Antonio Palacios | San Diego State University (original) (raw)

Papers by Antonio Palacios

SPIE Proceedings, 2005

In this work we discuss the implementation of sensing devices based on ring-coupled hysteretic sy... more In this work we discuss the implementation of sensing devices based on ring-coupled hysteretic systems. In particular, the emergent oscillations in a ring coupled system formed by overdamped nonlinear devices having an hysteretic magnetic and electric behaviour are considered with applications to B-field and E-field measurements, respectively. Details on the implementation strategy, on the materials adopted and on the technologies

AIP Conference Proceedings, 2004

Springer Proceedings in Mathematics & Statistics, 2015

In this work we explore the use of spin torque nano-oscillators (STNOs) to produce a spintronics ... more In this work we explore the use of spin torque nano-oscillators (STNOs) to produce a spintronics voltage oscillator in the microwave range. STNOs are quite small—on the order of 100 nm—and frequency agile. However, experimental results till date have produced power outputs that are too small for practical use. We attempt to increase power output by investigating the dynamics of a system of electrically-coupled STNOs. Transverse Lyapunov exponents are used to quantitatively measure the local stability of synchronized limit cycles. The synchronized solution is found to be stable for a large region of two-parameter space. However, a two-parameter bifurcation diagram reveals a competing out-of-phase solution, causing bistability.

Understanding Complex Systems

Overdamped bistable dynamics, of the generic form x = –∇U(x), underpin the behavior of numerous s... more Overdamped bistable dynamics, of the generic form x = –∇U(x), underpin the behavior of numerous systems in the physical world. The most-studied example is the overdamped Duffing system, the dynamics of a particle in a bistable potential U(x) = –ax 2 + bx 4. Absent an external forcing term, the state-point x(t) will rapidly relax to one of two stable

Physica D: Nonlinear Phenomena, 2015

Understanding Complex Systems, 2013

Multi-loop arrays of Josephson Junctions (JJ) with non-uniform area distributions, which are know... more Multi-loop arrays of Josephson Junctions (JJ) with non-uniform area distributions, which are known as Superconducting Quantum Interference Filters (SQIF), are the most highly sensitive sensors of changes in applied magnetic field as well as the absolute magnitude of magnetic fields. The non-uniformity of the loop sizes allows the array to produce a unique collective voltage response that has a pronounced single peak with a large voltage swing around zero magnetic field. To obtain high linear dynamic range, which is critical for a wide variety of applications, the linearity of the slope of the anti-peak response must be improved. We propose a novel scheme for enhancing linearity—a new configuration combining the SQIF array concept with the recently introduced bi-SQUID configuration, in which each individual SQUID loop is made up of three JJs as oppose to using two JJs per loop in standard DC SQUIDs. We show, computationally, that the additional junction offers a viable linearization method for optimizing the voltage response and dynamic range of SQIF arrays. We have realized SQIF arrays based on bi-SQUID cells and present first experimental results.

The European Physical Journal B, 2009

International Journal of Bifurcation and Chaos, 2020

Computational and experimental works reveal that the coupling of similar crystal oscillators lead... more Computational and experimental works reveal that the coupling of similar crystal oscillators leads to a variety of collective patterns, mainly various forms of discrete rotating waves and synchronization patterns, which have the potential for developing precision timing devices through phase drift reduction. Among all observed patterns, the standard traveling wave, in which consecutive crystals oscillate out of phase by [Formula: see text], where [Formula: see text] is the network size, leads to optimal phase drift error that scales down as [Formula: see text] as opposed to [Formula: see text] for an uncoupled ensemble. In this manuscript, we provide an analytical proof of the scaling laws, for uncoupled and coupled symmetric networks, and show that [Formula: see text] is the fundamental limit of phase-error reduction that one can obtain with a symmetric network of nonlinear oscillators of any type, not just crystals.

Lecture Notes in Networks and Systems

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

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 \(1{/}\sqrt{N}\) for an uncoupled assemble. This manuscript is aimed, however, at providing a complete classification of the various patterns of collective behavior that are created, mainly, ...

SIAM Journal on Applied Dynamical Systems

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

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.

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.

Physical Review B

Synchronization of Spin Torque Nano-Oscillators has been a subject of extensive research as vario... more Synchronization of Spin Torque Nano-Oscillators has been a subject of extensive research as various groups try to harness the collective power of STNOs to produce a strong enough microwave signal at the nanoscale. Achieving synchronization has proven to be, however, rather difficult for even small arrays while in larger ones the task of synchronization has eluded theorist and experimentalists altogether. In this work we solve the synchronization problem, analytically and computationally, for networks of STNOs connected in series. The procedure is valid for networks of arbitrary size and it is readily extendable to other network topologies. These results should help guide future experiments and, eventually, lead to the design and fabrication of a nanoscale microwave signal generator.

Physical Review E

that in networks with asymmetrically coupled oscillators, synchronization can only be found to be... more that in networks with asymmetrically coupled oscillators, synchronization can only be found to be stable when the oscillators are heterogenous or nonidentical. In this manuscript, it is proven, mathematically, that the conclusions in those works are incorrect, and that stable synchronization states can, and do, exist in asymmetrically coupled homogeneous oscillators. Theoretical results are confirmed with numerical simulations.

