Geometric Bias Research Articles

Sampling Confined Fission Tracks for Constraining Geological Thermal Histories

Fission-track modeling rests on etching, counting and measuring the lattice damage trails from uranium fission. The tools for interpreting fission-track data are advanced but the results are never better than the data. Confined-track samples must be an adequate size for statistical analysis, representative of the track population and consistent with the model assumptions and with the calibration data. Geometrical and measurement biases are understood and can be dealt with up to a point. However, the interrelated issues of etching protocol and track selection are more difficult to untangle. Our investigation favors a two-step protocol. The duration of the first step is inversely proportional to the apatite etch rate so that different apatites etch to the same Dpar. A long immersion reveals many more confined tracks, terminated by basal and prism faces. This allows consistent length measurements and permits orienting each track relative to the c-axis. Long immersion times combined with deep ion irradiation reveal confined tracks deep inside the grains. Provided it is long enough, the precise immersion time is not important if the effective etch times of the selected tracks are calculated from their measured widths. Then, whether the sample is mono- or multi-compositional, we can, post hoc, select tracks with the desired properties. The second part of the protocol has to do with the fact that fossil tracks in geological samples appear to be under-etched compared to induced tracks etched under the same conditions. This should be assumed if the semi-axes of a fitted ellipse plot above the induced-track line. In that case, an additional etch can increase the track lengths to a point where they are consistent with the model based on lab-annealing of induced tracks, a condition for valid thermal histories. Here too, it is possible to select a subset of tracks with effective etch times consistent with the model if the widths of confined tracks are measured along with their lengths and orientations.

Self-organization of mortal filaments and its role in bacterial division ring formation

Filaments in the cell commonly treadmill. Driven by energy consumption, they grow on one end while shrinking on the other, causing filaments to appear motile even though individual proteins remain static. This process is characteristic of cytoskeletal filaments and leads to collective filament self-organization. Here we show that treadmilling drives filament nematic ordering by dissolving misaligned filaments. Taking the bacterial FtsZ protein involved in cell division as an example, we show that this mechanism aligns FtsZ filaments in vitro and drives the organization of the division ring in living Bacillus subtilis cells. We find that ordering via local dissolution also allows the system to quickly respond to chemical and geometrical biases in the cell, enabling us to quantitatively explain the ring formation dynamics in vivo. Beyond FtsZ and other cytoskeletal filaments, our study identifies a mechanism for self-organization via constant birth and death of energy-consuming filaments.

Jet suppression and azimuthal anisotropy from RHIC to LHC

Azimuthal anisotropies of high-pT particles produced in heavy-ion collisions are understood as an effect of a geometrical selection bias. Particles oriented in the direction in which the QCD medium formed in these collisions is shorter suffer less energy loss, and thus, are over-represented in the final ensemble compared to those oriented in the direction in which the medium is longer. In this work we present the first semianalytical predictions, including propagation through a realistic, hydrodynamical background, of the elliptic azimuthal anisotropy for jets, obtaining a quantitative agreement with available experimental data as a function of the jet pT, its cone size R, and the collisions centrality. Jets are multipartonic, extended objects and their energy loss is sensitive to substructure fluctuations. This sensitivity is determined by the physics of color coherence that relates to the ability of the medium to resolve those partonic fluctuations. Specifically, color dipoles with an angular separation smaller than a critical angle, θc, are not resolved by the medium and they effectively act as a coherent source of energy loss. We find that elliptic jet azimuthal anisotropy has a specially strong dependence on coherence physics due to the marked length dependence of θc. By combining our predictions for the collision systems and center-of-mass energies studied at RHIC and the LHC, covering a wide range of typical values of θc, we show that the relative size of elliptic jet azimuthal anisotropies for jets with different cone sizes R follows a universal trend that indicates a transition from a coherent regime of jet quenching to a decoherent regime. These results suggest a way forward to reveal the role played by the physics of jet color decoherence in probing deconfined QCD matter. Published by the American Physical Society 2024

