Quantifying the reheating temperature of the universe

The aim of this paper is to determine an exact definition of the reheat temperature for a generic perturbative decay of the inflaton. In order to estimate the reheat temperature, there are two important conditions one needs to satisfy: (a) the decay products of the inflaton must dominate the energy density of the universe, i.e. the universe becomes completely radiation dominated, and (b) the decay products of the inflaton have attained local thermodynamical equilibrium. For some choices of parameters, the latter is a more stringent condition, such that the decay products may thermalise much after the beginning of radiation-domination. Consequently, we have obtained that the reheat temperature can be much lower than the standard-lore estimation. In this paper we describe under what conditions our universe could have efficient or inefficient thermalisation, and quantify the reheat temperature for both the scenarios. This result has an immediate impact on many applications which rely on the thermal history of the universe, in particular gravitino abundance.Comment: Discussion improved. New section added. Version matches the one accepted for publicatio

Applications of recurrent neural networks in batch reactors. Part I: NARMA modelling of the dynamic behaviour of the heat transfer fluid

This paper is focused on the development of nonlinear models, using artificial neural networks, able to provide appropriate predictions when acting as process simulators. The dynamic behaviour of the heat transfer fluid temperature in a jacketed chemical reactor has been selected as a case study. Different structures of NARMA (Non-linear ARMA) models have been studied. The experimental results have allowed to carry out a comparison between the different neural approaches and a first-principles model. The best neural results are obtained using a parallel model structure based on a recurrent neural network architecture, which guarantees better dynamic approximations than currently employed neural models. The results suggest that parallel models built up with recurrent networks can be seen as an alternative to phenomenological models for simulating the dynamic behaviour of the heating/cooling circuits which change from batch installation to installation.Publicad

Applications of recurrent neural networks in batch reactors. Part II: Nonlinear inverse and predictive control of the heat transfer fluid temperature

Although nonlinear inverse and predictive control techniques based on artificial neural networks have been extensively applied to nonlinear systems, their use in real time applications is generally limited. In this paper neural inverse and predictive control systems have been applied to the real-time control of the heat transfer fluid temperature in a pilot chemical reactor. The training of the inverse control system is carried out using both generalised and specialised learning. This allows the preparation of weights of the controller acting in real-time and appropriate performances of inverse neural controller can be achieved. The predictive control system makes use of a neural network to calculate the control action. Thus, the problems related to the high computational effort involved in nonlinear model-predictive control systems are reduced. The performance of the neural controllers is compared against the self-tuning PID controller currently installed in the plant. The results show that neural-based controllers improve the performance of the real plant.Publicad

PNNARMA model: an alternative to phenomenological models in chemical reactors

This paper is focused on the development of non-linear neural models able to provide appropriate predictions when acting as process simulators. Parallel identification models can be used for this purpose. However, in this work it is shown that since the parameters of parallel identification models are estimated using multilayer feed-forward networks, the approximation of dynamic systems could be not suitable. The solution proposed in this work consists of building up parallel models using a particular recurrent neural network. This network allows to identify the parameter sets of the parallel model in order to generate process simulators. Hence, it is possible to guarantee better dynamic predictions. The dynamic behaviour of the heat transfer fluid temperature in a jacketed chemical reactor has been selected as a case study. The results suggest that parallel models based on the recurrent neural network proposed in this work can be seen as an alternative to phenomenological models for simulating the dynamic behaviour of the heating/cooling circuits.Publicad

Una reflexión sobre la modelación desde la construcción social del conocimiento matemático

Se reportan los avances de una revisión bibliográfica sobre el estatus de la modelación en la literatura especializada y en particular de los aportes desde la Socioepistemología. Centrándonos en un par de posturas que desde la construcción social del conocimiento matemático discuten sobre la modelación, evidenciamos diferencias y puntos de encuentro con la finalidad de avanzar hacia una caracterización de la función de dicha categoría. Se destaca que la noción de práctica social modifica las relaciones con el conocimiento y por lo tanto la base de los diseños en modelación y los productos que se generan de ésta. La presente revisión forma parte de una investigación en curso que pretende posicionar a la modelación como una base epistemológica para el diseño de situaciones de aprendizaje como material auxiliar que pueda ser utilizado en cursos de Profesionalización de docentes del nivel básico-secundaria en México