Casimir forces for inhomogeneous planar media

Casimir forces arise from vacuum uctuations. They are fully understood only for simple models, and are important in nano- and microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases condence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green's functions is at the boundary of current computer algebra technology. We further demonstrate that Lifshitz theory of electromagnetic vacuum energy can not be directly applied to calculate the Casimir stress for models of this type, and produce results that have led to alternative regularisations. Using a combination of our new computational framework and the new theory based on our results, we provide specic calculations of Casimir forces for planar dielectrics having permittivity that declines exponentially. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and describe a combined numerical and symbolic computational framework for calculating Casimir forces for arbitrary planar models.Publisher PD

A Linear Programming Approach to Weak Reversibility and Linear Conjugacy of Chemical Reaction Networks

15 páginas, 2 figuras.-- The final publication is available at www.springerlink.comA numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and algebraic characteristics of weak reversibility to logical statements and solving the obtained set of linear (in)equalities in the framework of mixed integer linear programming. The unknowns in the problem are the reaction rate coefficients and the parameters of the linear conjugacy transformation. The efficacy of the approach is shown through numerical examples.Matthew D. Johnston and David Siegel acknowledge the support of D. Siegel’s Natural Sciences and Engineering Research Council of Canada Discovery Grant. Gàbor Szederkényi acknowledges the support of the Hungarian National Research Fund through grant no. OTKA K-83440 as well as the support of project CAFE (Computer Aided Process for Food Engineering) FP7-KBBE-2007-1 (Grant no: 212754).Peer reviewe

Planning and Patching Proof

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. We show how polynomial interpretations with negative coefficients, like x–1 for a unary function symbol or x–y for a binary function symbol, can be used to extend the class of rewrite systems that can be automatically proved terminating.Proceedings of the 7th International Conference, AISC 2004, Linz, Austria, September 22-24, 2004

Non-Standard Errors

In statistics, samples are drawn from a population in a data-generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence-generating process (EGP). We claim that EGP variation across researchers adds uncertainty: Non-standard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for better reproducible or higher rated research. Adding peer-review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants

Counting cases in substitope algorithms

We describe how to count the cases that arise in a family of visualization techniques, including Marching Cubes, Sweeping Simplices, Contour Meshing, Interval Volumes, and Separating Surfaces. Counting the cases is the first step toward developing a generic visualization algorithm to produce substitopes ( geometric substitutions of polytopes). We demonstrate the method using "GAP," a software system for computational group theory. The case-counts are organized into a table that provides a taxonomy of members of the family; numbers in the table are derived from actual lists of cases, which are computed by our methods. The calculations confirm previously reported case-counts for four dimensions that are too large to check by hand and predict the number of cases that will arise in substitope algorithms that have not yet been invented. We show how Polya theory produces a closed-form upper bound on the case counts.Publisher PDFPeer reviewe

On Vector Enumeration

AbstractWe develop further the linear Todd-Coxeter algorithm described previously. In particular, by slightly extending the algorithm, we obtain a simpler description of the calculation which it performs. We also describe an application of this method to a problem in computational representation theory, which itself has applications in algebraic topology and possibly other areas