Radial Dimension Research Articles

Adults born preterm exhibit bi‐ventricular hypercontractility and inefficiency

IntroductionIn the US, prematurity accounts for approximately 10% of all live births. Infants born preterm are at an increased risk of cardiopulmonary disease. Until recently, little was known about the long‐term sequelae in the myocardium in adult survivors of prematurity. One study demonstrated that adults born preterm had larger left (LV) and right ventricular (RV) masses, and lower RV ejection fraction compared to term born controls. To date, there is a paucity of information on the potential mechanism of altered ventricular mechanics in adult survivors of prematurity. Therefore, we hypothesized that preterm subjects would display reduced RV and LV strain.MethodsPreterm subjects were recruited from a prospectively followed cohort at UW‐Madison. Gestational ages for the preterm subjects were 28.2 ± 0.84 weeks and they weighed < 1500 grams. Term‐born subjects were recruited from the general public. Cardiac magnetic resonance imaging (MRI) was used to determine myocardial strain and stroke volume (SV) in adults born preterm (n = 10, age = 26.9 ± 0.3 years) and age‐matched term born controls (n = 12, age = 25.8 ± 0.2 years). Three slices from the RV and LV (apex, mid and base) short‐axis cine MR images were used to analyze RV and LV circumferential and LV radial dimensions (mean peak strain, systolic and diastolic strain rate). SV was obtained from the main pulmonary artery (MPA) and aorta (Ao) 2‐D phase contrast images. SV was normalized to body surface area (SVI) and was divided by peak RV and LV circumferential strain to obtain RV and LV efficiency. All MRI analysis was performed using Segment (http://segment.heiberg.se). A Mann‐Whitney test was performed to test differences between groups (p < 0.05).ResultsPreterm subjects demonstrated increased peak RV circumferential (−11.36 % ± 1.90 vs. −8.83 % ± 1.95; p = 0.003) and LV circumferential (−20.15 % ± 2.29 vs. −17.96 % ± 1.96; p = 0.025) strain compared to controls, respectively. Additionally, RV circumferential systolic strain rate, LV circumferential systolic and diastolic strain rate, and LV radial diastolic strain rate were greater (p < 0.05) in preterm adults as compared to controls. SVI as measured from the MPA and Ao flow was not different between groups. Preterm subjects exhibited reduced (p < 0.05) RV and LV (p = 0.06) efficiency as compared to controls.DiscussionWe used MRI to measure RV and LV strain, which is a measure of ventricular displacement during the cardiac cycle. Contrary to our hypothesis, these results demonstrate that adults born preterm exhibit a hypercontractile myocardium (increased strain) under resting conditions. The increased bi‐ventricular strain in the circumferential dimension in preterm born adults occurred despite no differences in SVI between groups. This results in reduced RV and LV efficiency in preterm subjects compared to controls, suggesting increased cardiac work may be required in adults born preterm for the same SVI. The implications for life‐time cardiovascular risk merit further study.Support or Funding InformationProject supported by funding from the National Institutes of Health: 1RO1 HL086897 (MWE) and RO1 HL38149 (MWE). Kara Goss is supported by the University of Wisconsin Clinical and Translational Science Award (CTSA) program, through the NIH National Center for Advancing Translational Sciences (NCATS), grant NIH UL1TR000427 (PI Drezner; 4KL2TR000428‐‐10).This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Anthropometric Study of the Radiocapitellar Joint.

