Residual Field Research Articles

Expanders on matrices over a finite chain ring, I

In this work and its sequel, we study the expanding phenomenon of matrices over a finite chain ring of large residue field. A sum-product estimate is proved. It is shown that [Formula: see text] is a moderate expander on [Formula: see text] matrices with exponent [Formula: see text]. These results generalize the main theorems in the recent work [29] of Xie and Ge. The proofs use spectral graph theory and elementary divisor theory.

Triangulations of non-archimedean curves, semi-stable reduction, and ramification

Let K be a complete discretely valued field with algebraically closed residue field and let ℭ be a smooth projective and geometrically connected algebraic K-curve of genus g. Assume that g⩾2, so that there exists a minimal finite Galois extension L of K such that ℭ L admits a semi-stable model. In this paper, we study the extension L∣K in terms of the minimal triangulation of C, a distinguished finite subset of the Berkovich analytification C of ℭ. We prove that the least common multiple d of the multiplicities of the points of the minimal triangulation always divides the degree [L:K]. Moreover, in the special case when d is prime to the residue characteristic of K, then we show that d=[L:K], obtaining a new proof of a classical theorem of T. Saito. We then discuss curves with marked points, which allows us to prove analogous results in the case of elliptic curves, whose minimal triangulations we describe in full in the tame case. In the last section, we illustrate through several examples how our results explain the failure of the most natural extensions of Saito’s theorem to the wildly ramified case.

Applications of Hochschild cohomology to the moduli of subalgebras of the full matrix ring

Let Moldn,d be the moduli of rank d subalgebras of Mn over Z. For x∈Moldn,d, let A(x)⊆Mn(k(x)) be the subalgebra of Mn corresponding to x, where k(x) is the residue field of x. In this article, we apply Hochschild cohomology to Moldn,d. The dimension of the tangent space TMoldn,d/Z,x of Moldn,d over Z at x can be calculated by the Hochschild cohomology H1(A(x),Mn(k(x))/A(x)). We show that H2(A(x),Mn(k(x))/A(x))=0 is a sufficient condition for the canonical morphism Moldn,d→Z being smooth at x. We also calculate Hi(A,Mn(k)/A) for several R-subalgebras A of Mn(R) over a commutative ring R. In particular, we summarize the results on Hi(A,Mn(k)/A) for all k-subalgebras A of Mn(k) over an algebraically closed field k in the case n=2,3.

A field map updating algorithm to improve fat-water spiral imaging.

An accurate field map is essential to separate fat and water signals in a dual-echo chemical shift encoded spiral MRI scan. A rapid low-resolution B0 map prescan is usually performed before each exam. Occasional inaccuracy in these field map estimates can lead to misclassification of the water and fat signals as well as blurring artifacts in the reconstruction. The present work proposes a self-consistent model to evaluate residual field offsets according to the image data to improve the reconstruction quality and facilitate the scan efficiency. The proposed method compares the phase differences of the two-echo data after correcting for fat frequency offsets. A more accurate field map is approximated according to the phase discrepancies and improved image quality. Experiments were conducted with simulated off-resonance on a numerical phantom, five volunteer head scans, and four volunteer abdominal scans for validation. The initial reconstruction of the demonstrated examples exhibit blurring artifacts and misregistration of fat and water because of the inaccuracy of the field map. The proposed method updates the field map to amend the fat and water estimation and improve image quality. This work presents a model to improve the quality of fat-water imaging of the spiral MRI by estimating a better field map from the acquired data. It allows reducing the field map pre-scans before each spiral scan under normal circumstances to increase scan efficiency.

Bitangents to plane quartics via tropical geometry: rationality, $$\mathbb {A}^1$$-enumeration, and real signed count

We explore extensions of tropical methods to arithmetic enumerative problems such as $$\mathbb {A}^1$$ -enumeration with values in the Grothendieck–Witt ring and rationality over Henselian valued fields, using bitangents to plane quartics as a test case. We consider quartic curves over valued fields whose tropicalizations are smooth and satisfy a mild genericity condition. We then express obstructions to rationality of bitangents and their points of tangency in terms of twisting of edges of the tropicalization; the latter depends only on the tropicalization and the initial coefficients of the defining equation modulo squares. We also show that the $${{\,\textrm{GW}\,}}$$ -multiplicity of a tropical bitangent, i.e. the multiplicity with which its lifts contribute to the $$\mathbb {A}^1$$ -enumeration of bitangents as defined by Larson and Vogt (Res Math Sci 8(26):1–21, 2021), can be computed from the tropicalization of the quartic together with the initial coefficients of the defining equation. As an application, we show that the four lifts of most tropical bitangent classes contribute $$2\mathbb {H}$$ , twice the class of the hyperbolic plane, to the $$\mathbb {A}^1$$ -enumeration. These results rely on a degeneration theorem relating the Grothendieck–Witt ring of a Henselian valued field to the Grothendieck–Witt ring of its residue field, in residue characteristic not equal to two.

