FORCulator: A micromagnetic tool for simulating first-order reversal curve diagrams

We describe a method for simulating first-order reversal curve (FORC) diagrams of interacting single-domain particles. Magnetostatic interactions are calculated in real space, allowing simulations to be performed for particle ensembles with arbitrary geometry. For weakly interacting uniaxial particles, the equilibrium magnetization at each field step is obtained by direct solution of the Stoner-Wohlfarth model, assuming a quasi-static distribution of interaction fields. For all other cases, the equilibrium magnetization is calculated using an approximate iterated solution to the Landau-Lifshitz-Gilbert equation. Multithreading is employed to allow multiple curves to be computed simultaneously, enabling FORC diagrams to be simulated in reasonable time using a standard desktop computer. Statistical averaging and post processing lead to simulated FORC diagrams that are comparable to their experimental counterparts. The method is applied to several geometries of relevance to rock and environmental magnetism, including densely packed random clusters and partially collapsed chains. The method forms the basis of FORCulator, a freely available software tool with graphical user interface that will enable FORC simulations to become a routine part of rock magnetic studies.The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC grant agreement 320750.This is the final published version of the article. It first appeared at http://onlinelibrary.wiley.com/doi/10.1002/2014GC005582/abstract

Formal Analysis of Linear Control Systems using Theorem Proving

Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation methods, however, both of these methods cannot provide accurate analysis due to their inherent limitations. Model checking has been widely used to analyze control systems but the continuous nature of their environment and physical components cannot be truly captured by a state-transition system in this technique. To overcome these limitations, we propose to use higher-order-logic theorem proving for analyzing linear control systems based on a formalized theory of the Laplace transform method. For this purpose, we have formalized the foundations of linear control system analysis in higher-order logic so that a linear control system can be readily modeled and analyzed. The paper presents a new formalization of the Laplace transform and the formal verification of its properties that are frequently used in the transfer function based analysis to judge the frequency response, gain margin and phase margin, and stability of a linear control system. We also formalize the active realizations of various controllers, like Proportional-Integral-Derivative (PID), Proportional-Integral (PI), Proportional-Derivative (PD), and various active and passive compensators, like lead, lag and lag-lead. For illustration, we present a formal analysis of an unmanned free-swimming submersible vehicle using the HOL Light theorem prover.Comment: International Conference on Formal Engineering Method

Micromagnetic simulation of magnetofossils with realistic size and shape distributions: Linking magnetic proxies with nanoscale observations and implications for magnetofossil identification

We build micromagnetic models to investigate the magnetic properties of biogenic magnetite - a common type of magnetic minerals that is responsible for recording a wide range of biological, geophysical and geological processes on earth. The geometry of modelled particles is based on realistic size and shape distributions from nanoscale observations. Systematic changes in microstructures of biogenic magnetite ensembles are built and their magnetic properties are calculated, which enables a quantitative and separate assessment of the effect of crystal morphology and chain structures. Although the same particle size and shape distributions are used in all calculations, simulation results document large variations in magnetic properties, i.e., wide distributions of coercivity (Bc = ~10-60 mT), coercivity of remanence (Bcr = ~14-81 mT), dispersion parameter (DP = ~0.1-0.5), and skewness values (S = ~0.7-1.1) due to variable degree of anisotropy and magnetostatic interactions. Previously, the commonly observed "biogenic soft" and "biogenic hard" components on biogenic magnetite-bearing samples were often interpreted to reflect crystal morphologies, and that the small DP values of coercivity distributions were an indication of narrow particle size distributions. Our simulations suggest that these speculations are not always the case and that magnetosome microstructures likely exert a dominant control over their magnetic properties. Our modelling results provide a new theoretical perspective on the magnetic properties of biogenic magnetite, which is important for understanding magnetic proxy signals from magnetofossils in a wide range of environmental and geological settings, and for the search for biogenic magnetite in terrestrial rocks and in extra-terrestrial materials.European Research Counci

Hysteresis of Natural Magnetite Ensembles: Micromagnetics of Silicate-Hosted Magnetite Inclusions Based on Focused-Ion-Beam Nanotomography

