Papers by Antonio Palacios
AIP Conference Proceedings, 2004
We present theoretical and experimental investigations of the fundamental idea that coupling-indu... more We present theoretical and experimental investigations of the fundamental idea that coupling-induced oscillations can enhance the sensitivity of an array of magnetic sensors. In particular, we consider arrays made up of fluxgate magnetometers inductively coupled through electronic circuits. The underlying dynamics of the coupled system is more complicated as it shows new spatio-temporal features that are not observed in a single fluxgate. Among these new features, self-induced oscillations in the form of a traveling wave pattern are of particular interest because they can lead to higher sensitivity levels at reduced costs. Details of the experiments, a new signal detection mechanism, and results from numerical bifurcation analyzes are described in this work.
The coupled-core fluxgate magnetometer (CCFM) is a magnetic sensor, which is an improvement upon ... more The coupled-core fluxgate magnetometer (CCFM) is a magnetic sensor, which is an improvement upon the single fluxgate sensor in signal measurement sensitivity. The proper operation of the CCFM requires oscillatory behavior in the dynamics of the device to drive it in and out of saturation. Though the dynamical equations well approximate the behavior of the actual device, a small time delay in the coupling is assumed due to finite signal transmission times. The simplest case of a CCFM system exhibiting oscillations (three coupled cores) is studied. The corresponding system of equations exhibits rich dynamical behavior in the region of operation of the device. It is determined in this region that a stable limit cycle and two nontrivial synchronous equilibria have large basins of attraction. The size of this basin of attraction varies for different values of coupling strength and time delay. For a small continuous band of values of the coupling strength (lambda), sufficiently increasing...
Symmetry, 2015
A large class of dynamic sensors have nonlinear input-output characteristics, often corresponding... more A large class of dynamic sensors have nonlinear input-output characteristics, often corresponding to a bistable potential energy function that controls the evolution of the sensor dynamics. These sensors include magnetic field sensors, e.g., the simple fluxgate magnetometer and the superconducting quantum interference device (SQUID), ferroelectric sensors and mechanical sensors, e.g., acoustic transducers, made with piezoelectric materials. Recently, the possibilities offered by new technologies and materials in realizing miniaturized devices with improved performance have led to renewed interest in a new generation of inexpensive, compact and low-power fluxgate magnetometers and electric-field sensors. In this article, we review the analysis of an alternative approach: a symmetry-based design for highly-sensitive sensor systems. The design incorporates a network architecture that produces collective oscillations induced by the coupling topology, i.e., which sensors are coupled to each other. Under certain symmetry groups, the oscillations in the network emerge via an infinite-period bifurcation, so that at birth, they exhibit a very large period of oscillation. This characteristic renders the oscillatory wave highly sensitive to symmetry-breaking effects, thus leading to a new detection mechanism. Model equations and bifurcation analysis are discussed in great detail. Results from experimental works on networks of fluxgate magnetometers are also included.
Procedia IUTAM, 2012
In this paper we discuss the existence and stability of heteroclinic cycles in coupled systems an... more In this paper we discuss the existence and stability of heteroclinic cycles in coupled systems and show how they can be exploited to design and fabricate a new generation of highly-sensitive, low-powered, sensor devices. More specifically, we present theoretical and experimental proof of concept that coupling-induced oscillations located near the bifurcation point of a heteroclinic cycle can significantly enhance the sensitivity of an array of magnetic sensors. In particular, we consider arrays made up of fluxgate magnetometers inductively coupled through electronic circuits.
Nonlinear Theory and Its Applications, IEICE, 2012
Theoretical and experimental works have shown that coupling similar overdamped bistable systems c... more Theoretical and experimental works have shown that coupling similar overdamped bistable systems can lead, under certain conditions that depend on the topology of connections and the number of units, to self-induced large-amplitude oscillations that emerge through a global bifurcation of heteroclinic connections between saddle-node equilibria. We have exploited this fundamental feature to model, design, and fabricate a new generation of highly-sensitive, low-powered, sensor devices, mainly detectors of magnetic-and electric-fields. In this article we review the fundamental principles and methods behind this new paradigm. These principles are device-independent so they can be readily adapted to a wide range of sensors, such as acoustic and gyroscopic sensors among many types. In this manuscript we describe the design and fabrication of a new class of highly-sensitive fluxgate-and electric-field magnetometers as a case study to review basic ideas and methods.