Compositional effects on etching of fossil confined fission tracks in apatite

Abstract Fission-track analysis is a thermochronologic method for dating rocks and reconstructing their low-temperature thermal histories. We investigate the influence of the apatite composition on the etching of fossil confined fission tracks, and its consequences for the fission-track method. We conducted step-etch experiments with 5.5 M HNO3 at 21 °C on samples with etch pit diameters (Dpar) spanning most of the range for natural apatites (Panasqueira: 1.60 µm, Slyudyanka: 2.44 µm, Brazil: 3.92 µm, and Bamble: 4.60 µm) to determine their apatite etch rates vR (the rate at which each lattice plane is displaced parallel to itself) as a function of crystallographic orientation (ϕ’). Our measurements revealed significant differences between the four samples. We fitted three-parameter functions, vR = a(Dpar) ϕ’ eb(Dpar)ϕ’ + c, describing vR as a function of the angle to the apatite c-axis for our hexagonal samples (excluding Bamble) and Durango apatite. The parameters a and b both exhibit a linear correlation with Dpar, whereas the constant c is small (~0.1 µm.min-1) and its between-sample variation negligible at the resolution of our measurements. Bamble exhibits a different, bimodal relationship between vR and ϕ’, which we fitted with a sum of two sine functions. In all cases, including Bamble, there is a striking correlation between the angular frequencies of horizontal confined tracks and the magnitude of the apatite etch rate vR perpendicular to the track axes. This shows that the sample of confined tracks selected for measurement and modeling is to a much greater degree determined by the etching properties of the apatite sample than by geometric or subjective biases. The track etch rate vT is constant along most of the track length but varies from track to track. The mean vT correlates with Dpar, so that tracks etch to their full lengths in a shorter time in faster etching apatites. The mean rate of length increase between etch steps, vL, also correlates with Dpar. The length increments of individual tracks are however irregular. This points to an intermittent structure at the ends of the tracks.

Biases in hand perception are driven by somatosensory computations, not a distorted hand model

To sense and interact with objects in the environment, we effortlessly configure our fingertips at desired locations. It is therefore reasonable to assume that the underlying control mechanisms rely on accurate knowledge about the structure and spatial dimensions of our hand and fingers. This intuition, however, is challenged by years of research showing drastic biases in the perception of finger geometry.1,2,3,4,5 This perceptual bias has been taken as evidence that the brain's internal representation of the body's geometry is distorted,6 leading to an apparent paradox regarding the skillfulness of our actions.7 Here, we propose an alternative explanation of the biases in hand perception-they are the result of the Bayesian integration of noisy, but unbiased, somatosensory signals about finger geometry and posture. To address this hypothesis, we combined Bayesian reverse engineering with behavioral experimentation on joint and fingertip localization of the index finger. We modeled the Bayesian integration either in sensory or in space-based coordinates, showing that the latter model variant led to biases in finger perception despite accurate representation of finger length. Behavioral measures of joint and fingertip localization responses showed similar biases, which were well fitted by the space-based, but not the sensory-based, model variant. The space-based model variant also outperformed a distorted hand model with built-in geometric biases. In total, our results suggest that perceptual distortions of finger geometry do not reflect a distorted hand model but originate from near-optimal Bayesian inference on somatosensory signals.

Psoas force recruitment in full-body musculoskeletal movement simulations is restored with a geometrically informed cost function weighting

