Cylindrical Approximation Research Articles

Distorted Magnetic Flux Ropes within Interplanetary Coronal Mass Ejections

Magnetic flux ropes (MFRs) at the center of interplanetary coronal mass ejections (ICMEs) are often characterized as simplistic cylindrical or toroidal tubes with field lines that twist around the cylinder or torus axis. Recent multipoint observations suggest that the overall geometry of these large-scale structures may be significantly more complex. As such, contemporary modeling approaches are likely insufficient to properly understand the global structure of any ICME. In an attempt to rectify this issue, we have developed a novel flux rope modeling approach that allows for the description of arbitrary distortions of the flux rope cross section or deformation of the magnetic axis. The resulting distorted MFR model is a fully analytic model that can be used to describe a complex geometry and is numerically efficient enough to be used for event reconstructions. To demonstrate the usefulness of our approach, we focus on a specific implementation of our model and apply it to an ICME event that was observed in situ on 2023 April 23 at the L1 point by the Wind spacecraft and also by the STEREO-A spacecraft, which was 10.°2 further east and 0.°9 south in heliographic coordinates. We demonstrate that our model can accurately reconstruct each observation individually and also gives a fair reconstruction of both events simultaneously using a multipoint reconstruction algorithm, which results in a geometry that is inconsistent with a cylindrical or toroidal approximation.

Mean-field neural networks: Learning mappings on Wasserstein space

We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems. Two classes of neural networks based on bin density and on cylindrical approximation, are proposed to learn these so-called mean-field functions, and are theoretically supported by universal approximation theorems. We perform several numerical experiments for training these two mean-field neural networks, and show their accuracy and efficiency in the generalization error with various test distributions. Finally, we present different algorithms relying on mean-field neural networks for solving time-dependent mean-field problems, and illustrate our results with numerical tests for the example of a semi-linear partial differential equation in the Wasserstein space of probability measures.

Fundamental Scaling of Adiabatic Compression of Field Reversed Configuration Thermonuclear Fusion Plasmas

Field Reversed Configuration (FRC) plasmas are plasma devices that have demonstrated that through magnetic compression they can be heated to thermonuclear fusion conditions in the parameter space of an energy-producing generator Kirtley et al. (IEEE Symposium on Fusion Engineering, 2021). Of particular interest, FRCs are high-beta, in that the plasma particle kinetic energy is in balance with an externally applied magnetic field at all stages of operation. The following work will show that a cylindrical approximation for the energy and particle distribution within an FRC can, within 11%, match the fusion performance results of both full Magnetohydrodynamic (MHD) simulations as well as all robust, modern theoretical spatial and energy distribution models. Further, by using the simplified cylindrical model, detailed fusion reaction, radiation, and energy transport equations are now numerically-tractable and can be modelled over a wide parameter space. In the second section of this work, a detailed numerical model will be presented with the key theoretical performance of the compression of high-beta fusion plasmas in both deuterium–tritium (D–T) and deuterium–helium-3 (D–He-3) fuels. As will be shown, a high-beta D–He-3 plasma outperforms a low-beta D–T fuel and can theoretically yield a net-positive fusion generator.

State of the Art of Continuous and Atomistic Modeling of Electromechanical Properties of Semiconductor Quantum Dots.

The main intent of this paper is to present an exhaustive description of the most relevant mathematical models for the electromechanical properties of heterostructure quantum dots. Models are applied both to wurtzite and zincblende quantum dot due to the relevance they have shown for optoelectronic applications. In addition to a complete overview of the continuous and atomistic models for the electromechanical fields, analytical results will be presented for some relevant approximations, some of which are unpublished, such as models in cylindrical approximation or a cubic approximation for the transformation of a zincblende parametrization to a wurtzite one and vice versa. All analytical models will be supported by a wide range of numerical results, most of which are also compared with experimental measurements.