International Journal of Bifurcation and Chaos, 2014
The fundamental principle of bistability is widely used across various disciplines, including bio... more The fundamental principle of bistability is widely used across various disciplines, including biology, chemistry, mechanics, physics, electronics and materials science. As the need for more powerful, efficient and sensitive complex-engineered systems grow, networks of coupled bistable systems have gained significant attention in recent years. Modeling and analysis of such higher-dimensional systems is usually focused on finding conditions for the existence and stability of typical invariant sets, i.e. steady states, periodic solutions and chaotic sets. High-dimensionality leads to complex patterns of collective behavior. Which type of behavior is exhibited by a network depends greatly on the initial conditions. Thus, it is also important to study the geometric structure and evolution of the basins of attraction of such patterns. In this manuscript, a complete study of the basins of attraction of a ring of bistable systems, coupled unidirectionally, is presented. 3D visualizations ar...
SPIE Proceedings, 2014
In this report, we report the investigation of energy harvesting with coupled resonators while us... more In this report, we report the investigation of energy harvesting with coupled resonators while using magnetostrictive material called Galfenol. Galfenol is an alloy iron with an approximate concentration of iron and gallium as 83 and 17%, respectively. Here, we describe a coupled system of meso-scale (1-to 10-cm) cantilever beams. The coupled system can be used for harvesting vibration energy to power and aid the performance of low-power wireless sensor nodes. The report is organized as follows. First we introduce the model of the transducer with Galfenol as the magnetostrictive material. Here, we discuss the model parameters derived from the experiment and show the simulations of a single beam. This is followed by the design of the power converters that are best suited for this device. Next, we analyze an all-to-all coupled system. Finally, we draw conclusions and describe the future course of the research.
In our ongoing work (on the single core fluxgate as well as the CCFM) we rely on a readout mechan... more In our ongoing work (on the single core fluxgate as well as the CCFM) we rely on a readout mechanism, based on a threshold crossing strategy, that consists of measuring the "residence times" of the ferromagnetic core(s) in the two stable states of the potential energy function. When the potential energy function is skewed due to the presence of a target dc signal, the residence times are no longer equal. Then either their difference or ratio can be used to quantify the signal. The sensitivity of this residence times distribution (RTD) based readout has been shown to increase with lowered bias frequency and amplitude; these conditions are the opposite of the requirements for enhancing sensitivity in traditional readouts, so that lower onboard power as well as far simpler electronics can be implemented, with benefit, for this (time domain based) readout strategy. Background of Dynamics: Standard Orientation A conventional (i.e. single core) fluxgate magnetometer can be treat...
Journal of Applied Physics, 2013
The public reporting burden for this collection of information is estimated to average 1 hour per... more The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports,
IEEE Transactions on Applied Superconductivity, 2013
We develop a two-dimensional (2D) Superconducting Quantum Interference Filter (SQIF) array based ... more We develop a two-dimensional (2D) Superconducting Quantum Interference Filter (SQIF) array based on recently introduced high-linearity tri-junction bi-SQUIDs. Our bi-SQUID SQIF array design is based on a tight integration of individual bi-SQUID cells sharing inductances with adjacent cells. We provide extensive computer simulations, analysis and experimental measurements, in which we explore the phase dynamics and linearity of the array voltage response. The non-uniformity in inductances of the bi-SQUIDs produces a pronounced zero-field single antipeak in the voltage response. The anti-peak linearity and size can be optimized by varying the critical current of the additional junction of each bi-SQUID. The layout implementation of the tight 2D array integration leads to a distinct geometrical diamond shape formed by the merged dual bi-SQUID cells. Different size 2D arrays are fabricated using standard HYPRES niobium 4.5 kA/cm 2 fabrication process. The measured linearity, power gain, and noise properties will be analyzed for different array sizes and the results will be compared with circuit simulations. We will discuss a design approach for the electrically small magnetic field antenna and low-noise amplifiers with high bandwidth based on these 2D bi-SQUID SQIF arrays. The results from this work will be used to design chips densely and completely covered in bi-SQUIDs that has optimized parameters such as linearity and power gain.
