Representing the Electromagnetic Field: How Maxwell��s Mathematics Empowered Faraday��s Field Theory

James Clerk Maxwell ??translated?? Michael Faraday??s experimentally-based field theory into the mathematical representation now known as ??Maxwell??s Equations.?? Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday??s theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell??s procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell??s training in ??Cambridge University?? mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of ??experiments in the mind?? and for sophisticated representations of theory.     

Simulated tennis matchplay in a controlled environment

The aim of this study was to develop an exercise protocol to simulate tennis matchplay on a 'category 2' surface. Match analyses were used to form the basis for the design of the protocol. The protocol involved playing against a tennis ball serving machine. Part A of the protocol comprised 92 min 46 s of simulated tennis matchplay; Part B consisted of continuous hitting to the point of 'volitional fatigue' or when the required hitting frequency for two consecutive ball feeds could no longer be maintained. Ten elite tennis players (5 males, 5 females) volunteered to participate in the study, which was performed on an indoor tennis court (Matchplay?, En-Tout-Cas)?. Their age, body mass and estimated maximal oxygen uptake were as follows: males, 21.7±1.0 years, 73.6±2.6 kg and 58.0±1.7 ml?·?kg^?1?·?min^?1, respectively; females, 21.9±1.3 years, 62.3±2.0 kg and 42.2±0.7 ml?·?kg?·?min^?1, respectively (mean±). Heart rate, change in body mass and time to volitional fatigue were monitored. The heart rate responses of the participants to the simulated matchplay (range: 140-157 beats?·?min^?1, 73-81% peak heart rate) were consistent with the results of previous studies, for 'actual' matchplay. This protocol was successful in simulating similar physiological responses in Part A to 'actual' matchplay on a 'category 2' surface, in a controlled environment; it was also a sensitive evaluation tool of skilled performance in Part B. The current protocol may be used as a baseline protocol for studying the influence of, for example, training and dietary intervention on performance.