Prismatic Spreading–Constriction Expression for the Improvement of Impedance Spectroscopy Models and a More Accurate Determination of the Internal Thermal Contact Resistances of Thermoelectric Modules

Thermoelectric (TE) devices can convert heat to electrical power or use electrical power to generate a temperature difference. Their characterization is essential to develop devices with higher efficiency. Impedance spectroscopy models have been developed in the last few years, and it has become a highly advantageous method for TE system characterization. Recently, it has been shown that this technique can also be used to determine internal thermal contacts (between the TE legs and the metallic strips that connect them and between the metallic strips and the outer layers). Here, we developed for the first time a spreading–constriction expression which does not assume cylindrical geometry. The enhanced model is also used to characterize four TE devices from different manufacturers, highlighting overestimations up to 13% when the previous cylindrical approximation is used. A code is provided in the Supporting Information ready to fit the experimental data. This study positions impedance spectroscopy as a powerful tool to detect and monitor issues during manufacturing or operation of TE devices, which typically occur at the contacts.

Van der Waals interaction energies for ferric ion sensors using prismatic and cylindrical pore approximations for a MOF pore.

Using the Lennard-Jones potential, we determine analytical expressions for van der Waals interaction energies between a point and a rectangular prism-shaped pore, writing them in terms of standard elementary functions. The parameter values for a new ferric ion sensor are used to compare these calculations with the cylindrical pore approximation for the interactions between an ion and a metal organic framework (MOF) pore. The results using the prismatic pore approximation predict the same qualitative outcomes as a cylindrical pore approximation. However, the prismatic approximation predicts lower magnitudes for both the interaction potential energy minimum and the force maximum, since the average distance from the centre-line to the surface of the prism is greater. We suggest that in some circumstances it is sufficient to use the simpler cylindrical approximation, provided that the cylinder radius is chosen so that the cross-sectional area is equal to the area of the prism pore opening. However, atoms at the nodes should remain approximated by semi-infinite lines. We also determine the interaction between a second ferric ion and a blocked MOF pore; as expected, the second ferric ion experiences a force away from the pore, implying that approaching ferric ions can only occupy vacant MOF pores.

Electric arc I–V modeling and related plasma spectrometry issues

This article is devoted to studying the properties of an electric arc column as a development of the authors’ early pioneer experiments. The object of modeling is a free-burning electric arc between evaporating copper electrodes in atmospheric air as the basis for the functioning of many modern technologies. It includes the determination of fundamental characteristics, such as the radial structure, and the current–voltage characteristics of the electric arc column under the assumption of plasma equilibrium. The middle cross section between the electrodes of a spheroidal shape arc is considered in order to limit the problem to a one-dimensional cylindrical approximation. It is strictly solved from the Elenbaas–Heller energy equation, with no resorting to the simplified channel model. The radial structure of the electric arc column is carefully considered with known temperature functions of electric and heat conductivities. Convenient functional approximations depending on temperature are proposed for the mentioned coefficients of copper–air plasma. The boundary between the arc column and atmospheric air is strictly located taking into account the chemical processes in the plasma of the copper–air mixture. The paper also presents some bases features of high-speed plasma spectrometry, substantiating the reliability of the obtained experimental data. As shown, the non-monotonicity of the current–voltage characteristics can arise due to the non-monotonicity of thermal conductivity as a function of temperature. Also, the loss of energy with the so-called ionization energy diffusion is insignificant in the overall energy balance of the arc. The results of the numerical simulation are compared with the experimental data.

Hydrogen Uptake Kinetics of 1,4-Bis(phenylethynyl)benzene Rubberized O-Rings: Measurements, Modeling, and Comparison with Additional Forms of Organic Getters

A class of molecules called “hydrogen getters” can react with, or scavenge, H2 in applications where the hydrogen presence and/or buildup are not desirable. One such “getter”, 1,4-bis(phenylethynyl)benzene or DEB, can be incorporated into a silicone matrix in the form of an O-ring for added flexibility, environmental resiliency, and convenient use as a gasket in sealed applications. However, the performance and kinetics of this DEB-loaded rubberized O-ring have not yet been characterized. In this work, the hydrogen uptake kinetics of the rubberized DEB O-ring were extracted by the isoconversional analysis from isothermal isobaric data under conditions of 13,332 Pa H2 and 305–325 K. The isoconversional and cylindrical diffusion approximations were then used to predict and model the hydrogen uptake of rubberized DEB O-rings under any arbitrary condition, as illustrated in this work for the simple case of a constant rate of hydrogen generation/input. In comparison with other Pd/carbon-based/organic getter systems, these rubberized DEB O-rings provide a type of hydrogen getter material with enhanced flexibility and catalyst protection in applications where an O-ring seal is needed.