Understanding Complex Systems
Coupled-Core Fluxgate Magnetometer Magnetic sensors are inherently nonlinear systems, which have ... more Coupled-Core Fluxgate Magnetometer Magnetic sensors are inherently nonlinear systems, which have been been used over many years to detect weak magnetic signals for a wide variety of applications. For instance: biomedical tracking of magnetic particles, e.g., MRI machines commonly used for diagnosing multiple sclerosis, brain tumors, and spinal infections; geological equipment, e.g., NASA explorers; homeland defense, e.g., detection of mines and explosives. Using ideas and methods from nonlinear dynamics research in Engineering, Mathematics, and Physics, we show that higher sensitivity, lower power consumption, and reduced costs, can all be achieved through an integrating approach that combines a new sensing technique, the Residence Time Detection (RTD), with a novel Network Sensor Architecture, where the power of multiple sensors is integrated into a single system, see Fig. 2.1. We demonstrate [168, 261, 262] that under the proposed approach, fluxgates magnetometers, in particular, can become very competitive against the most sensitive of all sensors, the SQUID (Superconducting Quantum Interference Devices), at a fraction of the cost and size of SQUIDs. The ideas are model-independent, so they can be used to enhance the performance of many other type of sensors such as electric field sensors and gyroscopes. 2.1 Fluxgate Technology Early development of fluxgate magnetometers started around World War II, when fluxgate sensors were used by airborne magnetic surveys and for the detection of submarines. They were further developed for geomagnetic studies and mineral prospecting, and later for work on the Moon [105], for magnetic measurement in outer space [290, 344, 365], and for many other applications [158, 169, 312] as well. Readers interested in the advances of fluxgates are referred to the article in [151].
Sustainability, 2021
The chief objective of this research was to analyze how the industrial heritage of three European... more The chief objective of this research was to analyze how the industrial heritage of three European capitals—Madrid, Brussels, and Copenhagen—has been integrated into the dynamics of their urban tourism, thereby generating new resources and cultural spaces. In regards to the latter point, this study poses the working hypothesis that industrial heritage can function as a tool for cultural sustainability, which allows for deconcentration away from historic city centers subjected to significant overtourism. To verify this hypothesis, a methodology has been designed based on the selection of specific indicators and the creation of maps, taking as reference data from the Tripadvisor travel portal. The results obtained are truly encouraging, and it would be interesting to expand this study by incorporating new case studies to allow us to discern additional patterns of behavior around urban industrial tourism.
Lecture Notes in Networks and Systems, 2017
Precise time dissemination and synchronization have been some of the most important technological... more Precise time dissemination and synchronization have been some of the most important technological tasks for several centuries. It was realized that precise time-keeping devices having the same stable frequency and precisely synchronized can have important applications in navigation. Satellite-based global positioning and navigation systems such as the GPS use the same principle. However, even the most sophisticated satellite navigation equipment cannot operate in every environment. In response to this need, we present a computational and analytical study of a network based model of a high-precision, inexpensive, Coupled Oscillator System and Timing device. Preliminary results from computer simulations seem to indicate that timing errors decrease as 1∕N when N crystals are coupled as oppose to 1∕ √ N for an uncoupled assemble. This manuscript is aimed, however, at providing a complete
Physical Review E, 2018
Precise time dissemination and synchronization have been some of the most important technological... more Precise time dissemination and synchronization have been some of the most important technological tasks for several centuries. No later than Harrison's time, it was realized that precise time-keeping devices having the same stable frequency and precisely synchronized can have important applications in navigation. In modern times, satellite-based global positioning and navigation systems such as the GPS use the same principle. However, even the most sophisticated satellite navigation equipment cannot operate in every environment. In response to this need, we present a computational and analytical study of a network-based model of a high-precision, inexpensive, Coupled Crystal Oscillator System and Timing (CCOST) device. A bifurcation analysis (carried out by the authors in a related publication) of the network dynamics shows a wide variety of collective patterns, mainly various forms of discrete rotating waves and synchronization patterns. Results from computer simulations seem to indicate that, among all patterns, the standard traveling wave pattern in which consecutive crystals oscillate out of phase by 2π/N , where N is the network size, leads to phase drift error that decreases as 1/N as opposed to 1/ √ N for an uncoupled ensemble. The results should provide guidelines for future experiments, design and fabrication tasks.
