Equivalent theories of liquid crystal dynamics

There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to show that the micropolar theory comprises the director theory. In this paper we show that this is the case by using symmetry reduction techniques and introducing a new system that is equivalent to the Ericksen-Leslie equations and includes disclination dynamics. The resulting equations of motion are verified to be completely equivalent, although one of the two different reductions offers the possibility of accounting for orientational defects. After applying these two approaches to the ordered micropolar theory of Lhuiller and Rey, all the results are eventually extended to flowing complex fluids, such as nematic liquid crystals.Comment: 37 pages. To Appear in Arch. Ration. Mech. Ana

Neuroprediction and A.I. in Forensic Psychiatry and Criminal Justice: A Neurolaw Perspective

Advances in the use of neuroimaging in combination with A.I., and specifically the use of machine learning techniques, have led to the development of brain-reading technologies which, in the nearby future, could have many applications, such as lie detection, neuromarketing or brain-computer interfaces. Some of these could, in principle, also be used in forensic psychiatry. The application of these methods in forensic psychiatry could, for instance, be helpful to increase the accuracy of risk assessment and to identify possible interventions. This technique could be referred to as ‘A.I. neuroprediction,’ and involves identifying potential neurocognitive markers for the prediction of recidivism. However, the future implications of this technique and the role of neuroscience and A.I. in violence risk assessment remain to be established. In this paper, we review and analyze the literature concerning the use of brain-reading A.I. for neuroprediction of violence and rearrest to identify possibilities and challenges in the future use of these techniques in the fields of forensic psychiatry and criminal justice, considering legal implications and ethical issues. The analysis suggests that additional research is required on A.I. neuroprediction techniques, and there is still a great need to understand how they can be implemented in risk assessment in the field of forensic psychiatry. Besides the alluring potential of A.I. neuroprediction, we argue that its use in criminal justice and forensic psychiatry should be subjected to thorough harms/benefits analyses not only when these technologies will be fully available, but also while they are being researched and developed

Modeling microalgae cell mass distributions using the Fokker-Planck equation

The modeling of the cell mass distribution for microalgae growth processes is addressed using the Fokker-Planck equation for a stochastic logistic growth model of a single cell. Relations between the proposed model and the classical Droop model used for mass-balance based modeling of the algae growth are established. The proposed model is evaluated using experimentally obtained cell mass distribution data for the microalgae Chlamydomonas reinhardtti showing a good correspondence between measurements and model predictions. The obtained model is considerably simpler in comparison to cell mass population balance models used so far to describe the temporal behavior of the cell mass distribution

A geometric observer-assisted approach to tailor state estimation in a bioreactor for ethanol production

In this work, a systematic approach based on the geometric observer is proposed to design a model-based soft sensor, which allows the estimation of quality indexes in a bioreactor. The study is focused on the structure design problem where the set of innovated states has to be chosen. On the basis of robust exponential estimability arguments, it is found that it is possible to distinguish all the unmeasured states if temperature and dissolved oxygen concentration measurements are combined with substrate concentrations. The proposed estimator structure is then validated through numerical simulation considering two different measurement processor algorithms: the geometric observer and the extended Kalman filter

Holonomy and vortex structures in quantum hydrodynamics

In this paper we consider a new geometric approach to Madelung's quantum hydrodynamics (QHD) based on the theory of gauge connections. Unlike previous approaches, our treatment comprises a constant curvature thereby endowing QHD with intrinsic non-zero holonomy. In the hydrodynamic context, this leads to a fluid velocity which no longer is constrained to be irrotational and allows instead for vortex filaments solutions. After exploiting the Rasetti-Regge method to couple the Schr\"odinger equation to vortex filament dynamics, the latter is then considered as a source of geometric phase in the context of Born-Oppenheimer molecular dynamics. Similarly, we consider the Pauli equation for the motion of spin particles in electromagnetic fields and we exploit its underlying hydrodynamic picture to include vortex dynamics.Comment: 34 pages, no figures. To appear in Math. Sci. Res. Inst. Pub

Different control strategies for a yeast fermentation bioreactor

Biological systems are usually highly sensitive to process conditions variations, such as temperature, pH, substrate concentration. For this reason, it is important to adequately control and monitor the process in order to guaranteeing product quality while maintaining adequate performance and productivity. The production of ethanol by fermentation is certainly one of the most important industrial bioprocesses, being ethanol an alternative source of energy. For this reason, valuable models of this process based on different kinetic considerations are available in literature, and they can be considered a valid benchmark to investigate control system and estimation techniques for biological reactors. Three different control strategies have been analysed: direct reactor temperature control, cascade control where the primary loop uses delayed ethanol measurements, and 2x2 control system with inferential control for the product concentration. The proposed configurations have been compared at different operating conditions and results show that the use of the inferential control is the most effective in case of severe disturbances

Modeling a biological reactor using sparse identification method

In this work a model-based controller for a fermentation bioreactor has been developed. By simulating the model of the process that acts as a virtual plant, input-output data have been generated and used to identify the system using sparse identification of nonlinear dynamics methodology. The obtained model is then used in a model-based algorithm to control the bioreactor temperature, where the manipulated action is obtained as a result of a constrained nonlinear optimization problem which minimizes the mismatch between the predicted trajectory and the desired one. Good performances have been obtained by applying the proposed control strategy for set-point changes and disturbance rejection

A Model-Based methodology to support the Space System Engineering (MBSSE)

International audienceThis paper presents a model based methodology that relies on the sound basis of the most recent and widespread applicable system engineering standards and model based practices, The methodology has been defined to support domain specific space system engineering standards and practices and assessed through the application on industrial case studies. A complementary formal verification approach has also been experimented

Adaptive feedback control for a pasteurization process

The milk pasteurization process is nonlinear in nature, and for this reason, the application of linear control algorithms does not guarantee the obtainment of the required performance in every condition. The problem is here addressed by proposing an adaptive algorithm, which was obtained by starting from an observer-based control approach. The main result is the obtainment of a simple PI-like controller structure, where the control parameters depend on the state of the system and are adapted online. The proposed algorithm was designed and applied on a simulated process, where the temperature dependence of the milk's physical properties was considered. The control strategy was tested by simulating different situations, particularly when time-varying disturbances entered the system. The use of the adaptive rule reduces the variance generally introduced by the PI or PID controller

On the dynamics and robustness of the chemostat with multiplicative noise

The stochastic dynamics of a two-state bioreactor model with random feed flow fluctuations and non-monotonic specific growth rate is analyzed. Using the Fokker-Planck equation approach for describing the probability density function (PDF) evolution the lack of stochastic robustness due to deterministic bifurcation phenomena for the open-loop reactor operating under optimal (maximum production) operation condition is established, and the associated stochastic stabilization problem is addressed. Inherent differences between the presence of multiplicative noise, due to the feed flow fluctuations, and additive background noise are analytically established. Numerical simulation results illustrate these inherent differences, the stochastic fragility of the open-loop operation yielding a stochastic extinction phenomenon, as well as the stochastic PDF stabilization with a proportional feedback control