Nuclear pasta structures at high temperatures

We investigate nuclear pasta structures at high temperatures in the framework of relativistic mean field model with Thomas-Fermi approximation. Typical pasta structures (droplet, rod, slab, tube, and bubble) are obtained, which form various crystalline configurations. The properties of those nuclear pastas are examined in a three-dimensional geometry with reflection symmetry, where the optimum lattice constants are fixed by reproducing the droplet/bubble density that minimizes the free energy adopting spherical or cylindrical approximations for Wigner-Seitz cells. It is found that different crystalline structures can evolve into each other via volume conserving deformations. For fixed densities and temperatures, the differences of the free energies per baryon of nuclear pasta in various shapes and lattice structures are typically on the order of tens of keV, suggesting the possible coexistence of those structures. As temperature increases, the thermodynamic fluctuations are expected to disrupt the long-range ordering in nuclear pasta structures. We then estimate the critical conditions for nuclear pasta to become disordered and behave like liquid, which are found to be sensitive to the densities, temperatures, proton fractions, and nuclear shapes. If we further increase temperature, eventually the nonuniform structures of nuclear pasta become unstable and are converted into uniform nuclear matter. The phase diagrams of nuclear matter are then estimated, which should be useful for understanding the evolutions of neutron stars, supernova dynamics, and binary neutron star mergers.

Nonlinear Dynamics in Isotropic and Anisotropic Magneto-Optical Traps

We briefly review some recent advances in the field of nonlinear dynamics of atomic clouds in magneto-optical traps. A hydrodynamical model in a three-dimensional geometry is applied and analyzed using a variational approach. A Lagrangian density is proposed in the case where thermal and multiple scattering effects are both relevant, where the confinement damping and harmonic potential are both included. For generality, a general polytropic equation of state is assumed. After adopting a Gaussian profile for the fluid density and appropriate spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived. These equations are applied to compare cylindrical and spherical geometry approximations. The results are restricted to potential flows.

Interface effects of quark matter: Light-quark nuggets and compact stars

The interface effects of quark matter play important roles in the properties of compact stars and small nuggets, such as strangelets and nonstrange quark matter ($ud\mathrm{QM}$) nuggets. By introducing a density derivative term to the Lagrangian density and adopting Thomas-Fermi approximation, we find it is possible to reproduce the results obtained by solving Dirac equations. Adopting certain parameter sets, the energy per baryon of $ud\mathrm{QM}$ nuggets decreases with baryon number $A$ and become more stable than nuclei at $A\ensuremath{\gtrsim}300$. The effects of quark matter symmetry energy are examined, where $ud\mathrm{QM}$ nuggets at $A\ensuremath{\approx}1000$ can be more stable than others if large symmetry energy is adopted. In such cases, larger $ud\mathrm{QM}$ nuggets will decay via fission and the surface of a $ud\mathrm{QM}$ star will fragment into a crust made of $ud\mathrm{QM}$ nuggets and electrons, which resembles the cases of a strange star's crust. The corresponding microscopic structures are then investigated adopting spherical and cylindrical approximations for the Wigner-Seitz cells, where the droplet phase is found to be the most stable configuration with $ud\mathrm{QM}$ stars' crusts and $ud\mathrm{QM}$ dwarfs made of $ud\mathrm{QM}$ nuggets ($A\ensuremath{\approx}1000$) and electrons. For the cases considered here, the crust thickness of $ud\mathrm{QM}$ stars is typically $\ensuremath{\sim}200\text{ }\text{ }\mathrm{m}$, which reaches a few kilometers if we neglect the interface effects and adopt Gibbs construction. The masses and radii of $ud\mathrm{QM}$ dwarfs are smaller than typical white dwarfs, which would increase if the interface effects are neglected.

