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Highlights • After severe SARS-CoV2 infection, radiological abnormalities such as encephalopathies may be seen. • An extensive radiological encephalopathy may not correlate with abnormalities in cerebrospinal fluid. • An extensive radiological encephalopathy does not correlate with the severity of symptoms., Concerning the letter by Moriguchi et al., we describe our experience with a case of encephalopathy with and atypical damage on magnetic resonance imaging (MRI) in a patient with severe infection due to the SARS-CoV2 virus. A 56-year-old woman, without previous pathologies, developed cough, fever, and respiratory failure for five days, after returning from a 6-day trip to Venice. Chest radiography shows a large bilateral interstitial infiltrate. In the first 24 hours, she was admitted to the Intensive Care Unit (ICU) for severe respiratory failure and positive protein chain reaction-PCR in nasal exudate. She needed intubation for ten days. In the first 48 hours outside the ICU, she developed an acute confusional syndrome (hyperactive delirium). Neurological examination showed temporal-spatial disorientation and incoherent fluent speech. An electroencephalogram (EEG) showed generalized hypovoltaic activity. Cranial magnetic resonance imaging showed a bilateral and symmetrical increase in the supratentorial white matter's signal intensity, with a discrete thickening of both temporal lobes, with a slight increase in signal intensity and a sequence of normal diffusion. The lumbar puncture showed no changes (glucose 71 mg/dL, protein 30 mg/dL, 1 leukocyte). Within 72 hours of starting symptoms, she was neurologically asymptomatic. Our final diagnosis was an inflammatory encephalopathy related to a SARS-CoV2 infection.

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, low-power, 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.

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.

The advent of novel engineered or smart materials, whose properties can be significantly altered in a controlled fashion by external stimuli, has stimulated the design and fabrication of smaller, faster, and more energy-efficient devices. As the need for even more powerful devices grows, networks have become popular alternatives to advance the fundamental limits of performance of individual units. In many cases, the collective rhythmic behavior of a network can be studied through the classical theory of nonlinear oscillators or through the more recent development of the coupled cell formalism. However, the current theory does not account yet for networks in which cells, or individual units, possess a Hamiltonian structure. One such example is a ring array of vibratory gyroscopes, where certain network topologies favor stable synchronized oscillations. Previous perturbation-based studies have shown that synchronized oscillations may, in principle, increase performance by reducing phase drift. The governing equations for larger array sizes are, however, not amenable to similar analysis. To circumvent this problem, the model equations are now reformulated in a Hamiltonian structure and the corresponding normal forms are derived. Through a normal form analysis, we investigate the effects of various coupling schemes and unravel the nature of the bifurcations that lead a ring of gyroscopes of any size into and out of synchronization. The Hamiltonian approach can, in principle, be readily extended to other symmetry-related systems.

We study the existence and stability of heteroclinic connections near "hopping" cellular flame patterns. These are dynamic patterns in which individual cells make sequential, and abrupt, changes in their angular positions while they rotate nonuniformly about the center of a circular domain. Normal form analysis and experimental works have shown that these patterns are associated with a homoclinic cycle connecting group related equilibria. In fact, they emerge through a codimension three steady-state bifurcation of three modes with wave numbers in a 2:3:4 ratio. While cycles are known to exist in the mode-2 and mode-4 interactions, here we show that mode-3 destabilizes the connection so that only remnants, i.e. intermittent flame patterns of the cycles can be observed.

Coupling-induced oscillations in a homogeneous network of overdamped bistable systems have been previously studied both theoretically and experimentally for a system of N (odd) elements, unidirectionally coupled in a ring topology. In this work, we extend the analysis of this system to include a network of nonhomogeneous elements with respect to the parameter that controls the topology of the potential function and the bistability of each element. In particular, we quantify the effects of the nonhomogeneity on the onset of oscillations and the response of the network to external (assumed to be constant and very small) perturbations, using our (recently developed) coupled core fluxgate magnetometer as a representative system. The potential applications of this work include signal detection and characterization for a large class of sensor systems.