There is scant knowledge about the relationship between the size of the radial head and the size of the capitellum. Also, no data exist comparing the size of the capitellum between the left and the right elbow. Eight pairs of elbows and 12 single elbows from fresh-frozen cadavers were obtained for this study. The vertical height and anterior width of the capitellum were measured with digital calipers. Four different measurements were performed at the radial head: longest outer diameter, shortest outer diameter, the long dish diameter, and short dish diameter. The Pearson intrarater intraclass correlation coefficients were obtained for all measurements. For the paired elbows, the correlations ranged between 0.95 and 0.96 for the capitellar dimensions and 0.77 and 0.98 for the radial head dimensions. The correlations between the long outer diameter of the radial head with the vertical height and the anterior width of the capitellum were 0.8 and 0.9, respectively. There is a high correlation between the long outer diameter of the radial head and the vertical height of the capitellum as well its anterior width. There is also a high correlation between the left and the right elbow. These findings are relevant to radiocapitellar arthroplasty and may be useful for radiocapitellar prosthetic design as well as in the preoperative planning of cases in which the radial head and/or the capitellum is destroyed.

Numerical and theoretical investigation of the high-speed compressible supercavitating flows

The objective of this paper is to investigate the high-speed compressible supercavitating flows with numerical and theoretical methods. In the numerical simulation, calculations are performed by solving the Unsteady Reynolds-averaged Navier-Stokes (URANS) Equations using a cell-centered finite-volume method, and the k-ω SST turbulence model is applied as the closure model. Compressibility effects in liquid phase are modified by the equation of state (EOS), and vapor phase is treated as ideal gas. Firstly, the numerical results are validated with experiments conducted by Hrubes (2001). Results are shown for high-subsonic and transonic projectiles, there is a general agreement between the predicted cavity profiles and the experimental data. Secondly, the influence of the Mach number on the flow structure and cavitation dynamics from subsonic to supersonic flows is investigated. The results show that with the increase of Mach number, the radial dimension of the front cavity is reduced, which is caused by the dramatic increase of pressure around the projectile. An expression is proposed to analyze the flow parameters before and behind the shock wave based on the isentropic and potential assumption at the Mach number on the interval 1 ≤ Ma≤2.2. The relationship between pressure and density across the shock wave is also investigated. Overall, these findings are great interest in engineering applications.

Morphological responses of plant roots to mechanical stress.

Roots are continuously exposed to mechanical pressure and this often results in their morphological modification. Most obvious are changes in the overall form of the root system as well as in the shapes of particular roots. These changes are often accompanied by modifications of the cell pattern and cell morphology. This review focuses on the morphological responses of roots to mechanical stress. Results of early and recent experiments in which roots have been exposed to mechanical pressure are assembled, analysed and discussed. Research applying different experimental sets, obstacles, media of various compactness and structure are reviewed. An effect of the combination of mechanical stresses with other abiotic stresses on roots, and results of estimating the force exerted by the roots are briefly discussed. Possible consequences of the cell pattern rearrangements are considered. Several modifications in root morphology are commonly reported: (1) decreased root size, (2) radial swelling accompanied by increased radial dimension of the cortex cell layers and (3) enhanced cap cell sloughing. Nevertheless, because of differences between species and individual plants, a universal scenario for root morphological changes resulting from externally applied pressures is not possible. Thus, knowledge of the root response to mechanical impedance remains incomplete. Studies on the mechanical properties of the root as well as on possible modifications in cell wall structure and composition as the elements responsible for the mechanical properties of the plant tissue are required to understand the response of root tissue as a biomaterial.

Thermal design of Earth-to-Air Heat Exchanger. Part I a new transient semi-analytical model for determining soil temperature