Enabling ambulatory movement in wearable magnetoencephalography with matrix coil active magnetic shielding

The ability to collect high-quality neuroimaging data during ambulatory participant movement would enable a wealth of neuroscientific paradigms. Wearable magnetoencephalography (MEG) based on optically pumped magnetometers (OPMs) has the potential to allow participant movement during a scan. However, the strict zero magnetic field requirement of OPMs means that systems must be operated inside a magnetically shielded room (MSR) and also require active shielding using electromagnetic coils to cancel residual fields and field changes (due to external sources and sensor movements) that would otherwise prevent accurate neuronal source reconstructions. Existing active shielding systems only compensate fields over small, fixed regions and do not allow ambulatory movement. Here we describe the matrix coil, a new type of active shielding system for OPM-MEG which is formed from 48 square unit coils arranged on two planes which can compensate magnetic fields in regions that can be flexibly placed between the planes. Through the integration of optical tracking with OPM data acquisition, field changes induced by participant movement are cancelled with low latency (25 ms). High-quality MEG source data were collected despite the presence of large (65 cm translations and 270° rotations) ambulatory participant movements.

Comparing of the analytical investigation with the FEM simulation for minimizing the total radiated sound from a vibrating plate

AbstractA theoretical model comprising Active‐Noise‐Control (ANC) systems is created to minimize interfering primary sound radiated from a vibrating simply supported plate with the destructive secondary sound radiated from loudspeakers. In this paper, a global noise reduction at low frequencies is achieved with local control of secondary sources while the most previous studies have already focused on a control of the sound pressure field over a large number of distributed microphones. The ANC systems are placed close to the primary noise. An optimal solution which is assigned to each loudspeaker is derived analytically in terms of the estimated active sound intensities in front of the loudspeakers. In addition, the model is investigated with the Finite‐Element‐Method (FEM). COMSOL Multiphysics is used to simulate the residual sound field by feeding the loudspeakers with the optimal solutions. The analytical results are compared with those results obtained from the FEM simulation. This study proofs the effectiveness of an ANC system and derives the optimal position and the required number of secondary sources to minimize the total radiated sound from a vibrating plate.

Henselian expansions of NIP fields

Let [Formula: see text] be an NIP field and let [Formula: see text] be a Henselian valuation on [Formula: see text]. We ask whether [Formula: see text] is NIP as a valued field. By a result of Shelah, we know that if [Formula: see text] is externally definable, then [Formula: see text] is NIP. Using the definability of the canonical [Formula: see text]-Henselian valuation, we show that whenever the residue field of [Formula: see text] is not separably closed, then [Formula: see text] is externally definable. In the case of separably closed residue field, we show that [Formula: see text] is NIP as a pure valued field.

Direct observation of quadrupolar strain fields surrounding Eshelby inclusions in metallic glasses.

For decades, scanning/transmission electron microscopy (S/TEM) techniques have been employed to analyze shear bands in metallic glasses and understand their formation in order to improve the mechanical properties of metallic glasses. However, due to a lack of direct information in reciprocal space, conventional S/TEM cannot characterize the local strain and atomic structure of amorphous materials, which are key to describe the deformation of glasses. For this work, we applied 4-dimensional STEM to map and directly correlate the local strain and the atomic structure at the nanometer scale in deformed metallic glasses. We observe residual strain fields with quadrupolar symmetry concentrated at dilated Eshelby inclusions. The strain fields percolate in a vortex-like manner building up the shear band. This provides a new understanding of the formation of shear bands in metallic glass. This article is protected by copyright. All rights reserved.

Local-global principle for projective homogeneous spaces of unitary groups

Let K be a complete discrete valued field with residue field k and F the function field of a curve over K. Let A∈2Br(F) be a central simple algebra with an involution σ of any kind and F0=Fσ. Let h be an hermitian space over (A,σ) and G=SU(A,σ,h) if σ is of first kind and G=U(A,σ,h) if σ is of second kind. Suppose that char(k)≠2 and ind(A)≤4. Then we prove that projective homogeneous spaces under G over F0 satisfy a local-global principle for rational points with respect to discrete valuations of F.