We study the effects of thermal noise in a stochastic, Langevin formulation, of a spatio-temporal pattern-forming Partial Differential Equation (PDE) model with circular domain. Modification of a recently developed numerical integration scheme reveals that the pattern-forming model exhibits, in the presence of noise, a greater tendency towards dynamic states and towards intermittent patterns in which ordered states appear randomly, preceded and succeeded by disorganized states. In order to gain additional insight, we focus on a region of parameter space where the patterns of the deterministic system arise from the steady-state interaction of two pairs of modes with wave numbers in a 1:2 ratio. Analysis of the associated stochastic normal form equations allows us to explain the underlying bifurcations of the noise-induced patterns, some of which had only been observed, until now, in laboratory experiments.

Recent theoretical and experimental work has shown that unidirectional coupling can induce oscillations in overdamped and undriven nonlinear dynamical systems that are non-oscillatory when uncoupled; in turn, this has been shown to lead to new mechanisms for weak (compared to the energy barrier height) signal detection and amplification. The potential applications include fluxgate magnetometers, electric field sensors, and arrays of Superconducting Quantum Interference Device (SQUID) rings. In the particular case of the fluxgate magnetometer, we have developed a “coupled-core fluxgate magnetometer” (CCFM); this device has been realized in the laboratory and its dynamics used to quantify many properties that are generic to this class of systems and coupling. The CCFM operation is underpinned by the emergent oscillatory behavior in a unidirectionally coupled ring of wound ferromagnetic cores, each of which can be treated as an overdamped bistable dynamic system when uncoupled. In particular, one can determine the regimes of existence and stability of the (coupling-induced) oscillations, and the scaling behavior of the oscillation frequency. More recently, we studied the effects of a (Gaussian) magnetic noise floor on a CCFM system realized with N = 3 coupled ferromagnetic cores. In this Letter, we first introduce a variation on the basic CCFM configuration that affords a path to enhanced device sensitivity, particularly for N 3 coupled elements. We then analyze the response of the basic CCFM configuration as well as the new setup to a

Numerical simulations of the flow in a one-stage turbine are carried out to investigate the feasibility of constructing a reduced-order model via Galerkin methods. The flow in the turbine is modeled by the unsteady Reynolds-averaged Navier-Stokes equations. The governing equations are written in the strong conservation form and solved using a fully implicit, finite difference approximation. By the use of the proper orthogonal decomposition (POD), spatial dominant features, also known as POD modes or eigenfunctions, are identified and separated from the spatiotemporal dynamics of the turbine flow. The POD reconstructed solutions indicate that a significant portion of the original dynamics is captured by a few modes. The solution reconstructed using the first 40 modes captures more than 99% of the energy spectrum, whereas the error of the energy variable is less than 0.6%, and the error of skin friction is less than 1.5%. Phase-space plots further indicate the existence of low-dimensional dynamics, which supports the validity of a reduced-order model for turbine flow.

In this paper we provide numerical simulations for modeling an array of non-locally coupled DC SQUIDs that are coupled through the magnetic field created by the circulating current. The motivation is based on work using an array of non-identical SQUID loops or SQIFs to produce a non-periodic voltage response with a unique anti-peak centered at the zero applied flux. Our approach differs by using an array of identical SQUID loops and varying the spacing between each of these loops. Certain distributions of spacing between SQUIDs demonstrate the anti-peak response as seen in the SQIF.

Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

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/cm2 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., 9 pages, 13 figures, Applied Superconductivity Conference (ASC'12)

This work investigates through numerical simulations a novel device that improvesdynamic range and linearity. The standard DC SQUID can increase in linearity by adding athird junction, changing to a device known as the bi-SQUID. It is known that the dynamicrange can increase by connecting SQUIDs in series, and it has been shown that nonuniformityin the loops sizes in arrays of SQUIDs can produce a unique 'anti'-peak at thezero magnetic flux (device know as a SQIF). Thus, combining these ideas we can improvethe dynamic range and design a highly linear device with a unique 'anti'-peak. Hence, this device can be referred to as a bi-SQIF or non-uniform bi-SQUID array. Results have shown that the maximum voltage swing increase proportional to N, where N is the number of loops connected in series. The spur free dynamic range also improves as N increases, which is directly related to the linearity of the device. Therefore, we have designed a device which can lead to improvements which can be applicable to low noise amplifier (LNA), and provide a platform for creating "electrically" small antennas.