Abstract This article is the first in a series about the thermal design of Earth-to-Air Heat Exchanger, EAHE, using a new developed semi-analytical method. The temperature distribution in the soil surrounding the EAHE is studied in the goal to determine the soil radius as a function of the operation duration. This radius is the first distance from the pipe axis where there is no effect of heat from EAHE. For that, a new transient semi-analytical model is developed in particular to facilitate the thermal design of EAHEs. The main application of the developed model is to predict the deterioration in EAHE's thermal performance as a function of the duration operation. This deterioration can be caused by soil thermal saturation where the nearby subsoil temperature becomes almost equal to the inlet air temperature resulting in minimum heat transfer between air and soil. The analytical solution of the proposed model has been integrated by means of the Bessel function method, for a constant heat flux per unit of length at the pipe surface in the radial dimension and constant inlet air temperature. The model has been verified with several results obtained from the literature. In addition, an investigation of continuous operation of an EAHE is made on thermal performance of the EAHE in the soil of the region of Biskra (Southern Algeria) (34°47′N - 005°43′E) by applying extreme ambient air temperature (57 °C). Results show that the deterioration in thermal performance of EAHE is observed for longer duration in hot and dry climate. In the case of 6 h of continuous operation, the soil radius can reach 0.55 m from the pipe surface. The model proposed in this paper can be considered as the first of its kind which gives a formula for calculating the soil radius (thickness) as a function of the: i) duration of operation, ii) soil thermal diffusivity, iii) pipe diameter and iv) air temperature.

Exploiting k-space/frequency duality toward real-time terahertz imaging

Imaging at terahertz frequencies has recently received considerable attention because many materials are semitransparent to THz waves. The principal challenge that impedes a widespread use of THz imaging is the slow acquisition time of a conventional point-by-point raster scan. In this work, we present a theoretical formulation and an experimental demonstration of a novel technique for fast compressionless terahertz imaging based on broadband Fourier optics. The technique exploits k-vector/frequency duality in Fourier optics that allows the use of a single-pixel detector to perform angular scans along a circular path, while the broadband spectrum is used to scan along the radial dimension in Fourier domain. The proposed compressionless image reconstruction technique (hybrid inverse transform) requires only a small number of measurements that scales linearly with an image’s linear size, thus promising real-time acquisition of high-resolution THz images. Additionally, our imaging technique handles equally well and on an equal theoretical footing amplitude contrast and phase contrast images, which makes this technique useful for many practical applications. A detailed analysis of the technique’s advantages and limitations is presented, and its place among other existing THz imaging techniques is clearly identified.

Impact of metal removal features in the reverse zones on shaping of the machined surface in the process of cylindrical grinding with traverse feed

This paper presents a model of the formation process of surface zones of external cylindrical grinding with traverse feed at a computer numerical control machine (CNC). This article, have investigated modelling features of the grinding process in reverse zones. On the basis of the model of grinding surface formation a detailed step by step calculations of the current values of the actual radial feed and radius dimension in different areas of a treated surface is presented. The model allows maintaining calculations with presence of the initial radial runout of the workpiece for estimated automatic cycle of radial and axial feeds changing and other technological parameters.

ОБОБЩЕННАЯ ДИНАМИЧЕСКАЯ ТЕОРИЯ ИЗМЕЛЬЧЕНИЯ ЧАСТИЦЫ ТВЕРДОГО ВЕЩЕСТВА ИМПУЛЬСНО-СИЛОВЫМ СЖАТИЕМ ДВУМЯ НЕДЕФОРМИРУЕМЫМИ ШАРАМИ

Machines such as ball mill, vibrating mill, planetary mill, and stirred mill using spherical grinding media as a destruction energy transmitter are widely used among the manufacturing equipment for materials grinding. Providing a necessary product particle size at an optimal energy efficiency and productivity during grinding makes it necessity to investigate new ways of improving the mentioned types of mills, supplementing them with a system for regulating the grinding regime, taking into account the physical and mechanical properties of the feed particle. As the grinding media motion is quite complicated, it is necessary to develop a new theory of a particle grinding for an accurate and adequate evaluation of a particle stress-strain state with the grinding media using simple physical and mathematical relations. So, we obtained a new general solution of the fundamental-applied multifunctional problem of materials resistance during a direct inelastic collision of two identical isotropic weightless balls of a small diameter and high rigidity with a given form moving towards each other. The solution is based on a complex application of classical Hertz-Staerman analytic dependences on the force contact of the spherical grinding media and the energy conservation law (the Reilly-Young method). In the corresponding quasi-static physical and mathematical model we considered local deformations within the framework of Hooke's law, own weight of spherical media, the impact time and the radial dimensions of the interacting elements of the constructively nonlinear mechanical system. To calculate the bearing capacity of the grinded particle and determine the crushing force, the well-known Galilei-Leibniz strength criterion is used. The criterion is interpreted by the largest tensile stress, which adequately characterizes the limiting state when a wide class of brittle homogeneous solids is destroyed. The results of the developed theory are presented by the formulae aimed to regulate and optimize the grinding process of stone materials.