Three-dimensional geometries of silicate-hosted magnetic inclusions from the Harcus intrusion, South Australia have been determined using focused-ion-beam nanotomography (FIB-nt). By developing an effective workflow, the geometries were reconstructed for magnetic particles in a plagioclase (162) and a pyroxene (282), respectively. For each inclusion, micromagnetic modelling using MERRILL provided averaged hysteresis loops and backfield remanence curves of 20 equidistributed field directions together with average Ms, Mrs, Hc, and Hcr . The micromagnetic structures within each silicate are single-domain, single-vortex, multi-vortex and multi-domain states. They have been analyzed using domain-state diagnostic plots, such as the Day plot and the Néel plot. SD particles can be subdivided into groups with dominant uniaxial anisotropy (Mrs/Ms ∼ 0.5 and 10 < Hc < 100 mT) and mixed uniaxial/multiaxial anisotropy (Mrs/Ms ∼ 0.7 and 10 < Hc < 30 mT). Most single-vortex particles lie on a trend with 0 < Mrs/Ms < 0.1 and 0 < Hc < 10 mT, while others dis- play a broad range of intermediate Mrs/Ms and Hc values. Single-vortex and multi-vortex states do not plot on systematic grain-size trends. Instead, the multi-component mixture of domain states within each silicate spans the entire range of natural variability seen in bulk samples. This questions the interpretation of bulk average hysteresis parameters in terms of grain size alone. FIB-nt combined with large-scale micromagnetic simulations provides a more complete characterization of silicate-hosted carriers of stable magnetic remanence. This approach will improve the understanding of single-crystal paleomagnetism, and enable primary paleomagnetic data to be extracted from ancient rocks

A New Differential Positioning Method using Modulation Correlation of Signals of Opportunity

Global Navigation Satellite Systems (GNSS) have become the positioning systems of choice for many applications. However, GNSS signals are susceptible to obstruction, interference and jamming. Therefore, to maximize robustness and integrity, it is necessary to employ a dissimilar positioning technology that can operate independently and back-up GNSS. One such technology exploits 'signals of opportunity' - signals that are designed for purposes other than navigation.This paper presents a system that uses amplitude modulation (AM) radio broadcasts in the medium frequency (MF) band. At these frequencies, the predominant ground-wave propagation mode offers better coverage in remote areas and over sea than is achievable with higher frequency signals.The system is differential and operates by correlating modulation information between the reference and user receivers. A system of this form mitigates the deterioration in and around buildings encountered in prior systems and can provide absolute position using fewer signals than a system using only carrier phase.The system presented in this paper uses generalized cross correlation to obtain time difference of arrival measurements that are subsequently used for position determination. Preliminary results indicate the system provides a robust position solution. Moreover, the system offers the potential to be combined with carrier phase measurements to achieve enhanced performance, while the modulation correlation technique is readily extendable to other types of signal

A Differential Positioning System Using Modulation Correlation of Signals of Opportunity

Global Navigation Satellite Systems (GNSS) have become the positioning systems of choice for many applications. However, GNSS signals are susceptible to obstruction, interference and jamming. Therefore, to maximize robustness and integrity, it is necessary to employ a dissimilar positioning technology that can operate independently and back-up GNSS. One such technology exploits ‘signals of opportunity’ – signals that are designed for purposes other than navigation. This paper presents a system that uses amplitude modulation (AM) radio broadcasts in the medium frequency (MF) band. At these frequencies, the predominant ground-wave propagation mode offers better coverage in remote areas and over sea than is achievable with higher frequency signals. The system is differential and operates by correlating modulation information between the reference and user receivers. A system of this form mitigates the deterioration in and around buildings encountered in prior systems and can provide absolute position using fewer signals than a system using only carrier phase. The system presented in this paper uses generalized cross correlation to obtain time difference of arrival measurements that are subsequently used for position determination. Preliminary results indicate the system provides a robust position solution. Moreover, the system offers the potential to be combined with carrier phase measurements to achieve enhanced performance, while the modulation correlation technique is readily extendable to other types of signal

