The SLH framework for modeling quantum input-output networks

Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving correction

Kinetic Intersections as a Source of Information on Rate Coefficients

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Optimal modularity and memory capacity of neural reservoirs

The neural network is a powerful computing framework that has been exploited by biological evolution and by humans for solving diverse problems. Although the computational capabilities of neural networks are determined by their structure, the current understanding of the relationships between a neural network's architecture and function is still primitive. Here we reveal that neural network's modular architecture plays a vital role in determining the neural dynamics and memory performance of the network of threshold neurons. In particular, we demonstrate that there exists an optimal modularity for memory performance, where a balance between local cohesion and global connectivity is established, allowing optimally modular networks to remember longer. Our results suggest that insights from dynamical analysis of neural networks and information spreading processes can be leveraged to better design neural networks and may shed light on the brain's modular organization

Fractional vs. ordinary control systems: What does the fractional derivative provide?

[EN] The concept of a fractional derivative is not at all intuitive, starting with not having a clear geometrical interpretation. Many different definitions have appeared, to the point that the need for order has arisen in the field. The diversity of potential applications is even more overwhelming. When modeling a problem, one must think carefully about what the introduction of fractional derivatives in the model can provide that was not already adequately covered by classical models with integer derivatives. In this work, we present some examples from control theory where we insist on the importance of the non-local character of fractional operators and their suitability for modeling non-local phenomena either in space (action at a distance) or time (memory effects). In contrast, when we encounter completely different nonlinear phenomena, the introduction of fractional derivatives does not provide better results or further insight. Of course, both phenomena can coexist and interact, as in the case of hysteresis, and then we would be dealing with fractional nonlinear models.Conejero, JA.; Franceschi, J.; Picó-Marco, E. (2022). Fractional vs. ordinary control systems: What does the fractional derivative provide?. Mathematics. 10(15):1-18. https://doi.org/10.3390/math10152719118101

Model Predictive Control Strategies for Advanced Battery Management Systems

Consumer electronics, wearable and personal health devices, power networks, microgrids, and hybrid electric vehicles (HEVs) are some of the many applications where Lithium-ion (Li-ion) batteries are employed. From a manufacturer point of view, the optimal design and management of such electrochemical accumulators are important aspects for ensuring safe and profitable operations. The adoption of mathematical models can support the achievement of the best performance, while saving time and money. In the literature, all the models used to describe the behavior of a Li-ion battery belong to one of the two following families: (i) Equivalent Circuit Models (ECMs), and (ii) Electrochemical Models (EMs). While the former family represents the battery dynamics by means of electrical circuits, the latter resorts to first principles laws of modeling. As a first contribution, this Thesis provides a thorough investigation of the pseudo-two-dimensional (P2D) Li-ion battery EM. In particular, the objectives are to provide: (i) a detailed description of the model formulation, (ii) the Li-ION SIMulation BAttery (LIONSIMBA) toolbox as a finite volume Matlab implementation of the P2D model, for design, simulation, and control of Li-ion cells or battery packs, (iii) a validation of the proposed tool with respect to the COMSOL MultiPhysics commercial software and the Newman's DUALFOIL code, and (iv) some demonstrative simulations involving thermal dynamics, a hybrid charge-discharge cycle emulating the throttle of an HEV, and a battery pack of series connected cells. The second contribution is related to the development of several charging strategies for Advanced Battery Management Systems (ABMSs), where predictive approaches are employed to attain optimal control. Model Predictive Control (MPC) refers to a particular family of control algorithms that, according to a mathematical model, predicts the future behavior of a plant, while considering inputs and outputs constraints. According to this paradigm, in this Thesis different ABMSs strategies have been developed, and their effectiveness shown through simulations. Due to the complexity of the P2D model, its inclusion within an MPC context could prevent the online application of the control algorithm. For this reason, different approximations of the P2D dynamics are proposed and their MPC formulations carefully explained. In particular, finite step response, autoregressive exogenous, piecewise affine, and linear time varying approximations are presented. For all the aforementioned reformulations, the closed-loop performance are evaluated considering the P2D implementation of LIONSIMBA as the real plant. The closed-loop simulations highlight the suitability of the MPC paradigm to be employed for the development of the future ABMSs. In fact, its ability to predict the future behavior of the cell while considering operating constraints can help in preventing possible safety issues and improving the charging performance. Finally, the reliability and efficiency of the proposed Matlab toolbox in simulating the P2D dynamics, support the idea that LIONSIMBA can significantly contribute in the advance of the battery field.Consumer electronics, wearable and personal health devices, power networks, microgrids, and hybrid electric vehicles (HEVs) are some of the many applications where Lithium-ion (Li-ion) batteries are employed. From a manufacturer point of view, the optimal design and management of such electrochemical accumulators are important aspects for ensuring safe and profitable operations. The adoption of mathematical models can support the achievement of the best performance, while saving time and money. In the literature, all the models used to describe the behavior of a Li-ion battery belong to one of the two following families: (i) Equivalent Circuit Models (ECMs), and (ii) Electrochemical Models (EMs). While the former family represents the battery dynamics by means of electrical circuits, the latter resorts to first principles laws of modeling. As a first contribution, this Thesis provides a thorough investigation of the pseudo-two-dimensional (P2D) Li-ion battery EM. In particular, the objectives are to provide: (i) a detailed description of the model formulation, (ii) the Li-ION SIMulation BAttery (LIONSIMBA) toolbox as a finite volume Matlab implementation of the P2D model, for design, simulation, and control of Li-ion cells or battery packs, (iii) a validation of the proposed tool with respect to the COMSOL MultiPhysics commercial software and the Newman's DUALFOIL code, and (iv) some demonstrative simulations involving thermal dynamics, a hybrid charge-discharge cycle emulating the throttle of an HEV, and a battery pack of series connected cells. The second contribution is related to the development of several charging strategies for Advanced Battery Management Systems (ABMSs), where predictive approaches are employed to attain optimal control. Model Predictive Control (MPC) refers to a particular family of control algorithms that, according to a mathematical model, predicts the future behavior of a plant, while considering inputs and outputs constraints. According to this paradigm, in this Thesis different ABMSs strategies have been developed, and their effectiveness shown through simulations. Due to the complexity of the P2D model, its inclusion within an MPC context could prevent the online application of the control algorithm. For this reason, different approximations of the P2D dynamics are proposed and their MPC formulations carefully explained. In particular, finite step response, autoregressive exogenous, piecewise affine, and linear time varying approximations are presented. For all the aforementioned reformulations, the closed-loop performance are evaluated considering the P2D implementation of LIONSIMBA as the real plant. The closed-loop simulations highlight the suitability of the MPC paradigm to be employed for the development of the future ABMSs. In fact, its ability to predict the future behavior of the cell while considering operating constraints can help in preventing possible safety issues and improving the charging performance. Finally, the reliability and efficiency of the proposed Matlab toolbox in simulating the P2D dynamics, support the idea that LIONSIMBA can significantly contribute in the advance of the battery field

Analog, hybrid, and digital simulation

Analog, hybrid, and digital computerized simulation technique

Bright bichromatic entanglement and quantum dynamics of sum frequency generation

We investigate the quantum properties of the well-known process of sum frequency generation, showing that it is potentially a very useful source of non-classical states of the electromagnetic field, some of which are not possible with the more common techniques. We show that it can produce quadrature squeezed light, bright bichromatic entangled states and symmetric and asymmetric demonstrations of the Einstein-Podolsky-Rosen paradox. We also show that the semiclassical equations totally fail to describe the mean-field dynamics when the cavity is strongly pumped