Structural Strength and Service Life of the Extrusion Forming Die for Agricultural Engine Piston Heads

Three-tier high-strength prestressed combination concave dies are designed to manufacture highpower corn combine harvester engine piston heads. This design integrates the advantages of traditional casting or hot die forging and warm extrusion. The following key parameters, viz radial dimensions of each mating layer, axial bonding and radial contact interaction, are obtained by theoretical calculation. Nonlinear analysis of the contact interaction was carried out, and the die contact condition was studied at no-load and full-load. Based on the Archard wear theory, thermomechanical bonding was studied in operation of the die. Through numerical simulation of the die wear in each operation cycle, the univariate linear regression equation of the die service life was derived, and the reliability of this equation was verified. The results show that the die contact is both stable and reliable if the radial contact interaction of the inner and outer layers is δ2 = 1.9716 mm and δ3 = 1.3870 mm, respectively. With the nitriding layer thickness of 0.24 mm, the extrusion die service life in the production of piston heads corresponds to 6357 pieces.

Multidimensional modeling of a microfibrous entrapped cobalt catalyst Fischer‐Tropsch reactor bed

Thermal management of highly exothermic Fischer‐Tropsch synthesis (FTS) has been a challenging bottleneck limiting the radial dimension of the packed‐bed (PB) reactor tube to 1.5 in. ID. A computational demonstration of a novel microfibrous entrapped cobalt catalyst (MFECC) in mitigating hot spot formation has been evaluated. Specifically, a two‐dimensional (2‐D) model was developed in COMSOL®, validated with experimental data and subsequently employed to demonstrate scale‐up of the FTS bed from 0.59 to 4 in. ID. Significant hot spot of 102.39 K in PB was reduced to 9.4 K in MFECC bed under gas phase at 528.15 K and 2 MPa. Improvement in heat transfer within the MFECC bed facilitates higher productivities at low space velocities (≥1000 h−1) corresponding to high CO conversion (≥90%). Additionally, the MFECC reactor provides an eightfold increase in the reactor ID at hot spots ≤ 30 K with CO% conversions ≥ 90%. This model was developed for a typical FTS cobalt‐based catalyst where CO2 production is negligible. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1723–1731, 2018

Electronic states and optical properties of single donor in GaN conical quantum dot with spherical edge

In this paper we present a theoretical investigation of quantum confinement effects on the electron and single donor states in GaN conical quantum dot with spherical edge. In the framework of the effective mass approximation, the Schrödinger equations of electron and donor have been solved analytically in an infinite potential barrier model. Our calculations show that the energies of electron and donor impurity are affected by the two characteristic parameters of the structure which are the angle Ω and the radial dimension R. We show that, despite the fact that the reduction of the two parameters Ω and R leads to the same confinement effects, the energy remains very sensitive to the variation of the radial part than the variation of the angular part. The analysis of the photoionization cross-section corresponding to optical transitions between the conduction band and the first donor energy level shows clearly that the reduction of the radius R causes a shift in resonance peaks towards the high energies. On the other hand, the optical transitions between 1s−1p, 1p−1d and 1p−2s show that the increment of the conical aperture Ω (or reduction of R) implies a displacement of the excitation energy to higher energies.