SPIE Proceedings, 2005

In this work we discuss the implementation of sensing devices based on ring-coupled hysteretic sy... more In this work we discuss the implementation of sensing devices based on ring-coupled hysteretic systems. In particular, the emergent oscillations in a ring coupled system formed by overdamped nonlinear devices having an hysteretic magnetic and electric behaviour are considered with applications to B-field and E-field measurements, respectively. Details on the implementation strategy, on the materials adopted and on the technologies

AIP Conference Proceedings, 2004

Springer Proceedings in Mathematics & Statistics, 2015

In this work we explore the use of spin torque nano-oscillators (STNOs) to produce a spintronics ... more In this work we explore the use of spin torque nano-oscillators (STNOs) to produce a spintronics voltage oscillator in the microwave range. STNOs are quite small—on the order of 100 nm—and frequency agile. However, experimental results till date have produced power outputs that are too small for practical use. We attempt to increase power output by investigating the dynamics of a system of electrically-coupled STNOs. Transverse Lyapunov exponents are used to quantitatively measure the local stability of synchronized limit cycles. The synchronized solution is found to be stable for a large region of two-parameter space. However, a two-parameter bifurcation diagram reveals a competing out-of-phase solution, causing bistability.

Understanding Complex Systems

Overdamped bistable dynamics, of the generic form x = –∇U(x), underpin the behavior of numerous s... more Overdamped bistable dynamics, of the generic form x = –∇U(x), underpin the behavior of numerous systems in the physical world. The most-studied example is the overdamped Duffing system, the dynamics of a particle in a bistable potential U(x) = –ax 2 + bx 4. Absent an external forcing term, the state-point x(t) will rapidly relax to one of two stable

Physica D: Nonlinear Phenomena, 2015

Understanding Complex Systems, 2013

Multi-loop arrays of Josephson Junctions (JJ) with non-uniform area distributions, which are know... more Multi-loop arrays of Josephson Junctions (JJ) with non-uniform area distributions, which are known as Superconducting Quantum Interference Filters (SQIF), are the most highly sensitive sensors of changes in applied magnetic field as well as the absolute magnitude of magnetic fields. The non-uniformity of the loop sizes allows the array to produce a unique collective voltage response that has a pronounced single peak with a large voltage swing around zero magnetic field. To obtain high linear dynamic range, which is critical for a wide variety of applications, the linearity of the slope of the anti-peak response must be improved. We propose a novel scheme for enhancing linearity—a new configuration combining the SQIF array concept with the recently introduced bi-SQUID configuration, in which each individual SQUID loop is made up of three JJs as oppose to using two JJs per loop in standard DC SQUIDs. We show, computationally, that the additional junction offers a viable linearization method for optimizing the voltage response and dynamic range of SQIF arrays. We have realized SQIF arrays based on bi-SQUID cells and present first experimental results.

The European Physical Journal B, 2009

International Journal of Bifurcation and Chaos, 2020

Computational and experimental works reveal that the coupling of similar crystal oscillators lead... more Computational and experimental works reveal that the coupling of similar crystal oscillators leads to a variety of collective patterns, mainly various forms of discrete rotating waves and synchronization patterns, which have the potential for developing precision timing devices through phase drift reduction. Among all observed patterns, the standard traveling wave, in which consecutive crystals oscillate out of phase by [Formula: see text], where [Formula: see text] is the network size, leads to optimal phase drift error that scales down as [Formula: see text] as opposed to [Formula: see text] for an uncoupled ensemble. In this manuscript, we provide an analytical proof of the scaling laws, for uncoupled and coupled symmetric networks, and show that [Formula: see text] is the fundamental limit of phase-error reduction that one can obtain with a symmetric network of nonlinear oscillators of any type, not just crystals.

Lecture Notes in Networks and Systems

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

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 \(1{/}\sqrt{N}\) for an uncoupled assemble. This manuscript is aimed, however, at providing a complete classification of the various patterns of collective behavior that are created, mainly, ...

SIAM Journal on Applied Dynamical Systems

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

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.

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.

Physical Review B

Synchronization of Spin Torque Nano-Oscillators has been a subject of extensive research as vario... more Synchronization of Spin Torque Nano-Oscillators has been a subject of extensive research as various groups try to harness the collective power of STNOs to produce a strong enough microwave signal at the nanoscale. Achieving synchronization has proven to be, however, rather difficult for even small arrays while in larger ones the task of synchronization has eluded theorist and experimentalists altogether. In this work we solve the synchronization problem, analytically and computationally, for networks of STNOs connected in series. The procedure is valid for networks of arbitrary size and it is readily extendable to other network topologies. These results should help guide future experiments and, eventually, lead to the design and fabrication of a nanoscale microwave signal generator.

Physical Review E

that in networks with asymmetrically coupled oscillators, synchronization can only be found to be... more that in networks with asymmetrically coupled oscillators, synchronization can only be found to be stable when the oscillators are heterogenous or nonidentical. In this manuscript, it is proven, mathematically, that the conclusions in those works are incorrect, and that stable synchronization states can, and do, exist in asymmetrically coupled homogeneous oscillators. Theoretical results are confirmed with numerical simulations.