency distributions of each species at a specified time.
BioSimulator.jl's interface allows users to build models programmatically
within Julia. A model is then passed to the simulate routine to generate
simulation data. The built-in tools allow one to visualize results and compute
summary statistics. Our examples highlight the broad applicability of our
software to systems of varying complexity from ecology, systems biology,
chemistry, and genetics. The user-friendly nature of BioSimulator.jl encourages
the use of stochastic simulation, minimizes tedious programming efforts, and
reduces errors during model specification.Comment: 27 pages, 5 figures, 3 table
Research in applied mathematics, numerical analysis, and computer science
Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers
Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming
An approach for incorporating embedded simulation and analysis capabilities
in complex simulation codes through template-based generic programming is
presented. This approach relies on templating and operator overloading within
the C++ language to transform a given calculation into one that can compute a
variety of additional quantities that are necessary for many state-of-the-art
simulation and analysis algorithms. An approach for incorporating these ideas
into complex simulation codes through general graph-based assembly is also
presented. These ideas have been implemented within a set of packages in the
Trilinos framework and are demonstrated on a simple problem from chemical
engineering
Foundations of Multi-Paradigm Modelling for Cyber-Physical Systems
This open access book coherently gathers well-founded information on the fundamentals of and formalisms for modelling cyber-physical systems (CPS). Highlighting the cross-disciplinary nature of CPS modelling, it also serves as a bridge for anyone entering CPS from related areas of computer science or engineering. Truly complex, engineered systems—known as cyber-physical systems—that integrate physical, software, and network aspects are now on the rise. However, there is no unifying theory nor systematic design methods, techniques or tools for these systems. Individual (mechanical, electrical, network or software) engineering disciplines only offer partial solutions. A technique known as Multi-Paradigm Modelling has recently emerged suggesting to model every part and aspect of a system explicitly, at the most appropriate level(s) of abstraction, using the most appropriate modelling formalism(s), and then weaving the results together to form a representation of the system. If properly applied, it enables, among other global aspects, performance analysis, exhaustive simulation, and verification. This book is the first systematic attempt to bring together these formalisms for anyone starting in the field of CPS who seeks solid modelling foundations and a comprehensive introduction to the distinct existing techniques that are multi-paradigmatic. Though chiefly intended for master and post-graduate level students in computer science and engineering, it can also be used as a reference text for practitioners
A Taxonomy of Automatic Differential Tools
Many of the current automatic differentiation (AD) tools have similar characteristics. Unfortunately, it is often the case that the similarities between these various AD tools can not be easily ascertained by reading the corresponding documentation. To clarify this situation, a taxonomy of AD tools is presented. The taxonomy places AD tools into the Elemental, Extensional, Integral, Operational, and Symbolic classes. This taxonomy is used to classify twenty-nine AD tools. Each tool is examined individually with respect to the mode of differentiation used and the degree of derivatives computed. A list detailing the availability of the surveyed AD tools is provided as an appendix
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
A framework for mathematics curricula in engineering education: a report of the mathematics working group.
This document adapts the competence concept to the mathematical education of engineers and
explains and illustrates it by giving examples. It also provides information for specifying the extent to
which a competency should be acquired. It does not prescribe a particular level of progress for
competence acquisition in engineering education. There are many different engineering branches
and many different job profiles with various needs for mathematical competencies; consequently it is
not appropriate to specify a fixed profile. The competence framework serves as an analytical
framework for thinking about the current state in one’s own institution and also as a design
framework for specifying the intended profile. A sketch of an example profile for a practice-oriented
study course in mechanical engineering is given in the document. This document retains the list of
content-related learning outcomes (slightly modified) that formed the ‘kernel’ of the previous
curriculum document. These are still important because lecturers teaching application subjects want
to be sure that students have at least an ‘initial familiarity’ with certain mathematical concepts and
procedures which they need in their application modelling.
In order to offer helpful orientation for designing teaching processes, teaching and learning
environments and approaches are outlined which help students to obtain the competencies to an
adequate degree. It is clear that such competencies cannot be obtained by simply listening to lectures,
so adequate forms of active involvement of students need to be included. Moreover, in a
competence-based approach the mathematical education must be integrated in the surrounding
engineering study course to really achieve the ability to use mathematics in engineering contexts.
The document presents several forms of how this integration can be realized. This integration is
essential to the development of competencies and will require close co-operation between mathematics
academics and their engineering counterparts. Finally, since assessment procedures determine
to a great extent the behaviour of students, it is extremely important to address competency
acquisition in assessment schemes. Ideas for doing this are also outlined in the document.
The main purpose of this document is to provide orientation for those who set up concrete
mathematics curricula for their specific engineering programme, and for lecturers who think about
learning and assessment arrangements for achieving the intended level of competence acquisition. It
also serves as a framework for the group’s future work and discussions
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