Similarity type of general solution for one-dimensional heat conduction in the cylindrical coordinate

One-dimensional heat conduction process in the cylindrical coordinate is investigated, and a similarity type of general solution is developed using the Kummer functions. The limiting behaviors of the general solution are studied using the properties of the Kummer functions, and some useful identities are deduced. As applications of the general solution, an infinite line source problem under power-type initial and boundary conditions and a one-phase Stefan problem with space-dependent latent heat in the cylindrical coordinate are studied. The analytical solutions for these two problems are established using the general solution directly. Computational examples for the analytical solutions are presented. For the infinite line source problem, the computational results are compared with those of the solid cylindrical surface model, and the computational error caused by neglecting the radial dimension of the heat source under time-varying source intensity is investigated. For the one-phase Stefan problem, both the coefficient in the solution and the development of the temperature field are presented; the computational results can be used to verify the accuracy of numerical solutions for Stefan problems.

Core Conversion of VVR-K Research Reactors

The conversion of the VVR-K research reactor to low-enrichment uranium fuel includes switching to a compact core with low-enrichment uranium and gradually transitioning from a light-water side reflector to a beryllium reflector with restoration of the working reactivity margin without makeup with fresh fuel. In 2015, the reactor was stopped in order to modernize the main elements of the core, the control and protection system for the channels of the working rods, and the emergency electric power source. First criticality of VVR-K with low-enrichment fuel followed by first start of the reactor occurred in spring 2016. The VVR-KN type FA specially developed for VVR-K make it possible to not only preserve but also improve the neutronphysical characteristics of the core. The design-basis reactivity margin of the working core load ~7%Δk/k is adequate for reactor operation for three 20-day cycles with ~10% average burnup reached in the central FA. The beryllium reflector is built up in stages starting at the fourth cycle. The beryllium reflector will make it possible to preserve the radial dimensions of the core and increase the neutron flux density in the central and peripheral irradiation channels.

An Analytical Model for the Time Constants of Optical Fiber Temperature Sensing

An optical fiber temperature sensor can be a useful in-pile temperature sensor for TREAT (Transient REAtor Test facility) due to its simplicity, size, and ability to measure temperatures along its length. However, the optical fiber would need to be encased in a protected capillary tube to survive the reactor environment for an extended period of time and to install the fiber in the reactor. Surrounding the fiber with a capillary tube reduces the heat transfer rate and, therefore, the temperature response of the fiber. The goal of this paper is to determine the time constants, and therefore to predict the response time, of the fiber for a fiber and capillary tube system of known dimensions and properties as well as to determine methods to improve the response of the sensors. For our analysis, a stainless steel capillary tube was chosen, and argon was selected to fill the gap between the capillary tube and the fiber. A mathematical model in the radial dimension was created using an electrical–thermal analogy with known thermal resistances and capacitances of the system. This model was used to analyze the temperature response of the fiber when: 1) a step change in temperature was applied to the outer surface of the fiber; 2) a step change in temperature was applied to the outer surface of the capillary tube in a capillary tube-gap-fiber system; and 3) the capillary tube-gap-fiber system is instantaneously plunged into a conducting medium. At each stage, the analytical results were compared with the predictions of an ANSYS finite-element model under the same conditions.

Theoretical and Experimental Research of Spherical Roller Transmissions

Передачи с промежуточными телами качения в настоящее время используются для решения специальных инженерных задач. Они имеют низкую материалоемкость и высокую нагрузочную способность, так как передача мощности осуществляется по нескольким параллельным потокам, число которых равно числу тел качения. К недостаткам многих конструкций, препятствующих широкому использованию в промышленности, относят низкий КПД и недостаточную надежность. В статье рассмотрены вопросы расчета и проектирования передач, у которых траектории центров масс тел качения расположены на сферических поверхностях. Ролики взаимодействуют со сферическими кулачками, образующими пространственные замкнутые периодические беговые дорожки. Преимуществами являются небольшие осевые и радиальные габариты, возможность объединения в конструкции одного механизма редукторного узла и угловой муфты. Рассмотрены конструкции сферических роликовых передач, проведен сравнительный анализ двух- и трехзвенных механизмов, представлены результаты силового анализа и произведена теоретическая оценка потерь мощности. Приведены результаты экспериментальных исследований КПД и шумовых характеристик разработанных редукторов. Обосновывается вывод о конкурентоспособности сферических роликовых передач как передач общемашиностроительного назначения в диапазонах передаточных отношений 3…15, частот вращения валов не более 3000 мин-1.

