Flows for rectangular matrix models

Several new results on the multicritical behavior of rectangular matrix models are presented. We calculate the free energy in the saddle point approximation, and show that at the triple-scaling point, the result is the same as that derived from the recursion formulae. In the triple-scaling limit, we obtain the string equation and a flow equation for arbitrary multicritical points. Parametric solutions are also examined for the limit of almost-square matrix models. This limit is shown to provide an explicit matrix model realization of the scaling equations proposed to describe open-closed string theory.Comment: 13 pages, LaTeX, McGill/93-2

Analyse de sensibilité paramétrique d'un modèle simulant le transport de pesticide dans le sol

Afin de protéger l'eau souterraine des pesticides épandus à la surface des sols agricoles, on doit être capable de prédire et d'évaluer a priori les risques de contamination. La modélisation mathématique, qui est basée sur la représentation des processus, s'avère être un outil à privilégier pour une telle prédiction. Cependant, la fiabilité des résultats de ces modèles est fonction de la précision et de la représentativité des différents paramètres d'entrée. A l'aide d'une analyse de sensibilité, il est possible d'évaluer l'impact de la variabilité de ces paramètres sur les résultats de la modélisation. Une étude de sensibilité menée avec le modèle Pesticide Rosit Zone Model (PRZM) a permis d'identifier les paramètres physiques d'entrée dont la variation apporte le plus de changements au niveau des principaux résultats, c'est-à-dire les paramètres d'entrée auxquels le modèle est le plus sensible. L'utilisation du coefficient de sensibilité relatif s'avère être à cet égard un outil de comparaison fort efficace dans le cadre d'une telle étude. Les paramètres d'apport en eau (précipitations) et en pesticide (taux d'application) sont ceux dont les variations provoquent le plus d'impact au niveau des résultais de la simulation. Egalement, les résultats des simulations sont aussi sensibles aux variations de la capacité au champ et de la densité du sol. La température, le point de flétrissement, ta profondeur d'évaporation et la dispersion sont des paramètres auxquels la modélisation est peu sensible.The ever increasing number of cases of groundwater contamination by pesticides has recently given rise to numerous experimental studies on the tale of these compounds within the soil-water system. In parallel with these experimental studies, the quick and intensive development of numerous simulation models bas emphasized the importance of the various factors and processes controlling the transport of pesticides in the unsaturated zone. The calibration and the validation of such deterministic models, which are especially used in groundwater management, requires the evaluation of several parameters related to the nature of the pesticide as well as to the pedologic and hydrogeological conditions of a given site. The reliability of results predicted by those models is mainly a function of the precision and the representativeness in the evaluation of those parameters at a specific site.The aim of this study was to evaluate the sensitivity of a simulation modes of pesticide movement in the unsaturated zone with regards to the variation in soil physical properties. More particularly, a sensitivity analysis was performed in order to determine the importance of the variation in these parameters with respect to simulation results obtained from the Pesticide Root Zone Model (PRZM). The spatial variability of the composition and structure of the soil, which comes from the site pedogenesis, is the main cause of the variability of the soil water distribution and of the soil transient properties. The sensitivity analysis of a model with respect to the variation in these parameters allows the evaluation of the impact of their representativeness on the model output results. Such an analysis thus allows the determination of an acceptable level of precision (or error) for which an increase of precision in the evaluation of a parameter does not anymore correspond to a significant gain in the representativeness of the model results. It also permits the estimation of the impact of a potential variation of a parameter on the prediction of pesticide transport in the unsaturated zone.The deterministic PRZM modal used in this study has been developed by the US-EPA and devoted to pesticide application on agricultural sites. This modal evaluates the pesticide leaching towards groundwater with respect to the type of culture and pesticide used, the climatic conditions, the soil characteristics and some agricultural practices. Output results from the model can he expressed in concentrations or masses of pesticide, in fluxes or cumulated quantities. Simulations were performed using characteristics and data of the Portneuf region (Quebec). This area of potato farming was until recently one of the Quebec most important sites for aldicarb application before the recommendation of its non use. Cultivated surfaces, which are rather homogeneous, consist of medium-size sand. Simulations were performed river a ten year period (1974 to 1984), implying one application of pesticide a1 the seed-time, and a trop for each year.The parameters of water and pesticide inputs (rain and application rates) are those that induce the higher impact on the simulation results. The simulation results were also influenced by the variation of the field capacity and of the soil bulk density. Temperature, wilting point, maximum evaporation depth and dispersion are the input parameters for which the PRZM model is the less sensitive. The simulation results of pesticide transport, which ultimately consist in predicting the groundwater contamination, are very sensitive to the variations of some physical parameters for which the precision and the representativeness in the measured values are thus very important for the reliability of the results. Considering the spatial variability of a site characteristics, the representativeness of these results is very uncertain if a limited number of data is used in order to determine the mean value. A particular attention has to be focused on the parameters that induce the higher sensitivity of the model. Finally, such a sensitivity analysis shows that a stochastic approach in modelling the solute transport through soil can be a good alternative to take into account the variability of parameters encountered in field situations

