Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

On Fermat's principle for causal curves in time oriented Finsler spacetimes

In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate the second variation of the time arrival functional along a geodesic in terms of the index form associated with the Finsler spacetime Lagrangian. Then the character of the critical points of the time arrival functional is investigated and a Morse index theorem in the context of Finsler spacetime is presented. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4765066]

Progress in the mathematical theory of quantum disordered systems

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition, including some joint work with Marchetti, the (quantum and classical) Edwards-Anderson (EA) spin-glass model and return to equilibrium for a class of spin-glass models, which includes the EA model initially in a very large transverse magnetic field. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770066]

Periodic averaging theorems for various types of equations

We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.

Co-metabolic models of Streptococcus thermophilus in co-culture with Lactobacillus bulgaricus or Lactobacillus acidophilus

To shed light on the interactions occurring in fermented milks when using co-cultures of Streptococcus thermophilus with Lactobacillus bulgaricus (StLb) or Lactobacillus acidophilus (StLa), a new co-metabolic model was proposed and checked either in the presence of Inulin as a prebiotic or not. For this purpose, the experimental data of concentrations of substrates and fermented products were utilized in balances of carbon, reduction degree and ATP. S. thermophilus exhibited always quicker growth compared to the other two microorganisms, while the percentage of lactose fermented to lactic acid, that of galactose metabolized, and the levels of diacetyl and acetoin formed strongly depended on the type of co-culture and the presence of inulin. The StLb co-culture led to higher acetoin and lower diacetyl levels compared to StLa, probably because of more reducing conditions or limited acetoin dehydrogenation. Inulin addition to StLa suppressed acetoin accumulation and hindered that of diacetyl, suggesting catabolite repression of alpha-acetolactate synthase expression in S. thermophilus. Both co-cultures showed the highest ATP requirements for biomass growth and maintenance at the beginning of fermentation, consistently with the high energy demand of enzyme induction during lag phase. Inulin reduced these requirements making biomass synthesis and maintenance less energy-consuming. Only a fraction of galactose was released from lactose, consistently with the galactose-positive phenotype of most dairy strains. The galactose fraction metabolized without inulin was about twice that in its presence, which suggests inhibition of the galactose transport system of S. thermophilus by fructose released from partial inulin hydrolysis. (C) 2012 Elsevier B.V. All rights reserved.