Stability of volcanic conduits during explosive eruptions

Geological evidences of volcanic conduit widening are common in most pyroclastic deposits (e.g. presence of lithic fragments from different depths), suggesting a continuous modification of the conduit geometry during volcanic eruptions. However, the controlling factors of the mechanisms driving conduit enlargement (e.g. erosion, local collapse) are still partially unclear, as well as the influence of conduit geometry on the eruptive dynamics. Although numerical models have been systematically employed to study volcanic conduits, their mechanical stability and the eruptive dynamics related to non-cylindrical conduits have been poorly addressed.We present here a 1D steady-state model which includes the main processes experimented by ascending magmas (i.e. crystallization, rheological changes, fragmentation, drag forces, outgassing and degassing), and the application of two mechanical stability criteria (Mohr–Coulomb and Mogi–Coulomb), in order to study the collapse conditions of volcanic conduits during a representative explosive rhyolitic eruption. It emerges that mechanical stability of volcanic conduits is mainly controlled by its radial dimension, and a minimum radius for reaching stable conditions can be computed, as a function of water content and inlet overpressure. Additionally, for a set of input parameters thought typical of explosive rhyolitic volcanism, we estimated a minimum magma flux for developing a mechanically stable conduit (~7∙107−3∙108kg/s). Results are consistent with the unsteady character usually observed in sub-Plinian eruptions, opposite to mainly stationary Plinian eruptions, commonly characterized by higher magma discharge rates. We suggest that cylindrical conduits represent a mechanically stable configuration only for large radii. Because the instability conditions are not uniform along the conduit, the widening processes probably lead to conduit geometries with depth-varying width. Consequently, as our model is able to consider volcanic conduits with depth-dependent radius, two plausible and previously untested geometries have been studied, evidencing major and complex modifications in some eruptive parameters (particularly, exit pressure and mass discharge rate), and suggesting that the geometry acquired by the conduit as it is widened influences the eruptive dynamics.

Experimental investigations for dimensional accuracy and surface finish of polyurethane prototypes fabricated by indirect rapid tooling: a case study

In this research work, an effort has been made to study the influence of selected input parameters on the dimensional accuracy (linear as well as radial) and surface finish of polyurethane prototypes fabricated by vacuum casting (VC) process as a case study. The master pattern required for making a silicone mould has been fabricated by fused deposition modelling and its surface finish has been enhanced by chemical vapour smoothing process. Maximum shrinkage of 2.29 and 4.77% has been observed in the selected linear and radial dimension, respectively, after the VC process. Optimal parameter settings that were different for both the dimensions as well as surface finish have been obtained using Taguchi’s L18 orthogonal array. Finally, parameter setting that simultaneously minimizes the dimensional deviation and surface roughness has been found out using response optimization module of Minitab 17 software and the results obtained have been verified by performing the confirmation experiments. The tolerance grades for the selected dimension of the prototypes were found to be acceptable as per the ISO standard UNI EN 20286-I (1995) and DIN16901 for plastic materials. In addition, the C pk value greater than 1.3 indicated that the proposed process is highly capable. The surface finish and dimensional accuracy of prototypes are at par with the traditional moulding patterns, and hence, they can be used as end-products or plastic-based master patterns for investment casting applications.