Spent Fuel Pool Dose Rate Calculations Using Point Kernel and Hybrid Deterministic-Stochastic Shielding Methods

This paper presents comparison of the Krško Power Plant simplified Spent Fuel Pool (SFP) dose rates using different computational shielding methodologies. The analysis was performed to estimate limiting gamma dose rates on wall mounted level instrumentation in case of significant loss of cooling water. The SFP was represented with simple homogenized cylinders (point kernel and Monte Carlo (MC)) or cuboids (MC) using uranium, iron, water, and dry-air as a bulk region materials. The pool is divided on the old and new section where the old one has three additional subsections representing fuel assemblies (FAs) with different burnup/cooling time (60 days, 1 year and 5 years). The new section represents the FAs with the cooling time of 10 years. The time dependent fuel assembly isotopic composition was calculated using ORIGEN2 code applied to the depletion of one of the fuel assemblies present in the pool (AC-29). The source used in Microshield calculation is based on imported isotopic activities. The time dependent photon spectrum with total source intensity from Microshield multigroup point kernel calculations was then prepared for two hybrid deterministic-stochastic sequences. One is based on SCALE6.2b3/MAVRIC (Monaco and Denovo) methodology and another uses Monte Carlo code MCNP6.1.1b and ADVANTG3.0.1. code. Even though this model is a fairly simple one, the layers of shielding materials are thick enough to pose a significant shielding problem for MC method without the use of effective variance reduction (VR) technique. For that purpose the ADVANTG code was used to generate VR parameters for the MCNP fixed-source calculation using continuous energy transport. ADVATNG employs a deterministic forward-adjoint transport solver Denovo which implements CADIS/FWCADIS methodology. Denovo uses a structured, Cartesian-grid SN solver based on the Koch- Baker-Alcouffe parallel transport sweep algorithm across x-y domain blocks. This was our first application of ANDVANTG/MCNP hybrid sequence for this type of calculation and the results where compared to SCALE/MAVRIC sequence which we regularly use for similar calculations. The comparison of gamma dose rates on different point detector locations (central above pool and at the top of pool periphery) showed a good agreement between Microshield (point-kernel) and deterministic-stochastic shielding methodologies for the cylindrical approximation of the pool geometry. More complicated cases for model with multi-source option and for cuboids showed very good agreement between SCALE/MAVRIC and ANDVANTG/MCNP calculations.

Optical Properties of Colloidal Silver Nanowires.

Silver nanowires are used in many applications, ranging from transparent conductive layers to Raman substrates and sensors. Their performance often relies on their unique optical properties that emerge from localized surface plasmon resonances in the ultraviolet. To tailor the nanowire geometry for a specific application, a correct understanding of the relationship between the wire’s structure and its optical properties is therefore necessary. However, while the colloidal synthesis of silver nanowires typically leads to structures with pentagonally twinned geometries, their optical properties are often modeled assuming a cylindrical cross-section. Here we highlight the strengths and limitations of such an approximation by numerically calculating the optical and electrical response of pentagonally twinned silver nanowires and nanowire networks. We find that our accurate modeling is crucial to deduce structural information from experimentally measured extinction spectra of colloidally synthesized nanowire suspensions and to predict the performance of nanowire-based near-field sensors. On the contrary, the cylindrical approximation is fully capable of capturing the optical and electrical performance of nanowire networks used as transparent electrodes. Our results can help assess the quality of nanowire syntheses and guide in the design of optimized silver nanowire-based devices.