Simulations of musculoskeletal models are useful for estimating internal muscle and joint forces. However, predicted forces rely on optimization and modeling formulations. Geometric detail is important to predict muscle forces, and greater geometric complexity is required for muscles that have broad attachments or span many joints, as in the torso. However, the extent to which optimized muscle force recruitment is sensitive to these geometry choices is unclear. We developed level, uphill and downhill sloped walking simulations using a standard (uniformly weighted, “fatigue-like”) cost function with lower limb and full-body musculoskeletal models to evaluate hip muscle recruitment with different geometric representations of the psoas muscle under walking conditions with varying hip moment demands. We also tested a novel cost function formulation where muscle activations were weighted according to the modeled geometric detail in the full-body model. Total psoas force was less and iliacus, rectus femoris, and other hip flexors’ force was greater when psoas was modeled with greater geometric detail compared to other hip muscles for all slopes. The proposed weighting scheme restored hip muscle force recruitment without sacrificing detailed psoas geometry. In addition, we found that lumbar, but not hip, joint contact forces were influenced by psoas force recruitment. Our results demonstrate that static optimization dependent simulations using models comprised of muscles with different amounts of geometric detail bias force recruitment toward muscles with less geometric detail. Muscle activation weighting that accounts for differences in geometric complexity across muscles corrects for this recruitment bias.

Thermodynamics-Informed Graph Neural Networks

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme. The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior with permutation invariant node and edge update functions. The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics. Several examples are provided in both Eulerian and Lagrangian description in the context of fluid and solid mechanics respectively, achieving relative mean errors of less than 3% in all the tested examples. Two ablation studies are provided based on recent works in both physics-informed and geometric deep learning.

Giant Outer Transiting Exoplanet Mass (GOT ‘EM) Survey. IV. Long-term Doppler Spectroscopy for 11 Stars Thought to Host Cool Giant Exoplanets

Discovering and characterizing exoplanets at the outer edge of the transit method’s sensitivity has proven challenging owing to geometric biases and the practical difficulties associated with acquiring long observational baselines. Nonetheless, a sample of giant exoplanets on orbits longer than 100 days has been identified by transit hunting missions. We present long-term Doppler spectroscopy for 11 such systems with observation baselines spanning a few years to a decade. We model these radial velocity observations jointly with transit photometry to provide initial characterizations of these objects and the systems in which they exist. Specifically, we make new precise mass measurements for four long-period giant exoplanets (Kepler-111 c, Kepler-553 c, Kepler-849 b, and PH-2 b), we place new upper limits on mass for four others (Kepler-421 b, KOI-1431.01, Kepler-1513 b, and Kepler-952 b), and we show that several confirmed planets are in fact not planetary at all. We present these findings to complement similar efforts focused on closer-in short-period giant planets, and with the hope of inspiring future dedicated studies of cool giant exoplanets.

Ammonia emissions from livestock facilities around an international airport, Tehran, Iran: An experimental and mathematical study

AbstractAmmonia emissions from livestock farms are a major problem for staff and residents near these centers. Anaerobic decomposition of livestock waste and the collection and stacking of waste are the main sources of ammonia gas on livestock farms. This article examined ammonia emissions from livestock facilities near Tehran Imam Khomeini International Airport. First, field measurements were made in the summer (30°C), and collected samples were examined using the indophenol technique. AERMOD, based on Gaussian fluctuating plume theory, was constructed to model ammonia emissions. According to AERMOD, the maximum periodic‐seasonal 2‐hourly and 8‐hourly ammonia concentrations were 15.9, 229, and 63.7 OU (odor unit per unit volume)/m3, respectively. The hourly ammonia emission rate from livestock sources is also 0.0168 gm−2 h−1. AERMOD results mathematical model indicated reasonable agreement with the field measurement, which the coefficient of determination (R2), index of agreement (d), and efficiency coefficient (E) were 0.95, 0.97, and 0.91, respectively. Moreover, Statistical indices, including geometric mean bias (MG), geometric variance (VG), fraction of predictions within a factor of two of observations (FAC2), and normalized mean square error (NMSE), the root mean square error (RMSE) and mean absolute error (MAE) are also indicated by 1.36 and 0.67, respectively, were used to assess the reliability of the model results showed that AERMOD had a good agreement with the field measurement.