Dimensional accuracy analysis of coupled fused deposition modeling and vapour smoothing operations for biomedical applications

Abstract Fused Deposition Modeling (FDM) is one of the most extensively used Additive Manufacturing technique which has substantially shortened the product development time and cost. The application has been extended to fabricate biomedical implants through investment casting process. But the FDM replicas exhibit poor surface quality which requires further post finishing. Thus, it is very difficult to achieve adequate dimensional accuracy as surface finishing techniques resulted in material removal and erosion of upper surface. The vapour smoothing is an advanced finishing technique which eliminates tool-workpiece contact and yield ultra smooth finish but dimensional accuracy of FDM replicas is yet to be ascertained. In present research, the efforts are made to explore the influence of FDM and VS process parameters in dimensional features of complex designs. The influence of six parameters on radial (head diameter) and linear dimensions (neck and stem thickness) is studied using Taguchi orthogonal array. The CMM measurements showed shrinkage in head diameter while positive deviation has been observed in linear dimensions before vapour smoothing with maximum impact of orientation angle. The vapour smoothing process caused shrinkage in both linear and radial dimensions with maximum effect of smoothing time. The process parameters and their levels are optimized and confirmatory experiments indicated reduced deviations in dimensional features with consistency in IT grades.

Energy levels of a quantum particle on a cylindrical surface with non-circular cross-section in electric and magnetic fields

We calculate the energy levels of a quantum particle on a cylindrical surface with non-circular cross-section in uniform electric and magnetic fields. Using separation of variables method and a change of independent variable, we show that the problem can be reduced to a one-dimensional Schrödinger equation for a periodic potential. The effects of varying the shape of the cross-section while keeping the same perimeter and the strengths of the electric and magnetic fields are investigated for elliptical, corrugated, and nearly-rectangular tubes with radial dimensions of the order of a nanometer. The geometric potential has minima at the angular positions where there is a significant amount of curvature. For the elliptical and corrugated tubes, it is shown that as the tube departs from the circular shape of cross-section the double-degeneracy between the energy levels is lifted. For the nearly-rectangular tube, it is shown that energy level crossings occur as the horizontal dimension of the tube is varied while keeping the same perimeter and radius of circular corners. The interplay between the curvature and the strength of the electric and magnetic fields determines the overall behavior of the energy levels. As the strength of the electric field increases, the overall potential gets skewed creating a potential well on the side corresponding to the more negative electric potential. The energy levels of the first few excited states approach more positive values while the ground state energy level approaches a more negative value. For large electric fields, all bound state energy levels tend to more negative values. The contribution of weak magnetic fields to the overall potential behaves in the same way as the electric field contribution but with its sign depending on the direction of the component of the momentum parallel to the cylindrical axis. Large magnetic fields lead to pairing of energy levels reminiscent of 2D Landau levels for the elliptical and nearly-rectangular tubes.

Longitudinal gradient coils with enhanced radial uniformity in restricted diameter: Single-current and multiple-current approaches

An important requirement for a gradient coil is that the uniformity of the generated magnetic field gradient should be maximal within the active volume of the coil. For a cylindrical geometry, the radial uniformity of the gradient turns critic, particularly in cases where the gradient-unit has to be designed to fit into the inner bore of a compact magnet of reduced dimensions, like those typically used in fast-field-cycling NMR. In this paper we present two practical solutions aimed to fulfill this requirement. We propose a matrix-inversion optimization algorithm based on the Biot-Savart law, that using a proper cost function, allows maximizing the uniformity of the gradient and power efficiency. The used methodology and the simulation code were validated in a single-current design, by comparing the computer simulated field map with the experimental data measured in a real prototype. After comparing the obtained results with the target field approach, a multiple-element coil driven by independent current sources is discussed, and a real prototype evaluated. Opposed equispaced independent windings are connected in pairs conforming an arrangement of independent anti-Helmholtz units. This last coil seizes 80% of its radial dimension with a gradient uniformity better than 5%. The design also provides an adaptable region of uniformity along with adjustable coil efficiency.