The complex behaviours of gyroscope systems have been scientifically researched and thoroughly studied for decades. Most of scientific research involving gyroscopes specifically concentrates on studying the designs and fabrications at the circuitry level. Although gaining a recent popularity with the low cost of MEMS device that offers an attractive approach for gyroscope fabrications, its performance is far from meeting the requirements for an inertial grade guidance system. To improve the performance, our current research is theoretically focusing upon investigating the dynamics of vibratory gyroscopes coupled in a ring configuration. Particularly, a certain topology of arrangements among coupled gyroscopes can be designed and studied to enhance robustness. The main operation depends mostly on an external source for a stable oscillation in the drive axis, while an oscillatory motion in the sense axis, which is used to detect an angular rate of rotation, is enabled through the transfers of energy from th...

In this work we numerical model series and parallel non‐uniform superconducting quantum interference device (SQUID) array. Previous work has shown that series SQUID array constructed with a random distribution of loop sizes, (i.e. different areas for each SQUID loop) there exists a unique ‘anti‐peak’ at the zero magnetic field for the voltage versus applied magnetic field (V‐B). Similar results extend to a parallel SQUID array where the difference lies in the arrangement of the Josephson junctions. Other system parameter such as bias current, the number of loops, and mutual inductances are varied to demonstrate the change in dynamic range and linearity of the V‐B response. Application of the SQUID array as a low noise amplifier (LNA) would increase link margins and affect the entire communication system. For unmanned aerial vehicles (UAVs), size, weight and power are limited, the SQUID array would allow use of practical ‘electrically small’ antennas that provide acceptable gain.

In the search for small, fast and low power electronic circuits the microelectronic engineering community is increasingly faced with understanding the physical and non-ideal properties of the circuit at the transistor level. This is especially true with regard to the use of modern fabrication processes where transistor gate length is measured in tens of nanometers and physical properties such as leakage current and non-ideal sub-threshold behavior become more prevalent. The purpose of this work is to present the construction of some simple electronic circuits that possess nonlinear and dynamical properties and to illustrate their utility in a few applications. Specifically, the construction of oscillating, pattern forming and mixed signal reconfigurable circuits is discussed. In these examples, the nonlinear and dynamical properties of the circuits play a critical role in their operation. Experimental results from fabricated circuits are presented. Useful analytical tools are also discussed in the context of constructing and understanding the operation of the circuits. Similarities in the construction of several circuits lead to the development of a generic analog and nonlinear electronic fabric, similar to field-programmable gate arrays. Experimental results demonstrating configurability are shown. The array is constructed using non-volatile floating-gate based transistors. This type of proposed circuit construction and operation takes advantage of the nonlinear properties of the circuit and illustrates how many undesirable properties can actually provide utility.

The natural behavior of most processes is that whenever they are effected by an external phenomenon the outcome of the system is changed. Hence the output of a process can be changed by the input of the system. Many of these processes have the capability of either being in a steady state while at others times they may be induced into a periodic or oscillating state. This type of behavior is common in a system of equations which is used to detect and measure an external phenomena which will change the state of the system. These systems are generally referred to as sensors. Quite often a sensor’s effectiveness is increased once it is in a region where it is oscillating. This, however, is not the only way to enhance effectiveness. If one is to connect the sensors in one of many different ways, generally referred to as a coupling, the sensitivity may be increased. In this work we will demonstrate the behavior of a particular type of sensor, known as dc-SQUID (Superconducting Quantum Interference Device) coupled in a nearest-neighboring scheme. We show that the response of the coupled system to an external magnetic field is greatly increased compared to that of a single SQUID element. Applications of this work include: geological equipment, biomedical equipment such as MRI machines, and applications to homeland defense such as mine detection.