Post-deformation effects of Indo-Eurasia convergence on major geological features of north-central India: New insights from satellite gravity observations

The north-central region of the Indian subcontinent, which lies close to the Indo-Eurasian convergence zone, is concealed by ∼66 Ma Deccan volcanics and thick Proterozoic-Tertiary sedimentation, and as such its sub-surface structural configuration is not well understood. In the present study, we analyse high-resolution satellite gravity data over this region in order to probe deep structural fabric of the major geotectonic blocks and associated sedimentary sequences. The residual gravity field, deduced using Finite Element Method, clearly demarcates boundaries of the major geotectonic units of this region, which remained unknown. Our study indicates that the extent of the Bundelkhand cratonic segment is much larger than hitherto known, which extends from the eastern margin of Aravalli-Delhi Fold Belt to almost central part of the Indo Gangetic Plain. Similarly, Shillong Plateau located in northeastern part of India, characterized by a broad high-order positive residual gravity anomaly closure, extends between 86° E to 94° E, far beyond its currently known extent. Importantly, this massif is undergoing in-land rifting due to the regional neotectonic activities associated with Indo-Eurasia convergence and the compressive forces generated between India and Indo-Burmese collision zone. We modelled the gravity anomalies along four N-S profiles across the Narmada-Son Lineament (NSL), which clearly reveal that the Vindhyan sediments, whose extent were considered to be limited to the north of NSL only, was found to be extending further south across this lineament. In addition, a prominent ENE-WSW high-density ridge structure, paralleling the Himalayan arc, is also identified, which is also possibly formed due to N-S stresses, generated by the collision between Indian and Eurasian plates during early Tertiary period.

Spin noise in Er3+ single-ion magnets surrounded by ferromagnetic microparticles

Ferromagnetic microparticles significantly affect spin relaxation in the Er3+ single-ion magnet sandwiched in a composite material. The balance of thermal spin noise corresponding to Orbach, Raman, quantum tunneling, and direct relaxation channels is shifted in Er3+ complexes under the influence of surrounding ferromagnetic matrix. There are two competing sources of the electron spin noise controlled by ferromagnetic media. First, internal residual magnetic field delays spin relaxation in the Er3+ complexes due to the Zeeman interaction of the Er3+ spin even in the absence of external magnetic field. Second, chemical bonding between the Er 4d shell and the O 1s shell accelerates magnetic relaxation in the Er3+ ions on the surface of microparticles. Significance of these results is that composite media can be sliced into small elements with a variable frequency of spin noise depending on individual magnetization programmed within each element.

Weathering of 3-component synthetic food cones: effects on residual amount, release rate, and field capture of 3 pest species of fruit flies (Diptera: Tephritidae).

Food-based baits are an important component of trapping networks designed to detect invasive tephritid fruit flies (Diptera: Tephritidae). An aqueous solution of torula yeast plus borax (TYB) is widely used, but synthetic food lures have been developed to facilitate field procedures, ensure standard composition, and lengthen the interval of bait attractiveness. Cone-shaped dispensers, containing ammonium acetate, putrescine, and trimethylamine (so-called 3C food cones), are currently being used in some large-scale trapping systems (e.g., Florida). Prior work in Hawaii showed that traps baited with 3C food cones capture similar numbers of Mediterranean fruit flies (medflies), Ceratitis capitata (Wiedemann), as TYB-baited traps after 1-2 wk of weathering but capture fewer medflies thereafter. In addition, 3C food cones attract fewer oriental fruit flies, Bactrocera dorsalis (Hendel), and melon flies, Zeugodacuscucurbitae (Coquillett) than TYB even when the food cones are freshly deployed. The current study describes an additional trapping experiment that expands upon earlier work by (i) presenting 3C food cones either unbagged (as done previously) or in nonporous or breathable bags to possibly reduce volatilization and lengthen bait effectiveness and (ii) measuring the content of the 3 components over time to potentially associate fruit fly captures with the loss of these food cone constituents. Implications of these findings for fruit fly surveillance programs are discussed.

Gray level residual field: an effective metric for pixelwise matching quality evaluation in local digital image correlation

Gray level residual (GLR), also known as correlation residual field or image difference, reflects the intensity differences between reference and deformed images. In finite element-based global digital image correlation (DIC), GLR field can be readily computed and has been successfully used for crack or damage detection. The computation of pixelwise GLR field requires dense displacement results, which can be obtained using mesh interpolation in global DIC. To obtain the GLR field in subset-based local DIC, in which results are obtained at discrete calculation points, a simple, efficient and practical computation method for GLR field is presented, which accounts for the influence of illumination variations unavoidably occurred in real DIC tests. The proposed method can be easily implemented on both central process unit and graphics process unit to realize real-time visualization. Experiments showed that the GLR field can quantitatively and intuitively evaluate the pixelwise matching quality and provide clearer and finer locations for new components or textures (e.g. cracks) presented in deformed images. By fully leveraging the pixelwise matching quality information provided by the GLR field, the capability and robustness of local DIC is expected to be further enhanced.