Face the Music and Glance: How Nonverbal Behaviour Aids Human Robot Relationships Based in Music

It is our hypothesis that improvised musical interaction will be able to provide the extended engagement often failing others during long term Human Robot Interaction (HRI) trials. Our previous work found that simply framing sessions with their drumming robot Mortimer as social interactions increased both social presence and engagement, two factors we feel are crucial to developing and maintaining a positive and meaningful relationship between human and robot. For this study we investigate the inclusion of the additional social modalities, namely head pose and facial expression, as nonverbal behaviour has been shown to be an important conveyor of information in both social and musical contexts. Following a 6 week experimental study using automatic behavioural metrics, results demonstrate those subjected to nonverbal behaviours not only spent more time voluntarily with the robot, but actually increased the time they spent as the trial progressed. Further, that they interrupted the robot less during social interactions and played for longer uninterrupted. Conversely, they also looked at the robot less in both musical and social contexts. We take these results as support for open ended musical activity providing a solid grounding for human robot relationships and the improvement of this by the inclusion of appropriate nonverbal behaviours

Constraints on non-minimally coupled curved space electrodynamics from astrophysical observations

We study interactions of electro-magnetic fields with the curvature tensor of the form $\lambda R_{\mu \nu \alpha \beta}F^{\mu \nu}F^{\alpha \beta}$. Such coupling terms though are invariant under general coordinate transformation and CPT, however violate the Einstein equivalence principle. These couplings do not cause any energy dependent dispersion of photons but they exhibit birefringence. We put constraints on the coupling constant $\lambda$ using results from solar system radar ranging experiments and millisecond-pulsar observations. We find that the most stringent constraint comes from pulsar observations and is given by $\lambda < 10^{11} cm^2$ obtained from the timing of binary pulsar PSR B1534+12.Comment: 9 pages latex, accepted in CQ

Self-dual gravity and self-dual Yang-Mills in the context of Macdowell-Mansouri formalism

In this work we propose an action which unifies self-dual gravity and self-dual Yang-Mills in the context of the Macdowell-Mansouri formalism. We claim that such an action may be used to find the S-dual action for both self-dual gravity and self-dual Yang-Mills.Comment: 8 pages, Revtex, no figures, submitted to Phys. Rev.

Black Hole Entropy without Brick Walls

We present evidence which confirms a suggestion by Susskind and Uglum regarding black hole entropy. Using a Pauli-Villars regulator, we find that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula, S=\A/(4G). Our calculation also yields a constant contribution to the black hole entropy, a contribution associated with the one-loop renormalization of higher curvature terms in the gravitational action.Comment: 15 pages, plain LaTex minor additions including some references; version accepted for publicatio