The giant nature of WD 1856 b implies that transiting rocky planets are rare around white dwarfs

ABSTRACT White dwarfs (WDs) have roughly Earth-sized radii – a fact long recognized to facilitate the potential discovery of sub-Earth-sized planets via transits, as well as atmospheric characterization including biosignatures. Despite this, the first (and still only) transiting planet discovered in 2020 was a roughly Jupiter-sized world, found using Transiting Exoplanet Survey Satellite (TESS) photometry. Given the relative paucity of giant planets compared to terrestrials indicated by both exoplanet demographics and theoretical simulations (a ‘bottom-heavy’ radius distribution), this is perhaps somewhat surprising. Here, we quantify the surprisingness of this fact accounting for geometric bias and detection bias assuming (1) a bottom-heavy Kepler-derived radius distribution and (2) a top-heavy radial velocity-inspired radius distribution. Both are concerning, with the latter implying that rocky planets are highly unusual and the former implying that WD 1856 b would have to be highly surprising event at the <0.5 per cent level. Using a hierarchical Bayesian model, we infer the implied power-law radius distribution conditioned upon WD 1856 b and arrive at a top-heavy distribution, such that 0.1–2 R⊕ planets are an order-of-magnitude less common than 2–20 R⊕ planets in the period range of 0.1–10 d. The implied hypothesis is that transiting WD rocky planets are rare. We discuss ways to reconcile this with other evidence for minor bodies around WDs, and ultimately argue that it should be easily testable.

Inverse-problem versus principal component analysis methods for angular differential imaging of circumstellar disks

Context. Circumstellar disk images have highlighted a wide variety of morphological features. Recovering disk images from high-contrast angular differential imaging (ADI) sequences is, however, generally affected by geometrical biases, leading to unreliable inferences of the morphology of extended disk features. Recently, two types of approaches have been proposed to recover more robust disk images from ADI sequences: iterative principal component analysis (I-PCA) and inverse problem (IP) approaches. Aims. We introduce mustard, a new IP-based algorithm specifically designed to address the problem of the flux invariant to rotation in ADI sequences – a limitation inherent to the ADI observing strategy – and discuss the advantages of IP approaches with respect to PCA-based algorithms. Methods. The mustard model relies on the addition of morphological priors on the disk and speckle field to a standard IP approach to tackle rotation-invariant signals in circumstellar disk images. We compared the performance of mustard, I-PCA, and standard PCA on a sample of high-contrast imaging data sets acquired in different observing conditions, after injecting a variety of synthetic disk models at different contrast levels. Results. Mustard significantly improves the recovery of rotation-invariant signals in disk images, especially for data sets obtained in good observing conditions. However, the mustard model inadequately handles unstable ADI data sets and provides shallower detection limits than PCA-based approaches. Conclusions. Mustard has the potential to deliver more robust disk images by introducing a prior to address the inherent ambiguity of ADI observations. However, the effectiveness of the prior is partly hindered by our limited knowledge of the morphological and temporal properties of the stellar speckle halo. In light of this limitation, we suggest that the algorithm could be improved by enforcing a data-driven prior based on a library of reference stars.

Are there more galaxies than we see around high-z quasars?

Context. It is still debated whether z ≳ 6 quasars lie in the most massive dark matter haloes of the Universe. While most theoretical studies support this scenario, current observations yield discordant results when they probe the halo mass through the detection rate of quasar companion galaxies. Feedback processes from supermassive black holes and dust obscuration have been blamed for this discrepancy, but these effects are complex and far from being clearly understood. Aim. This paper aims to improve the interpretation of current far-infrared observations by taking the cosmological volume probed by the Atacama Large Millimeter/submillimeter Array Telescope into account and to explain the observational discrepancies. Methods. We statistically investigated the detection rate of quasar companions in current observations and verified whether they match the expected distribution from various theoretical models when they are convolved with the ALMA field of view through the use of Monte Carlo simulations. Results. We demonstrate that the telescope geometrical bias is fundamental and can alone explain the scatter in the number of detected satellite galaxies in different observations. We conclude that the resulting companion densities depend on the chosen galaxy distributions. According to our fiducial models, current data favour a density scenario in which quasars lie in dark matter haloes with a viral mass of Mvir ≳ 1012 M⊙, in agreement with most theoretical studies. According to our analysis, each quasar has about two companion galaxies, with a [CII] luminosity L[CII] ≳ 108 L⊙, within a distance of about 1 Mpc from the quasar.

