Imperfect Field Research Articles

Implementing a two-stage, shim field-calibrated superconducting shimming method on a 7 T cryogen-free small animal MRI magnet

Ultrahigh field systems (≥ 7 T) can increase the signal-to-noise ratio of magnetic resonance imaging (MRI), improving imaging performance compared to systems with lower fields. However, these enhancements heavily rely on a high B0 magnetic field homogeneity level, which can be achieved through superconducting shimming. This paper presents a novel two-stage superconducting shimming method designed to achieve precise shimming for a 7 T MRI superconducting magnet. In the initial stage, detailed measurements and fittings were conducted to determine the current polarity and the axial or circumferential positions of the shim fields. Subsequently, an optimization strategy was implemented to determine the optimal shim currents with a flexible target field. The second stage involves an iterative process to fine-tune the current of a specific shim coil, identified as having the most significant impact on field homogeneity. The overall fitness of 99.5% underscores the precision in determining the current polarity and position of the shim fields. Significantly, the calibrated shim system substantially improves the peak-to-peak and Root Mean Square Error (RMSE) field homogeneities from 107.42 ppm and 37.00 ppm to 11.12 ppm and 3.26 ppm, respectively, representing improvements of 89.65% and 91.19%. Furthermore, the simulation results of the fine-tuning stage demonstrate additional enhancements in peak-to-peak field homogeneity, to 9.9 ppm by reducing the current of the Z2 shim coil by 51.3 mA. Additionally, the shimmed magnetic field exhibited high time stability, with a maximum variation of only 27 µT observed within 48 h. Thus, the proposed two-stage superconducting shimming framework effectively addresses the challenge of imperfect B0 magnetic fields, enhancing peak-to-peak and RMSE field homogeneity. The stepwise optimized approach also mitigates deviations caused by shim-to-shim coupling, demonstrating its efficacy in achieving precise shimming in ultrahigh-field MRI systems.

On regular but non-smooth integral curves

Let C be a regular geometrically integral curve over an imperfect field K and assume that it admits a non-smooth point p which — seen as a prime of the separable function field K(C)|K — is non-decomposed in the base field extension K‾⊗KK(C)|K‾. In this paper we establish a bound for the number of iterated Frobenius pullbacks needed in order to transform p into a rational point. This provides an algorithm to compute geometric δ-invariants of non-smooth points and a procedure to construct fibrations with moving singularities of prescribed δ-invariants. We show that the bound is sharp in characteristic 2. We further study the geometry of a pencil of plane projective rational quartics in characteristic 2 whose generic fibre attains our bound. On our way, we prove several results on separable and non-decomposed points that might be of independent interest.

The effect of elimination of gibbs ringing, noise and systematic errors on the DTI metrics and tractography in a rat brain

Diffusion tensor imaging (DTI) metrics and tractography can be biased due to low signal-to-noise ratio (SNR) and systematic errors resulting from image artifacts and imperfections in magnetic field gradients. The imperfections include non-uniformity and nonlinearity, effects caused by eddy currents, and the influence of background and imaging gradients. We investigated the impact of systematic errors on DTI metrics of an isotropic phantom and DTI metrics and tractography of a rat brain measured at high resolution. We tested denoising and Gibbs ringing removal methods combined with the B matrix spatial distribution (BSD) method for magnetic field gradient calibration. The results showed that the performance of the BSD method depends on whether Gibbs ringing is removed and the effectiveness of stochastic error removal. Region of interest (ROI)-based analysis of the DTI metrics showed that, depending on the size of the ROI and its location in space, correction methods can remove systematic bias to varying degrees. The preprocessing pipeline proposed and dedicated to this type of data together with the BSD method resulted in an even − 90% decrease in fractional anisotropy (FA) (globally and locally) in the isotropic phantom and − 45% in the rat brain. The largest global changes in the rat brain tractogram compared to the standard method without preprocessing (sDTI) were noticed after denoising. The direction of the first eigenvector obtained from DTI after denoising, Gibbs ringing removal and BSD differed by an average of 56 and 10 degrees in the ROI from sDTI and from sDTI after denoising and Gibbs ringing removal, respectively. The latter can be identified with the amount of improvement in tractography due to the elimination of systematic errors related to imperfect magnetic field gradients. Based on the results, the systematic bias for high resolution data mainly depended on SNR, but the influence of non-uniform gradients could also be seen. After denoising, the BSD method was able to further correct both the metrics and tractography of the diffusion tensor in the rat brain by taking into account the actual distribution of magnetic field gradients independent of the examined object and uniquely dependent on the scanner and sequence. This means that in vivo studies are also subject to this type of errors, which should be taken into account when processing such data.