A fluxgate magnetometer is a magnetic field sensor that is used to detect relatively low intensity magnetic fields. It belongs to a class of nonlinear systems known as the overdamped bistable system whose dynamics can be described by the generic form x(t)=-ΔU(x). It is well known that an overdamped system will not oscillate on its own. It is usually driven with a known periodic signal with an amplitude large enough to overcome the potential barrier height. Instead of this approach, we will show how similar oscillations can be generated with a carefully selected coupling scheme, coupling parameters, and initial conditions [1, 2], thus eliminating the need for expensive driving signals. We will show that the coupled-core fluxgate magnetometer can not only detect DC magnetic fields, but it can detect and classify AC magnetic fields as well.

Nowadays, the global positioning system (GPS) is popularly used by the U.S. Navy in navigation systems to gain precise position, velocity, and time information. One of the biggest issues for using GPS is its susceptibility to jamming and other inferences. The received GPS signal is approximately 20 dB below the thermal noise level from a distance 11,000 miles away. Because of these weakness and vulnerability, many other alternative navigation methods are needed to improve performance and reduce the dependency on GPS. One of the main alternative methods is the Inertial Guidance System (IGS) that can operate wherever GPS signals are jammed or denied. A prototypical IGS is composed of three accelerometers to measure linear movement and three angular rate sensors (gyroscopes) to gauge the rotational movement. The main benefit of IGS is its low cost relatively to other methods. Current MEMS (Micro-Electro-Mechanical Systems) gyroscopes are compact and inexpensive, but their performance does not meet the requirements for an inertial grade guidance system. In this work, a difference approach was examined on the dynamics of coupled gyroscopes to improve performance through synchronization referred as vibratory coupled gyroscopes with drive amplitudes’ coupling. One of the main discoveries from the coupled gyroscopes’ mathematical model is a Torus bifurcation, which leads to synchronized behavior in and array of three gyroscopes uni-directionally coupled.

Recently, we have shown the emergence of oscillatory behaviour in unforced bistable systems having dynamics of the general form: tx /spl equiv/ /spl part/U(x,t)//spl part/x, subject to carefully crafted coupling schemes. Here, we present experimental results obtained on a physical system implemented with N=3 coupled ferromagnetic cores; the oscillatory behaviour is triggered when the coupling constant exceeds a threshold value, and, more importantly, the oscillation characteristics are sensitive to weak external dc magnetic fields. The oscillations afford then a novel detection scheme for fluxgate magnetometer. In this paper, we introduce another idea; using the coupled core fluxgate, in the detection of time-periodic fields of very low frequency. In this case measurements can be realized in a "power-saver" mode wherein the coupled setup can be, initially, subthreshold (i.e. non-oscillating) and be triggered into oscillation by the advent of the target (oscillatory) field. Preliminary experiments of this novel operation mode are here presented.

Dynamical systems that operate near the onset of coupling-induced oscillations can exhibit enhanced sensitivity to external perturbations under suitable operating parameters. This cooperative behavior and the attendant enhancement in the system response (quantified here via a signal-to-noise ratio at the fundamental of the coupling-induced oscillation frequency) are investigated in this work. As a prototype, we study an array of dc superconducting quantum interference device (SQUID) rings locally coupled, unidirectionally as well as bidirectionally, in a ring configuration; it is well known that each individual SQUID can be biased through a saddle-node bifurcation to oscillatory behavior. We show that biasing the array near the bifurcation point of coupling-induced oscillations can lead to a significant performance enhancement.

Recently, we have shown the emergence of oscillations in overdamped undriven nonlinear dynamic systems subject to carefully crafted coupling schemes and operating conditions. Here, we summarize experimental results obtained on a system of N = 3 coupled ferromagnetic cores, the underpinning of a “coupled-core fluxgate magnetometer” (CCFM); the oscillatory behaviour is triggered when the coupling constant exceeds a threshold value (bifurcation point), and the oscillation frequency exhibits a characteristic scaling behaviour with the “separation” of the coupling constant from its threshold value, as well as with an external target DC magnetic flux signal. The oscillations, which can be induced at frequencies ranging from a few Hz to high-kHz, afford a new detection scheme for weak target magnetic signals. We also present the first (numerical) results on the effects of a (Gaussian, exponentially correlated) noise floor on the spectral properties of the system response.  2005 Elsevier B.V. All rights reserved.