Can Cold Jupiters Sculpt the Edge-of-the-multis?

Compact systems of multiple close-in super-Earths/sub-Neptunes (compact multis) are a ubiquitous outcome of planet formation. It was recently discovered that the outer edges of compact multis are located at smaller orbital periods than expected from geometric and detection biases alone, suggesting some truncation or transition in the outer architectures. Here we test whether this edge-of-the-multis might be explained in any part by distant giant planets in the outer regions (≳1 au) of the systems. We investigate the dynamical stability of observed compact multis in the presence of hypothetical giant (≳0.5 M Jup) perturbing planets. We identify what parameters would be required for hypothetical perturbing planets if they were responsible for dynamically sculpting the outer edges of compact multis. Edge-sculpting perturbers are generally in the range of P ∼ 100–500 days for the average compact multi, with most between P ∼ 200 and 300 days. Given the relatively close separation, we explore the detectability of the hypothetical edge-sculpting perturbing planets, finding that they would be readily detectable in transit and radial velocity data. We compare to observational constraints and find it unlikely that dynamical sculpting from distant giant planets contributes significantly to the edge-of-the-multis. However, this conclusion could be strengthened in future work by a more thorough analysis of the detection yields of the perturbing planets.

Geometric Inductive Biases for Identifiable Unsupervised Learning of Disentangled Representations

The model identifiability is a considerable issue in the unsupervised learning of disentangled representations. The PCA inductive biases revealed recently for unsupervised disentangling in VAE-based models are shown to improve local alignment of latent dimensions with principal components of the data. In this paper, in additional to the PCA inductive biases, we propose novel geometric inductive biases from the manifold perspective for unsupervised disentangling, which induce the model to capture the global geometric properties of the data manifold with guaranteed model identifiability. We also propose a Geometric Disentangling Regularized AutoEncoder (GDRAE) that combines the PCA and the proposed geometric inductive biases in one unified framework. The experimental results show the usefulness of the geometric inductive biases in unsupervised disentangling and the effectiveness of our GDRAE in capturing the geometric inductive biases.

Numerical simulation of the radioactive contamination of Ukraine after the Chornobyl disaster: the influence of the input meteorological data on the results uncertainty

In this article we assess the sensitivity of the numerical simulations of the radioactive 137Cs contamination of Ukraine caused by the Chornobyl nuclear power plant accident in 1986 to the input meteorological data. The atmospheric transport, dispersion, and deposition (dry scavenging and rain washout) of the radioactive aerosols was simulated using the CALPUFF dispersion model. The source parameterization of the 137Cs emissions during the active phase of the catastrophe (26 April—May 5 of 1986) was adopted from the previously published literature results. Seventeen different versions/realizations of the input meteorology for CALPUFF simulations were prepared with the regional prognostic meteorological model WRF by combining the available global atmospheric reanalyses for 1986 (NNRP, ERA-Interim, ERA5, CFSR) and the model’s physical parameterizations (microphysics, radiation processes, boundary/surface layer physics). The assessment of the simulation uncertainty was carried out in two different ways. In the first approach, the uncertainty was estimated as the width of the distribution of the calculated 137Cs surface concentrations (adjusted to the logarithmic scale), which were obtained with different versions of the input meteorology. The second approach was based on the statistical comparison of the calculated 137Cs contaminations and the corresponding measured values obtained during a complex assessment of the aftermath of the disaster made at the beginning of 1990s. Two statistical metrics were used: the geometric mean bias and the geometric mean variance. The results of our study demonstrate that even when using somewhat unified meteorological data (atmospheric reanalysis), the results of the radioactive contamination calculations at the same spatial locations can differ by several orders of magnitude. We find that the uncertainty depends not only on the distance to the source of the emissions but also on the physical mechanism (wet or dry deposition) responsible for the formation of the local contamination