On Jacobians of geometrically reduced curves and their Néron models

We study the structure of Jacobians of geometrically reduced curves over arbitrary (i.e., not necessarily perfect) fields. We show that, while such a group scheme cannot in general be decomposed into an affine and an Abelian part as over perfect fields, several important structural results for these group schemes nevertheless have close analoga over imperfect fields. We apply our results to prove two conjectures due to Bosch-Lütkebohmert-Raynaud about the existence of Néron models and Néron lft-models over excellent Dedekind schemes in the special case of Jacobians of geometrically reduced curves. Finally, we prove some existence results for semi-factorial models and related objects for general geometrically integral curves in the local case.

Angular Integral Autocorrelation for Speed Estimation in Shear-Wave Elastography

The utilization of a reverberant shear-wave field in shear-wave elastography has emerged as a promising technique for achieving robust shear-wave speed (SWS) estimation. However, many types of estimators cannot accurately measure SWS within such a complicated 3D wave field. This study introduces an advanced autocorrelation estimator based on angular integration known as the angular integral autocorrelation (AIA) approach to address this issue. The AIA approach incorporates all the autocorrelation data from various angles during measurements, resulting in enhanced robustness to both noise and imperfect distributions in SWS estimation. The effectiveness of the AIA estimator for SWS estimation is first validated using a k-Wave simulation of a stiff branching tube in a uniform background. Furthermore, the AIA estimator is applied to ultrasound elastography experiments, magnetic resonance imaging (MRI) experiments, and optical coherence tomography (OCT) studies across a range of different excitation frequencies on tissues and phantoms, including in vivo scans. The results verify the capacity of the AIA approach to enhance the accuracy of SWS estimation and the signal-to-noise ratio (SNR), even within an imperfect reverberant shear-wave field. Compared to simple autocorrelation approaches, the AIA approach can also successfully visualize and define lesions while significantly improving the estimated SWS and SNR in homogeneous background materials and providing improved elastic contrast between structures within the scans. These findings demonstrate the robustness and effectiveness of the AIA approach across a wide range of applications, including ultrasound elastography, magnetic resonance elastography (MRE), and optical coherence elastography (OCE), for accurately identifying the elastic properties of biological tissues in diverse excitation scenarios.

A decomposition theorem for 0-cycles and applications to class field theory

We describe the abelian {e}tale fundamental group with modulus in terms of 0-cycles on a class of smooth quasi-projective varieties over finite fields which may not admit smooth compactifications. Using a limit process, this yields a cycle-theoretic analogue of the $K$-theoretic reciprocity theorem of Kato-Saito for such varieties. The proof is based on a decomposition theorem for the cohomological Chow group of 0-cycles on the double of a quasi-projective $R_1$-scheme over a field along a closed subscheme in terms of the Chow groups with and without modulus of the scheme. This also extends the decomposition theorem of Binda-Krishna to smooth schemes over imperfect fields.

On a certain functional identity involving inverses in division rings and local rings

Let [Formula: see text] be a division ring, [Formula: see text] an automorphism of [Formula: see text] and [Formula: see text] a fixed element. We determine the forms of additive maps [Formula: see text] satisfying the identity [Formula: see text] for every nonzero [Formula: see text]. We show that [Formula: see text] and [Formula: see text] are both generalized [Formula: see text]-derivations of [Formula: see text] except possibly when [Formula: see text] is the identity automorphism and [Formula: see text] is an imperfect field of characteristic [Formula: see text]. We further study the same rational identity in the context of local rings under some mild assumptions.