A fluxgate magnetometer is one of the numerous devices that belong to a class of nonlinear systems known as the overdamped bistable system. Its dynamics can be described by the generic form x=-/spl nabla/U(x), where U(x) is the potential energy function with two minima that form the bases for the bistability. It is well known that an overdamped system does not oscillate on its own. To switch states, the system is forced by an external periodic signal with large enough amplitude to overcome the potential energy barrier that separates the two minima. However, well-designed coupling schemes, together with the appropriate choice of initial conditions can induce oscillations when a control parameter exceeds a threshold value. The self-induced oscillation, therefore, eliminates the necessity of the forcing function. We demonstrate these concepts numerically and experimentally using three single-domain fluxgate magnetometers that are coupled unidirectionally in a ring.

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.

SQUID arrays are promising candidates for low profile antennas and low noise amplifier applications. We present the integrated circuit designs and results of DC and RF measurements of the wideband serial arrays based on integration of linear bi-SQUID cells forming a Superconducting Quantum Interference Filter (bi-SQUID SQIF). Various configurations of serial arrays designs are described. The measured linearity, power gain, and noise temperature are analyzed and compared. The experimental results are matched to results of mathematical modeling. A serial bi-SQUID SQIF arrays are mounted into a coplanar waveguide (CPW) and symmetrically grounded to corresponding sides of CPW. The RF output comes out from the central common line, which is also used for DC biasing and forms a symmetrical balanced output. The signal and DC flux biasing line is designed as coplanar lines passed in parallel over each bi-SQUID cell in a bidirectional fashion concentrating magnetic flux inside of each cell. Serial bi-SQUID SQIF arrays are fabricated on 5 mm x 5 mm chips using standard HYPRES niobium 4.5 kA/cm2 fabrication process., Comment: 7 pages, 10 figures, Applied Superconductivity Conference (ASC'12)

A critical component of many Inertial Navigation Systems (INS) is the gyroscope — a device used for detecting rotation rates and orientation. Gyroscopes are subject to material imperfections and manufacturing defects, potentially reducing their ability to detect signals and to minimize phase drift. This manuscript explores the idea of performance enhancement by combining the input–output response of an ensemble of gyroscopes coupled bidirectionally, through the driving- and sensing-modes, in a ring fashion. Numerical simulations and bifurcation analysis via perturbation methods show the existence of a stable synchronization state in which all gyroscopes vibrate with the same phase and amplitude. In this state, the sum output of the sensing modes is significantly larger than any individual sensing mode, which leads to significant reductions in phase drift caused by material imperfections, fabrication variations, and system noise. Similarities and differences with respect to a system of gyroscopes coupled only along the driving-axis are discussed in great detail as well.

Multi-loop arrays of Josephson junctions (JJs) with non-uniform area distributions, which are known as superconducting quantum interference filters (SQIFs), 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-superconductive quantum interference device (SQUID) configuration, in which each individual SQUID loop is made up of three JJs as opposed to using two JJs per loop in standard dc SQUIDs. We show, computationally, that the additional junction offe...

Unforced bistable dynamical systems having dynamics of the general form cannot oscillate (i.e. switch between their stable attractors). However, a number of such systems subject to carefully crafted coupling schemes have been shown to exhibit oscillatory behavior under carefully chosen operating conditions. This behavior, in turn, affords a new mechanism for the detection and quantification of target signals having magnitude far smaller than the energy barrier height in the potential energy function U(x) for a single (uncoupled) element. The coupling-induced oscillations are a feature that appears to be universal in systems described by bi- or multi-stable potential energy functions U(x), and are being exploited in a new class of dynamical sensors being developed by us. In this work we describe one of these devices, a coupled-core fluxgate magnetometer (CCFM), whose operation is underpinned by this dynamic behavior. We provide an overview of the underlying dynamics and, also, quantify the performance of our test device; in particular, we provide a quantitative performance comparison to a conventional (single-core) fluxgate magnetometer via a 'resolution' parameter that embodies the device sensitivity (the slope of its input–output transfer characteristic) as well as the noise floor.