SIAM Journal on Applied Dynamical Systems, 2018
Symmetry is used to investigate the existence and stability of collective patterns of oscillation... more Symmetry is used to investigate the existence and stability of collective patterns of oscillations in rings of coupled crystal oscillators. We assume N identical crystal oscillators, where each oscillator is described by a two-mode nonlinear oscillatory circuit. We also assume the coupling to be identical and consider two different topologies, unidirectional and bidirectional, which lead to networks with Γ = ZN and Γ = DN symmetry, respectively. The whole system can be seen as an ε-perturbation of N uncoupled, two-mode oscillators. The spectrum of eigenvalues of the linearized system near the origin leads to expressions not amenable to analysis. To circumvent this problem, we apply the method of averaging and rewrite the model equations, via near identity transformations, in the socalled full-averaged equations. The truncation to the average part, expressed in complex coordinates, is O(2) × O(2) × Γ-equivariant. Then, we present new theoretical results linking symmetry and averaging theory to study the existence and stability of steady-states of the truncated averaged systems, and show that they persist as periodic solutions of the full-averaged system for small ε. A decomposition of the phase-space dynamics along irreducible representations of the symmetry groups ZN and DN leads to a block diagonalization of the linearized averaged equations. Direct computation of eigenvalues leads to the desired identification of periodic solutions that emerge via symmetry-preserving and symmetry-breaking steady-state bifurcations leading to the corresponding periodic solutions with spatio-temporal symmetries. Numerical simulations are conducted to show representative examples of emergent rotating waves. The motivation for this work is to aid future design and fabrication of novel precision timing devices.
Dynamical Systems, 2016
The coupled cell formalism is a systematic way to represent and study coupled nonlinear different... more The coupled cell formalism is a systematic way to represent and study coupled nonlinear differential equations using directed graphs. In this work, we focus on coupled cell systems in which individual cells are also Hamiltonian. We show that some coupled cell systems do not admit Hamiltonian vector fields because the associated directed graphs are incompatible. In broad terms, we prove that only systems with bidirectionally coupled digraphs can be Hamiltonian. Aside from the topological criteria, we also study the linear theory of regular Hamiltonian coupled cell systems, i.e., systems with only one type of node and one type of coupling. We show that the eigenspace at a codimension one bifurcation from a synchronous equilibrium of a regular Hamiltonian network can be expressed in terms of the eigenspaces of the adjacency matrix of the associated directed graph. We then prove results on steady-state bifurcations and a version of the Hamiltonian Hopf theorem.
Pramana, 2015
Over the past twelve years, ideas and methods from nonlinear dynamics system theory, in particula... more Over the past twelve years, ideas and methods from nonlinear dynamics system theory, in particular, group theoretical methods in bifurcation theory, have been used to study, design, and fabricate novel engineering technologies. For instance, the existence and stability of heteroclinic cycles in coupled bistable systems has been exploited to develop and deploy highly sensitive, lowpower, magnetic and electric field sensors. Also, patterns of behaviour in networks of oscillators with certain symmetry groups have been extensively studied and the results have been applied to conceptualize a multifrequency up/down converter, a channelizer to lock into incoming signals, and a microwave signal generator at the nanoscale. In this manuscript, a review of the most recent work on modelling and analysis of two seemingly different systems, an array of gyroscopes and an array of energy harvesters, is presented. Empirical values of operational parameters suggest that damping and external forcing occur at a lower scale compared to other parameters, so that the individual units can be treated as Hamiltonian systems. Casting the governing equations in Hamiltonian form leads to a common approach to study both arrays. More importantly, the approach yields analytical expressions for the onset of bifurcations to synchronized oscillations. The expressions are valid for arrays of any size and the ensuing synchronized oscillations are critical to enhance performance.
The evolution of a large class of biological, physical and engineering systems can be studied thr... more The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with symmetry, is already well developed and has been used extensively on a wide variety of spatio-temporal systems. There are, however, fewer results on higher-dimensional Hamiltonian systems with symmetry. This lack of results has lead us to investigate the role of symmetry, in particular dihedral symmetry, on high-dimensional coupled Hamiltonian systems. As a representative example, we consider the model equations of a ring of vibratory gyroscopes. The equations are reformulated in a Hamiltonian structure and the corresponding normal forms are derived. Through a normal form analysis, we investigated the effects of various coupling schemes and unraveled the nature of the bifurcations that lead the ring of gyroscopes into and out of synchronization. The Hami...
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Papers by Antonio Palacios