Simulation analysis on the synergistic effect of vegetation ashes and charged particles on the gap electric field distortion

Hill fires, a sort of ultra-natural disaster that poses a severe threat to the safe and stable operation of transmission lines, have become more frequent in recent years. Currently, the modeling research on the transmission line gap electric field distortion under hill fire conditions does not consider the synergistic effect of charged particles and ash particles, which would lead to the imperfect gap electric field distortion mechanism. Herein, a coupled multi-physics field simulation model of electric, thermal, fluid, chemical field and particle motion was constructed to analyze the electric field distribution and particle motion. Compared to the related simulation models, this study improves the simulation accuracy by around 407% by optimizing the structure and parameters of the simulation model. The FEM software COMSOL Multiphysics simulation results show that the percentage of ash entering the examined region of the AC conductor was 34.1% higher, and the percentage of connected ash was 45% higher, increasing the likelihood of gap breakdown compared to the DC conductor; the charge of ash (10−14 to 10−11) is significantly less than the saturation charge of ash (⩾10−3). Therefore, the charged particles change the motion characteristics of the ash primarily through the electric field force and dielectrophoresis force, while the ash-induced distortion of the electric field affects the spatial distribution of the charged particles, eventually, the background electric field undergoes significant distortion by the synergistic effect of the two. The results examine the inherent mechanism of gap electric field distortion at the microscopic level, which can provide theoretical support for understanding the transition phase of transmission line gaps from insulation to break down under hill fire conditions.

Strongly divisible lattices and crystalline cohomology in the imperfect residue field case

Strongly divisible lattices and crystalline cohomology in the imperfect residue field case

Graded quotients of ramification groups of local fields with imperfect residue fields

abstract: We prove that the graded quotients of the filtration by ramification groups of any henselian discrete valuation field of residue characteristic $p>0$ are ${\bf F}_p$-vector spaces. We define an injection of the character group of each graded quotient to a twisted cotangent space defined using a cotangent complex.

Albanese Maps for Open Algebraic Spaces

Abstract We show that for each algebraic space that is separated and of finite type over a field, and whose affinization is connected and reduced, there is a universal morphism to a para-abelian variety. The latter are schemes that acquire the structure of an abelian variety after some ground field extension. This generalizes classical results of Serre on universal morphisms from algebraic varieties to abelian varieties. Our proof relies on corresponding facts for the proper case, together with the structural properties of group schemes, removal of singularities by alterations, and ind-objects. It turns out that the formation of the Albanese variety commutes with base-change up to universal homeomorphisms. We also give a detailed analysis of Albanese maps for algebraic curves and algebraic groups, with special emphasis on imperfect ground fields.

Optimizing molecular potential models by imposing kinetic constraints with path reweighting.

Empirical force fields employed in molecular dynamics simulations of complex systems are often optimized to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the interconversion rates between metastable states in such systems is hardly ever incorporated in a force field due to a lack of an efficient approach. Here, we introduce such a framework based on the relationship between dynamical observables, such as rate constants, and the underlying molecular model parameters using the statistical mechanics of trajectories. Given a prior ensemble of molecular dynamics trajectories produced with imperfect force field parameters, the approach allows for the optimal adaption of these parameters such that the imposed constraint of equally predicted and experimental rate constant is obeyed. To do so, the method combines the continuum path ensemble maximum caliber approach with path reweighting methods for stochastic dynamics. When multiple solutions are found, the method selects automatically the combination that corresponds to the smallest perturbation of the entire path ensemble, as required by the maximum entropy principle. To show the validity of the approach, we illustrate the method on simple test systems undergoing rare event dynamics. Next to simple 2D potentials, we explore particle models representing molecular isomerization reactions and protein-ligand unbinding. Besides optimal interaction parameters, the methodology gives physical insights into what parts of the model are most sensitive to the kinetics. We discuss the generality and broad implications of the methodology.

On behavior of conductors, Picard schemes, and Jacobian numbers of varieties over imperfect fields

In this paper, we study invariants and related phenomena of regular but not necessarily geometrically regular varieties and rings over imperfect fields, as exemplified by Tate's genus change theorems. In particular, we (i) give a geometric-normality criterion of such rings, (ii) study the Picard schemes of curves, and (iii) define new invariants relating to δ-invariants, genus changes, conductors, and Jacobian numbers. As an application of (iii), we give refinements of Tate's genus change theorem and [18, Theorem 1.2], and show that the Jacobian number of a curve is 2p/(p−1) times of the genus change.

The model theory of Cohen rings

The aim of this article is to give a self-contained account of the algebra and model theory of Cohen rings, a natural generalization of Witt rings. Witt rings are only valuation rings in case the residue field is perfect, and Cohen rings arise as the Witt ring analogon over imperfect residue fields. Just as one studies truncated Witt rings to understand Witt rings, we study Cohen rings of positive characteristic as well as of characteristic zero. Our main results are a relative completeness and a relative model completeness result for Cohen rings, which imply the corresponding Ax-Kochen/Ershov type results for unramified henselian valued fields also in case the residue field is imperfect.

