On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond.
We study the behavior of the chemical reactions A+A-->A+S and A+A-->S+S (where the reactive species A and the inert species S are both assumed to be immobile) embedded on Bethe lattices of arbitrary coordination number z and on a two-dimensional (2D) square lattice. For the Bethe lattice case, exact solutions for the coverage in the A species in terms of the initial condition are obtained. In particular, our results hold for the important case of an infinite one-dimensional (1D) lattice (z=2). The method is based on an expansion in terms of conditional probabilities which exploits a Markovian property of these systems. Along the same lines, an approximate solution for the case of a 2D square lattice is developed. The effect of dilution in a random initial condition is discussed in detail, both for the lattice coverage and for the spatial distribution of reactants.
Fractal reaction kinetics: exciton fusion on clusters
Etude de reactions bimoleculaires ou pseudo-monomoleculaires de marcheurs aleatoires dans de grands agregats, au moyen d'equations de vitesse simples, resolvables analytiquement. La variation temporelle du coefficient de vitesse est simple: K(t)∞t −h ou 1≥h≥0 et h=1-f ou 2f est la dimension «fracton» effective de Alexander et Orbach, h, mesure le degre d'heterogeneite locale
Inferring Learning Strategies from Students ’ Errors
Student models in an Intelligent Tutoring System (ITS) aim at representing both correct and incorrect knowledge of the student in a particular domain of learning. This data serves as the basis upon which the Tutor can dispense remedial feedback. This paper presents a framework in which learners’ errors are diagnosed, classified and linked to cognitive processes associated with learning. The cognitive processes we identify are those of generalization, misattribution and ignorance. Our system applies to the domain of Second Language Acquisition and our approach uses Chomsky’s linguistic theory of Principles and Parameters. We particularly concentrate on the acquisition of the Phrase Structure component.