Novel Environmental Features for Robust Multisensor Navigation

Many navigation techniques have now become so reliant on GNSS that there is no back up when there is limited or no signal reception. If there is interference, intentional or otherwise, with the signal, navigation could be lost or become misleading [1]. Other navigation techniques harness different technologies such as Wi-Fi [2], eLoran and inertial navigation. However, each of these techniques has its own limitations, such as coverage, degradation in urban areas or solution drift [3]. Therefore there is a need for new navigation and positioning techniques that may be integrated with GNSS to increase the reliability of the system as a whole. This paper presents the results of a feasibility study to identify a set of novel environmental features that could be used for navigation in the temporary absence of GNSS or degradation of the signal. By measuring these features during times of GNSS availability a map can be produced. This can be referred to during times of limited reception, a principle already used for some Wi-Fi positioning techniques [2]. Therefore a “measurable” can be defined as a feature either man-made or natural that is spatially distinct and has limited temporal variation. Possibilities considered include magnetic anomalies [4], light intensity and road signs. Firstly, a brainstorming exercise and a literature study were conducted to generate a list of possible environmental features that was assessed for the viability of each candidate. The features were ranked according to three criteria: practicality, precision and coverage. The definition of practicality for each measurable was that a suitable detector must be installable on a road vehicle, particularly an emergency vehicle, at a reasonable cost with minimal alterations to the vehicle. Precision was defined in terms of the spatial variation of the environmental feature and thus the accuracy with which position information might be derived from it. Coverage was assessed in terms of the availability of the feature over a range of different environments. Continuous coverage is not required because the new measurables may be used in combination and integrated with dead reckoning techniques, such as odometry and inertial navigation [3]. The outcome of the viability study was used to determine which features are to be experimentally tested. Magnetic anomalies, road texture and a dozen other environmental features were found to be worth investigation. Features which were discounted include wind speed and pulsars [5]. The initial experiment was carried out on foot in Central London. The same tests were repeated on two separate days, with a closed loop circuit walked three times on each occasion. This experiment used an Inertial Measurement Unit (IMU), comprising accelerometer and gyro triads, together with a barometer, three-axis magnetometer and GNSS receiver. The experiment was also recorded using a camcorder from the point of view of a pedestrian, enabling visual and audio features of the environment to be assessed. Magnetic anomalies were found to be a promising source of position information. Peaks in the magnetometer data were observed on all rounds at approximately the same positions. There were also similarities seen in the temperature profiles after correcting for the temporal variation of the background temperature. Another potential source of position information was found to be text-based signs. It is relatively simple to extract text from camera images and it is easily stored in a feature database. However, methods of dealing with identically-worded signs in close proximity will need to be developed. Sound levels were analysed in 10s intervals for the mean, minimum and maximum sound volume. There was no clear correlation observed between the different rounds of the experiment. Due to the pedestrian experimental results sound levels of the surroundings will not be used in further experimentation. An alternative area of enquiry for using sound (in the vehicular experiments) is using microphones to indirectly measure road texture based on the noise from the wheel contact with the road [6]. The paper will also present results of road vehicle experiments. Multiple circuits of the same routes will be compared. Different environments will be assessed including rural, dual carriageways, suburban and urban roads. Sensors to be used include the IMU and 3-axis magnetometer from the pedestrian experiment, a barometer, gas sensors, a microphone, an axle-mounted accelerometer, an ambient light sensor and a thermometer. These will be placed either on, inside or under the vehicle as determined by the individual needs of the sensors. The results will be used to determine which of these sensors could be potentially used for a multisensor integrated navigation system and also the environments in which they work optimally. Using the results of the three feasibility study phases (literature review, pedestrian and road experiment) the next project stage will be to produce a demonstration system that uses the most feasible features of the environment and creates a map database during times GNSS is present. This database will then be used for navigation in times of need. In the long term, it is envisaged that this technique will be implemented cooperatively, with a batch of vehicles collecting feature data and contributing it to a common shared database. / References [1] Thomas, M., et al., Global Navigation Space Systems: Reliance and Vulnerabilities, London, UK: Royal Academy of Engineering, 2011. [2] Jones, K., L. Liu, and F. Alizadeh-Shabdiz, “Improving Wireless Positioning with Look-ahead Map-Matching,” Proc. MobiQuitous 2007, Phildaelphia, PA, February 2008, pp. 1-8. [3] Groves, P.D., Principles of GNSS, Inertial, and Multisensor Intergrated Navigation Systems, Second Edition, Artech House, 2013. [4] Judd, T., and T. Vu, “Use of a New Pedometric Dead Reckoning Module in GPS Denied Environments,” Proc. IEEE/ION PLANS, Monterey, CA, May 2008, pp. 120?128. [5] Walter, D. J., "Feasibility study of novel environmental feature mapping to bridge GNSS outage," Young Navigator Conference, London, 2012. [6] Mircea, M., et al., “Strategic mapping of the ambient noise produced by road traffic, accordingly to European regulations,” Proc. IEEE International Conference on Automation, Quality and Testing, Robotics, Cluj Napoca, Romania, May 2008

Magnetic record of deglaciation using FORC-PCA, sortable-silt grain size, and magnetic excursion at 26 ka, from the Rockall Trough (NE Atlantic)