Post-buckling analysis of axially loaded two-dimensional quasicrystal cylindrical shells with initial geometric imperfection

In this paper, the nonlinear post-buckling analysis of imperfect two-dimensional quasicrystal cylindrical shells is performed. The nonlinear governing equations are established by considering initial geometric imperfection, higher-order shear deformation theory and phonon-phason fields coupling effect. The load-shortening curves and buckling modes are obtained by the Galerkin’s method. Numerical results are compared with the existing results and excellent agreements are obtained. Effects of geometrical parameters, initial imperfection and phonon-phason fields coupling effect on the critical load and imperfection sensitivity of two-dimensional quasicrystal cylindrical shells are discussed in detail.

Reliability analysis and design of randomly imperfect thin cylindrical shells against post-critical drops

Thin-walled cylindrical shells are employed for high specific bending stiffness and light design. Elastic buckling of shell is a critical design consideration. The Knock Down Factors (KDFs) are stipulated for accounting the markedly reduced experimental critical load by multiplying the linearized critical load by the KDF. Key to such reductions is the nonlinearity induced modal interactions among the closely spaced buckling modes, over which, the geometric imperfections act in synergy. Being the lower bound of an extensive experimental dataset; the stipulated design KDFs are largely over-conservative; which can be relaxed by accounting for imperfections. With this as the eventual goal, this study first demonstrate the feasibility of modeling the KDFs as uniformly distributed Uncertain-but-Bounded (UBB) type variable. The UBB description is employed to obtain the reliability bounds and the design variables (radius-to-thickness R/t and L/R ratio) for achieving a target reliability index through Reliability Based Design (RBD). Repeated computations of KDFs for reliability assessment are bypassed by fitting the KDFs vs. R/t relations for given L/R. The approach is demonstrated on a thin cylindrical shell with a zero-mean, stationary, gaussian, stochastic imperfection fields. The Riks method is employed for the nonlinear finite element analysis of the shell using the code ABAQUS. The KDFs and reliability bounds are provided for varying imperfections and are compared with an existing study on refining the KDFs. Furthermore, the RBD presents the desired R/t for a given L/R for achieving a target reliability index and the respective KDF for a given imperfection level. The L/R dependency is shown to reduce the over-conservatism in the design stipulation.

Serrated periodic electrode for high energy efficiency and large bandwidth acousto-optic modulators

In an acousto-optic modulator, the electrode shape plays an important role in performance, since it affects the distribution of the acoustic field. The acousto-optic modulator based on the conventional rectangular electrode has the problems of low energy efficiency and small modulation bandwidth due to an imperfect acoustic field. In this paper, a new serrated periodic electrode has been proposed for using acousto-optic modulator transducers. The proposed electrode has the following advantages. By using serrated periodic electrodes to suppress the sidelobes, the collimation of the acoustic field in the direction perpendicular to the light incidence is improved. This makes the acousto-optic modulator have a stable diffraction efficiency fluctuation and high energy efficiency. In addition, the electrode has a large divergence angle in the direction of light incidence, so a large bandwidth can be obtained. The simulations and experiments demonstrate that the serrated periodic electrode has an increased bandwidth and high energy efficiency.

On the log minimal model program for threefolds over imperfect fields of characteristic p>5$p>5$

We prove that many of the results of the log minimal model program hold for threefolds over fields of characteristic p > 5 $p>5$ which are not necessarily perfect. This includes the existence of flips, the cone theorem, the contraction theorem for birational extremal rays and the existence of log minimal models. As well as pertaining to the geometry of fibrations of relative dimension 3 over algebraically closed fields, they have applications to tight closure in dimension 4.

Degree 2 cohomological invariants of linear algebraic groups

The paper deals with the cohomological invariants of smooth and connected linear algebraic groups over an arbitrary field. More precisely, we study degree $2$ invariants with coefficients $\mathbb{Q}/\mathbb{Z}(1)$, that is invariants taking values in the Brauer group. Our main tool is the \'etale cohomology of sheaves on simplicial schemes. We get a description of these invariants for \emph{every} smooth and connected linear groups, in particular for non reductive groups over an imperfect field.

Integral Models and Torsors of Inseparable Forms of Ga

After recalling some basic facts about F-wound commutative unipotent algebraic groups over an imperfect field F, we study their regular integral models over Dedekind schemes of positive characteristic and compute the group of isomorphism classes of torsors of one-dimensional groups.