Fast In-Situ Triaxial Remanent Magnetic Field Measurement for Single-Beam SERF Atomic Magnetometer Based on Trisection Algorithm

We demonstrate a method for quickly and automatically detecting all three components of a remanent magnetic field around a shielded spin-exchange relaxation-free (SERF) atomic magnetometer (AM) using the trisection algorithm (TSA) for zero-field resonance (ZFR). To satisfy the measurement of AMs, a resonance light of the 87Rb D1 line with a spectral width of less than 1MHz is converted to circular polarization by a linear polarizer and a quarter-wave plate. After the light beam has passed through the alkali metal vapor cell, the residual magnetic field can be measured by searching for triaxial ZFR optical peaks. The TSA stably reduces the measurement time to 2.41 s on average and improves the measurement accuracy, significantly outpacing existing methods. The weighted averages of all measurements with corresponding uncertainties are (−15.437 ± 0.022)nT, (6.062 ± 0.021)nT, and (−14.158 ± 0.052)nT on the x-, y-, and z-axes, respectively. These improvements could facilitate more extremely weak magnetic studies in real time, such as magnetoencephalography (MEG) and magnetocardiography (MCG) measurements.

Features of Gravity Anomalies and Oil-Gas Distribution Rules in Central and Western Sichuan Basin, China

In order to explore the rules between gravity anomalies and oil-gas distribution characteristics in central and western Sichuan Basin, we divided the tectonic unit in central and western Sichuan basin on the base of the analysis of gravity anomaly characteristics, and studied the correlation between the oil–gas distribution and the local gravity anomaly in the study area. The results show that the variation in the range of the Bouguer gravity field in the interior of the basin is relatively small, and the southern part shows a clear gravity high zone, with gradual gravity gradient zones all around the basin periphery. The abnormal value of the residual gravity field in the basin is an obvious high–value gravity belt in the north and west, and the interior is arranged alternately with local high gravity and low gravity in the north–east direction. The tectonic units of the central and western Sichuan Basin can be divided into five regions, based on the characteristics of the Bouguer gravity field, namely, the Central Sichuan uplift zone, the West Sichuan depressional zone, the East Sichuan high steep zone, the South Sichuan low steep zone, and the North Sichuan low slow zone. Combined with geological data and Bouguer gravity anomaly processing results, the distribution of oil and gas fields in the central and western Sichuan Basin is certain correlated with the local gravity high zone and the transition zone between the local gravity high zone and the local gravity low zone. They are the major areas of oil and gas.

Concomitant magnetic-field compensation for 2D spiral-ring turbo spin-echo imaging at 0.55T and 1.5T.

To develop 2D turbo spin-echo (TSE) imaging using annular spiral rings (abbreviated "SPRING-RIO TSE") with compensation of concomitant gradient fields and B0 inhomogeneity at both 0.55T and 1.5T for fast T2 -weighted imaging. Strategies of gradient waveform modifications were implemented in SPRING-RIO TSE for compensation of self-squared concomitant gradient terms at the TE and across echo spacings, along with reconstruction-based corrections to simultaneously compensate for the residual concomitant gradient and B0 field induced phase accruals along the readout. The signal pathway disturbance caused by time-varying and spatially dependent concomitant fields was simulated, and echo-to-echo phase variations before and after sequence-based compensation were compared. Images from SPRING-RIO TSE with no compensation, with compensation, and Cartesian TSE were also compared via phantom and in vivo acquisitions. Simulation showed how concomitant fields affected the signal evolution with no compensation, and both simulation and phantom studies demonstrated the performance of the proposed sequence modifications, as well as the readout off-resonance corrections. Volunteer data showed that after full correction, the SPRING-RIO TSE sequence achieved high image quality with improved SNR efficiency (15%-20% increase), and reduced RF SAR (˜50% reduction), compared to the standard Cartesian TSE, presenting potential benefits, especially in regaining SNR at low-field (0.55T). Implementation of SPRING-RIO TSE with concomitant field compensation was tested at 0.55T and 1.5T. The compensation principles can be extended to correct for other trajectory types that are time-varying along the echo train and temporally asymmetric in TSE-based imaging.