Experimental and numerical analysis of gas flow in nodeless antiresonant hollow-core fibers for optimization of laser gas spectroscopy sensors

In this paper, we present the pressure-driven gas flow studies in nodeless antiresonant hollow-core fibers (ARHCFs) for laser absorption spectroscopy (LAS) applications. The OpenFOAM® software was used for gas flow modeling for comparison with experimental data. The experimental LAS-based setup utilizing a 14.73 m long fiber, was used to gas exchange time measurements for various pressure differences (1.5–5 bar). The obtained results have shown that the application of a precise fiber geometrical representation and a compressible flow model improves the correlation between simulations and experiments for nodeless ARHCFs, in comparison to cylindrical channel approximation and an incompressible model. We believe that our work will help optimize the selection of the proper ARHCF during sensor design, where the fiber type and length can significantly determine the obtainable response time of the detector and its overall compactness.

Unified nuclear matter equations of state constrained by the in-medium balance in density-dependent covariant density functionals

Considering the effects of charge screening, we propose a new numerical recipe within the framework of Thomas-Fermi approximation, where the properties of nuclear matter throughout a vast density range can be obtained self-consistently. Assuming spherical and cylindrical approximations for the Wigner-Seitz cell, typical nuclear matter structures (droplet, rod, slab, tube, bubble, and uniform) are observed. We then investigate the EOSs and microscopic structures of nuclear matter with both fixed proton fractions and $\beta$-equilibration, where two covariant density functionals DD-LZ1 and DD-ME2 are adopted. Despite the smaller slope $L$ of symmetry energy obtained with the functional DD-LZ1, the curvature parameter $K_\mathrm{sym}$ is much larger than that of DD-ME2, which is attributed to the peculiar density-dependent behavior of meson-nucleon couplings guided by the restoration of pseudo-spin symmetry around the Fermi levels in finite nuclei. Consequently, different mass-radius relations of neutron stars are predicted by the two functionals. Different microscopic structures of nonuniform nuclear matter are obtained as well, which are expected to affect various physical processes in neutron star properties and evolutions.

Spectral methods for nonlinear functionals and functional differential equations

We present a rigorous convergence analysis for cylindrical approximations of nonlinear functionals, functional derivatives, and functional differential equations (FDEs). The purpose of this analysis is twofold: First, we prove that continuous nonlinear functionals, functional derivatives, and FDEs can be approximated uniformly on any compact subset of a real Banach space admitting a basis by high-dimensional multivariate functions and high-dimensional partial differential equations (PDEs), respectively. Second, we show that the convergence rate of such functional approximations can be exponential, depending on the regularity of the functional (in particular its Fréchet differentiability), and its domain. We also provide necessary and sufficient conditions for consistency, stability and convergence of cylindrical approximations to linear FDEs. These results open the possibility to utilize numerical techniques for high-dimensional systems such as deep neural networks and numerical tensor methods to approximate nonlinear functionals in terms of high-dimensional functions, and compute approximate solutions to FDEs by solving high-dimensional PDEs. Numerical examples are presented and discussed for prototype nonlinear functionals and for an initial value problem involving a linear FDE.

Photogrammetric Measurement and Analysis of the Shape Profile of Pneumatic Artificial Muscles

Inaccuracies in modeling of the geometric shape of PAMs has long been cited as a probable source of error in modeling and design efforts. The geometric shape and volume of PAMs is commonly approximated using a cylindrical shape profile, even though its shape is non-cylindrical. Correction factors—based on qualitative observations of the PAM’s general shape—are often implemented to compensate for error in this cylindrical shape approximation. However, there is little evidence or consensus on the accuracy and form of these correction factors. Approximations of the shape profile are also used to calculate the internal volume of PAMs, as experimental measurements of the internal volume require intrusive testing methods and specialized equipment. This research presents a photogrammetric method for measuring the shape profile and internal volume of PAMs. A test setup, method of image data acquisition, and a preliminary analysis of the image data, is presented in this research. A 22.2 mm (7/8 in) diameter PAM is used to demonstrate the photogrammetric procedure and test its accuracy. Analysis of the tested PAM characterizes trends of the shape profile with respect to pressure and contraction. The common method of estimating the diameter—through the use of the cylindrical approximation and initial geometry of the PAM—is tested by comparison to the measured shape profile data. Finally, a simple method of calculating the internal volume using the measured shape profile data is developed. The presented method of acquiring photogrammetric measurements of PAM shape produces an accurate characterization of its shape profile, thereby mitigating uncertainty in PAM shape in analysis and other efforts.

