Conceptual modelling: Towards detecting modelling errors in engineering applications

Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems

NASA Center for Intelligent Robotic Systems for Space Exploration

NASA's program for the civilian exploration of space is a challenge to scientists and engineers to help maintain and further develop the United States' position of leadership in a focused sphere of space activity. Such an ambitious plan requires the contribution and further development of many scientific and technological fields. One research area essential for the success of these space exploration programs is Intelligent Robotic Systems. These systems represent a class of autonomous and semi-autonomous machines that can perform human-like functions with or without human interaction. They are fundamental for activities too hazardous for humans or too distant or complex for remote telemanipulation. To meet this challenge, Rensselaer Polytechnic Institute (RPI) has established an Engineering Research Center for Intelligent Robotic Systems for Space Exploration (CIRSSE). The Center was created with a five year $5.5 million grant from NASA submitted by a team of the Robotics and Automation Laboratories. The Robotics and Automation Laboratories of RPI are the result of the merger of the Robotics and Automation Laboratory of the Department of Electrical, Computer, and Systems Engineering (ECSE) and the Research Laboratory for Kinematics and Robotic Mechanisms of the Department of Mechanical Engineering, Aeronautical Engineering, and Mechanics (ME,AE,&M), in 1987. This report is an examination of the activities that are centered at CIRSSE

Quantum Trajectories, State Diffusion and Time Asymmetric Eventum Mechanics

We show that the quantum stochastic unitary dynamics Langevin model for continuous in time measurements provides an exact formulation of the Heisenberg uncertainty error-disturbance principle. Moreover, as it was shown in the 80's, this Markov model induces all stochastic linear and non-linear equations of the phenomenological "quantum trajectories" such as quantum state diffusion and spontaneous localization by a simple quantum filtering method. Here we prove that the quantum Langevin equation is equivalent to a Dirac type boundary-value problem for the second-quantized input "offer waves from future" in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the "trajectories of the output particles". This result supports the wave-particle duality in the form of the thesis of Eventum Mechanics that everything in the future is constituted by quantized waves, everything in the past by trajectories of the recorded particles. We demonstrate how this time arrow can be derived from the principle of quantum causality for nondemolition continuous in time measurements.Comment: 21 pages. See also relevant publications at http://www.maths.nott.ac.uk/personal/vpb/publications.htm

Unitary Representations of Wavelet Groups and Encoding of Iterated Function Systems in Solenoids

For points in $d$ real dimensions, we introduce a geometry for general digit sets. We introduce a positional number system where the basis for our representation is a fixed $d$ by $d$ matrix over \bz. Our starting point is a given pair $(A, \mathcal D)$ with the matrix $A$ assumed expansive, and $\mathcal D$ a chosen complete digit set, i.e., in bijective correspondence with the points in \bz^d/A^T\bz^d. We give an explicit geometric representation and encoding with infinite words in letters from $\mathcal D$. We show that the attractor $X(A^T,\mathcal D)$ for an affine Iterated Function System (IFS) based on $(A,\mathcal D)$ is a set of fractions for our digital representation of points in \br^d. Moreover our positional "number representation" is spelled out in the form of an explicit IFS-encoding of a compact solenoid \sa associated with the pair $(A,\mathcal D)$. The intricate part (Theorem \ref{thenccycl}) is played by the cycles in \bz^d for the initial $(A,\mathcal D)$-IFS. Using these cycles we are able to write down formulas for the two maps which do the encoding as well as the decoding in our positional $\mathcal D$-representation. We show how some wavelet representations can be realized on the solenoid, and on symbolic spaces