10,460 research outputs found
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
Formalization of Transform Methods using HOL Light
Transform methods, like Laplace and Fourier, are frequently used for
analyzing the dynamical behaviour of engineering and physical systems, based on
their transfer function, and frequency response or the solutions of their
corresponding differential equations. In this paper, we present an ongoing
project, which focuses on the higher-order logic formalization of transform
methods using HOL Light theorem prover. In particular, we present the
motivation of the formalization, which is followed by the related work. Next,
we present the task completed so far while highlighting some of the challenges
faced during the formalization. Finally, we present a roadmap to achieve our
objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201
Exact Eigenfunctions of -Body system with Quadratic Pair Potential
We obtain all the exact eigenvalues and the corresponding eigenfunctions of
-body Bose and Fermi systems with Quadratic Pair Potentials in one
dimension. The originally existed first excited state level is missing in one
dimension, which results from the operation of symmetry or antisymmetry of
identical particles. In two and higher dimensions, we give all the eigenvalues
and the analytical ground state wave functions and the number of degeneracy.
Through the comparison with Avinash Khare's results, we have perfected his
results.Comment: 7 pages,1 figur
Students' epistemological framing in quantum mechanics problem solving
Students' difficulties in quantum mechanics may be the result of unproductive
framing and not a fundamental inability to solve the problems or misconceptions
about physics content. We observed groups of students solving quantum mechanics
problems in an upper-division physics course. Using the lens of epistemological
framing, we investigated four frames in our observational data: algorithmic
math, conceptual math, algorithmic physics, and conceptual physics. We discuss
the characteristics of each frame as well as causes for transitions between
different frames, arguing that productive problem solving may occur in any
frame as long as students' transition appropriately between frames. Our work
extends epistemological framing theory on how students frame discussions in
upper-division physics courses.Comment: Submitted to Physical Review -- Physics Education Researc
Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program
Computer programs may go wrong due to exceptional behaviors, out-of-bound
array accesses, or simply coding errors. Thus, they cannot be blindly trusted.
Scientific computing programs make no exception in that respect, and even bring
specific accuracy issues due to their massive use of floating-point
computations. Yet, it is uncommon to guarantee their correctness. Indeed, we
had to extend existing methods and tools for proving the correct behavior of
programs to verify an existing numerical analysis program. This C program
implements the second-order centered finite difference explicit scheme for
solving the 1D wave equation. In fact, we have gone much further as we have
mechanically verified the convergence of the numerical scheme in order to get a
complete formal proof covering all aspects from partial differential equations
to actual numerical results. To the best of our knowledge, this is the first
time such a comprehensive proof is achieved.Comment: N° RR-8197 (2012). arXiv admin note: text overlap with
arXiv:1112.179
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