Core MD04-2822 from the Rockall Trough has apparent sedimentation rates of ∼ 1 m/kyr during the last deglaciation (Termination I). Component magnetization directions indicate a magnetic excursion at 16.3 m depth in the core, corresponding to an age of 26.5 ka, implying an excursion duration of ∼350 years. Across Termination I, the mean grain size of sortable silt implies reduced bottom-current velocity in the Younger Dryas and Heinrich Stadial (HS)−1A, and increased velocities during the Bølling-Allerød warm period. Standard bulk magnetic parameters imply fining of magnetic grain size from the mid-Younger Dryas (∼12 ka) until ∼ 8 ka. First-order reversal curves (FORCs) were analyzed using ridge extraction to differentiate single domain (SD) from background (detrital) components. Principal component analysis (FORC-PCA) was then used to discriminate three end members corresponding to SD, pseudo-single domain (PSD), and multidomain (MD) magnetite. The fining of bulk magnetic grain size from 12 to 8 ka is due to reduction in concentration of detrital (PSD + MD) magnetite, superimposed on a relatively uniform concentration of SD magnetite produced by magnetotactic bacteria. The decrease in PSD+MD magnetite concentration from 12 to 8 ka is synchronized with increase in benthic δ13C, and with major (∼70 m) regional sea-level rise, and may therefore be related to detrital sources on the shelf that had reduced influence as sea level rose, and to bottom-water reorganization as Northern Source Water (NSW) replaced Southern Source Water (SSW).Research supported by US NSF grants 0850413 and 1014506, and the European R12esearch Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 320750. The UK NERC and BGS funded the recovery of Core MD04-2822

An Improved Algorithm For Unmixing First‐Order Reversal Curve Diagrams Using Principal Component Analysis

First‐order reversal curve (FORC) diagrams of synthetic binary mixtures with single‐domain, vortex state, and multi‐domain end members (EMs) were analyzed using principal component analysis (FORC‐PCA). Mixing proportions derived from FORC‐PCA are shown to deviate systematically from the known weight percent of EMs, which is caused by the lack of reversible magnetization contributions to the FORC distribution. The error in the mixing proportions can be corrected by applying PCA to the raw FORCs, rather than to the processed FORC diagram, thereby capturing both reversible and irreversible contributions to the signal. Here we develop a new practical implementation of the FORC‐PCA method that enables quantitative unmixing to be performed routinely on suites of FORC diagrams with up to four distinct EMs. The method provides access not only to the processed FORC diagram of each EM, but also to reconstructed FORCs, which enables objective criteria to be defined that aid identification of physically realistic EMs. We illustrate FORC‐PCA with examples of quantitative unmixing of magnetic components that will have widespread applicability in paleomagnetism and environmental magnetism

Pallasite paleomagnetism: Quiescence of a core dynamo

Recent paleomagnetic studies of two Main Group pallasites, the Imilac and Esquel, have found evidence for a strong, late-stage magnetic field on the parent body. It has been hypothesized that this magnetic field was generated by a core dynamo, driven by compositional convection during core solidification. Cooling models suggest that the onset of core solidification occurred ∼200 Ma after planetary accretion. Prior to core solidification, a core dynamo may have been generated by thermal convection; however a thermal dynamo is predicted to be short-lived, with a duration of ∼10 Ma to ∼40 Ma after planetary accretion. These models predict, therefore, a period of quiescence between the thermally driven dynamo and the compositionally driven dynamo, when no core dynamo should be active. To test this hypothesis, we have measured the magnetic remanence recorded by the Marjalahti and Brenham pallasites, which based on cooling-rate data locked in any magnetic field signals present ∼95 Ma to ∼135 Ma after planetary accretion, before core solidification began. The cloudy zone, a region of nanoscale tetrataenite islands within a Fe-rich matrix was imaged using X-ray photoemission electron microscopy. The recovered distribution of magnetisation within the cloudy zone suggests that the Marjalahti and Brenham experienced a very weak magnetic field, which may have been induced by a crustal remanence, consistent with the predicted lack of an active core dynamo at this time. We show that the transition from a quiescent period to an active, compositionally driven dynamo has a distinctive paleomagnetic signature, which may be a crucial tool for constraining the time of core solidification on differentiated bodies, including Earth.We acknowledge the Helmholtz-Zentrum Berlin for the use of the synchrotron radiation beam time at beamline UE49 of BESSY II. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC grant agreement numbers 320750 and 312284, and the Natural Environment Research Council. We thank the Natural History Museum, London for samples.This is the final version of the article. It first appeared from Elsevier via https://doi.org/10.1016/j.epsl.2016.02.03