Relationship between stress and magnetic signal of steel box girder based on magnetic memory method

Metal magnetic memory testing (MMMT) is a nondestructive testing technique that can detect early signs of damage in components. Many scholars have studied the effect of uniform stress on the self-leakage magnetic field (SLMF) strength of ferromagnetic materials. However, there is still insufficient research on the stress concentration caused by uneven stress, under the combined action of bending and shear. In this study, we studied the law of distribution of the magnetic signal, HP(y) and magnetic gradient, K, on a part of the surface of a steel box girder damaged by buckling, using a four-point bending pattern. The results showed that combining the three peak positions, namely, the magnetic signal, its newly added comparing initial magnetic signal, and magnetic gradient distribution curves, could accurately determine all stress concentration positions on the flange of the steel box girder, and reduce the interference of the initial complex residual magnetic field. Furthermore, we studied the quantitative relationship between normal stress, shear stress, and a magnetic signal. It was found that the stress-magnetic relationship conformed to the Jiles–Atherton model. The peak value of HP(y) – 𝜎, |HP(y)|a – 𝜎, and Kmax – 𝜎 relationship curves could be used as the characteristic point of the critical yield stress at the action of normal and shear stress. The degree of stress concentration of the flange and web could be quantitatively evaluated by fitting the Kmax – 𝜎 relationship. This study can provide an experimental reference for the application of MMMT in the evaluation and early warning of the state of damage to a steel box girder.

Fracture failure analysis of insulation with initial crack defect for stator end-winding in induction motor by using magnetic-structural coupling model

The insulation mechanic failure in stator end-winding of induction motor is usually an early and serious cause to weaken the residual breakdown electrical field strength and produce the short-circuit fault, especially subjecting to the combination of dynamical electromagnetic forces, mechanical stress and vibration. In this paper, the fracturebehavior of insulation layer with considering the initial crack defects and end-hoop support failures in end-windings were analyzed by using magnetic-structural coupling model and finite element method (FEM). Firstly, the distributions of magnetic flux density and electromagnetic force around the stator end region were determined by injecting three-phase alternating current. Secondly, the dynamic characteristics of deformation, stress and strain in winding insulation were respectively calculated by coupling the transient electromagnetic and structural analysis. Furthermore, the weak points of the concentrated stress and strain were located. Thirdly, the crack model mounted in winding insulation is defined and simulated by employing three-dimensional (3-D) semi-elliptical crack element. To evaluate the fracture mechanism and the degree of crack expansion quantitatively, the stress intensity factor (SIF) was introduced. Finally, the influence of crack location, direction, depth and end-hoop support failure on SIF and crack propagation were investigated. Results show that the concentrated stress at knuckle part of the coil insulation is lager quite larger than that of other parts. The SIF of transverse crack is larger than that of longitudinal cracks. The larger the initial crack depth in the stator end-winding insulation, the more serious the tendency and degree of crack fracture. Local end-hoop support failure also has an important influence on the crack propagation. Results in this study may contribute to the understanding of fracturefailure behaviors in insulation under dynamical electromagnetic vibration and provide necessary theoretical reference for fault diagnosis and prediction of stator winding in induction motors.

Residual magnetic field induced by superconducting magnets of Large Helical Device

The residual magnetic field was measured to investigate its source for the Large Helical Device, the superconducting magnet system of which consists of two Helical Coils (HCs), two Inner Vertical (IV) coils, two Inner Shaping (IS) coils, and two Outer Vertical (OV) coils. NbTi cable-in-conduit conductors were adopted for the IV, IS, and OV coils. Firstly, Hall probes were installed at five periodic positions on the mid-plane of the inner cylinder of the cryostat. Since the residual field was changed by around 0.1 mT at all the positions during the warm-up of the superconducting coils, a major part of the residual field had to be induced by magnetization of the coils. In the next campaign (cool-down, plasma experiment, and warm-up), the Hall probes were moved to the five different vertical positions in order to measure the distribution of the residual field. Calculation of the residual field has been carried out under the assumption that NbTi filaments in each conductor are magnetized in the same direction as the field at the center of the conductor during excitation. From comparison between the measured and calculated values, we conclude that the residual field from the coils that had been excited to high currents should be reduced by around 35%, due to the self-field in strands in the conductor. The best fitted critical current densities of the IV and IS coils are 1.31 and 2.81 × 1010 A/m2, respectively, which are consistent with the field dependence obtained from the magnetization curve of each strand.