The comparison between in-situ monitored data and modelled results of nitrogen dioxide (NO2): case-study, road networks of Kigali city, Rwanda

The incomplete combustion of fossil fuels from petrol, natural gas, and fuel oil in the engine of vehicles contributes to air quality degradation through traffic-related air pollutant emissions. The Real-time affordable multi-pollutant (RAMPs) monitors were installed in Kigali, the capital of Rwanda, to fill the gap in air quality datasets. Using RAMPs, this is the first air quality modelling research in Rwanda aiming to report the concentration of NO2 by comparing In-situ monitored data and modelled results. We targeted NO2 emissions from 27 road networks of Kigali to address the impacts of traffic emissions on air quality over 2021. The American Meteorological Society and Environmental Protection Agency regulatory models (AERMOD and ISCST3) were used for simulation. Statistical indexes include fractional bias (FB), the fraction of the prediction within the factor of two of the observations (FAC2), normalized mean square error (NMSE), geometric mean bias (MG), and geometric variance (VG) used to assess models' reliability. Monitoring shows the annual mean of 16.07 μg/m3, 20.35 μg/m3, and 15.46 μg/m3 at Mont-Kigali, Gacuriro, and Gikondo-Mburabuturo stations, respectively. Modelling shows the daily mean of 111.77 μg/m3 and annually mean of 50.42 μg/m3 with AERMOD and daily mean of 200.26 μg/m3 and annually mean of 72.26 μg/m3 with ISCST3. The FB, NMSE, and FAC2 showed good agreement, while MG and VG showed moderate agreement with AERMOD. The FB, NMSE, and MG showed moderate agreement, while FAC2 and VG disagreed with ISCST3. Traffic and urban residential emissions were identified as potential sources of NO2. Results indicated that Kigali residents are exposed to a significant level of NO2 exceeding World Health Organisation limits. Findings will help track the effectiveness of Rwanda’s recently executed pollution-control policy, suggest evidence based on the recommendations to reduce NO2, and use further dispersion models to support ground-based observations to improve public health.

Analysis of the arm-like structure in the outer disk of PDS 70

Context. Observing dynamical interactions between planets and disks is key to understanding their formation and evolution. Two protoplanets have recently been discovered within the PDS 70 protoplanetary disk, along with an arm-like structure toward the northwest of the star. Aims. Our aim is to constrain the morphology and origin of this arm-like structure, and to assess whether it could trace a spiral density wave caused by the dynamical interaction between the planet PDS 70c and the disk. Methods. We analyzed polarized and angular differential imaging (PDI and ADI) data taken with VLT/SPHERE, spanning six years of observations. The PDI data sets were reduced using the irdap polarimetric data reduction pipeline, while the ADI data sets were processed using mustard, a novel algorithm based on an inverse problem approach to tackle the geometrical biases spoiling the images previously used for the analysis of this disk. Results. We confirm the presence of the arm-like structure in all PDI and ADI data sets, and extract its trace by identifying local radial maxima in azimuthal slices of the disk in each data set. We do not observe a southeast symmetric arm with respect to the disk minor axis, which seems to disfavor the previous hypothesis that the arm is the footprint of a double-ring structure. If the structure traces a spiral density wave following the motion of PDS 70c, we would expect 11°.28−0°.86+2°.20 rotation for the spiral in six years. However, we do not measure any significant movement of the structure. Conclusions. If the arm-like structure is a planet-driven spiral arm, the observed lack of rotation would suggest that the assumption of rigid-body rotation may be inappropriate for spirals induced by planets. We suggest that the arm-like structure may instead trace a vortex appearing as a one-armed spiral in scattered light due to projection effects. The vortex hypothesis accounts for both the lack of observed rotation and the presence of a nearby sub-millimeter continuum asymmetry detected with ALMA. Additional follow-up observations and dedicated hydrodynamical simulations could confirm this hypothesis.

Exploiting geometric biases in inverse nano-optical problems using artificial neural networks.

Solving the inverse problem is a major challenge in contemporary nano-optics. However, frequently not just a possible solution needs to be found but rather the solution that accommodates constraints imposed by the problem at hand. To select the most plausible solution for a nano-optical inverse problem additional information can be used in general, but how to specifically formulate it frequently remains unclear. Here, while studying the reconstruction of the shape of an object using the electromagnetic field in its proximity, we show how to take advantage of artificial neural networks (ANNs) to produce solutions consistent with prior assumptions concerning the structures. By preparing suitable datasets where the specific shapes of possible scatterers are defined, the ANNs learn the underlying scatterer present in the datasets. This helps to find a plausible solution to the otherwise non-unique inverse problem. We show that topology optimization, in contrast, can fail to recover the scatterer geometry meaningfully but a hybrid approach that is based on both, ANNs and a topology optimization, eventually leads to the most promising performance. Our work has direct implications in fields such as optical metrology.

Microtubule organization and cell geometry.

A characteristic feature of nondividing animal cells is the radial organization of microtubules (MTs), emanating from a single microtubule organizing center (MTOC). As generically these cells are not spherically symmetric, this raises the question of the influence of cell geometry on the orientational distribution of microtubules. We present a systematic study of this question in a simplified setting where MTs are nucleated from a single fixed MTOC in the center of an elliptical cell geometry. Within this context we introduce four models of increasing complexity, each one introducing additional mechanisms that govern the interaction of the MTs with the cell boundary. In order, we consider the cases: MTs that can bind to the boundary with a fixed mean residence time (M0), force-producing MTs that can slide on the boundary towards the cell poles (MS), MTs that interact with a generic polarity factor that is transported and deposited at the boundary, and which in turn stabilizes the MTs at the boundary (MP), and a final model in which both sliding and stabilization by polarity factors is taken into account (MSP). In the baseline model (M0), the exponential length distribution of MTs causes most of the interactions at the cell boundary to occur along the shorter transverse direction in the cell, leading to transverse biaxial order. MT sliding (MS) is able to reorient the main axis of this biaxial order along the longitudinal axis. The polarization mechanism introduced in MP and MSP overrules the geometric bias towards bipolar order observed in M0 and MS, and allows the establishment of unipolar order either along the short (MP) or the long cell axis (MSP). The behavior of the latter two models can be qualitatively reproduced by a very simple toy model with discrete MT orientations.

Validation of thermodynamic magneto-mechanical finite-element model on cantilever-beam type magnetostrictive energy harvester

This paper presents the validation of a thermodynamic magneto-mechanical model to analyze a galfenol based cantilever beam type energy harvesting device. As compared to some earlier modeling approaches that were tested only on specific harvester geometries, the thermodynamic model has already been validated on rod-type harvesters and is now shown to be suitable for analyzing also beam-type devices. Moreover, the paper discusses the influence of magnetostriction upon resonant frequency. The thermodynamic model is implemented in a 3D finite element solver using COMSOL Multiphysics software. This allows optimizing the device design by tuning the geometric parameters and magnetic bias under available operating conditions (amplitude and frequency of vibrations) easily and efficiently. A unimorph cantilever beam type prototype harvester device consisting of a galfenol beam bonded to an aluminum substrate is constructed for validating the model. Simulated and measured results are compared at base excitation amplitudes of 0.5 to 2 g under varying vibration frequencies. The results show that the maximum induced voltage is obtained at the resonant frequency which decreases slightly with an increase in the vibration amplitude. Furthermore, it is shown that the resonant frequency decreases from 201 Hz to 187 Hz at 1 g base acceleration when the magnetic bias is removed. The comparison of measured and simulated results show that the model can accurately predict the resonant frequency with a relative error of less than 2 %, validating the modeling approach. The model can also reasonably determine the open circuit voltage with some discrepancies at large vibration amplitudes.