A Dynamic expansion of a cylindrical cavity in a compressible elastic-plastic medium. The Analysis of medium resistance to dynamic penetration of a sharp-nosed impactor

This paper presents the solution of the problem related to the dynamic cylindrical cavity expansion in a compressible elastic-plastic medium. Finite strains, nonlinear compressibility and dependence of the yield stress versus pressure are taken into account in the problem formulation. The study targets at developing a new engineering model on the penetration of a sharp-nosed impactor in the range of middle impact velocities based on the problem analysis results of the cylindrical cavity expansion in a half-space (cylindrical cavity expansion approximation). Based on the analytical approach a model is obtained that determines the resistance of the medium to dynamic cavity expansion. The main parameters of the model depend on the mechanical properties of the medium. For these dependences we proposed approximating relations based on manipulation of the mechanical properties of a number of materials (some alloys and soils). To derive the dynamic penetration model the A.Ya. Sagomonyan assumption of the radial expansion of the hole is used. It is assumed that particles of the medium material move in a radial direction from the surface of the impactor penetrating into the shield. Such assumption can be applied for the class of impactors in the form of slender sharp-nosed bodies of revolution. Based on the assumptions we obtained a model of the medium resistance to the dynamic penetration of a slender sharp-nosed body of revolution. The new model, in addition to the "standard" strength and inertial components, contains the "attached mass", which changes during the penetration process. The experimental validation of the new penetration model using a series of experimental studies on the penetration of various forms of impactors into aluminum alloys is considered. The influence of the “attached mass” and inertial forces of the medium resistance to the penetration is estimated. The conditions of applicability of the new model are obtained: the penetration model is applicable for estimation of the resistance of a compressible medium to penetration of a thin sharp-nosed body of revolution at impact velocities of 200-800 m/s.

Sex- and age-related variations in the three-dimensional orientations and curvatures of the articular surfaces of the human talus.

The high prevalence of foot pathologies in women and the elderly could be associated with gender and age difference in the morphology of the foot, particularly the morphology of the keystone of the foot, the talus. The present study investigated the orientation and curvature of the three articular surfaces of the talus in relation to sex and age based on computer tomography (CT), to identify possible morphological factors of the higher prevalence of foot disorders in women and elderly. Fifty-six participants were included in this study. The orientations of the talocrural, subtalar, and talonavicular joints were quantified three-dimensionally by calculating normal and principal axes of the articular surfaces defined by planar approximation. The curvature radii of the articular surfaces were quantified by cylindrical and spherical approximations. The talonavicular surface was significantly more twisted in the frontal plane and less adducted in the transverse plane in females than in males. With aging, the subtalar articular surface was significantly facing more posteriorly. Moreover, it was found that the curvature radii of the trochlea and navicular articular surfaces significantly increased with aging, indicating a flattening of these surfaces. The identified changes in the talar morphology with aging could potentially lead to a higher prevalence of foot disorders in the elderly.

Extraction of the plasma current contribution from the numerically integrated magnetic signals in ISTTOK

ISTTOK tokamak operates in AC mode allowing to have consecutive cycles of positive and negative plasma current. The plasma centroid position is estimated from the reconstruction of the signals obtained from a poloidal array of twelve magnetic probes. In the previous setup, this reconstruction relied on a cylindrical approximation algorithm in which the error fields generated by active coils and currents in the passive structures were not taken into account, leading to some centroid position inaccuracy. Although this approach has been able to produce flat top current AC discharges with reasonable reliability, a better solution was implemented as a preferred plasma position estimator. The signals are currently corrected subtracting the contribution from external magnetic fields following a method that relies on state-space models which use data collected from a systematic vacuum calibration procedure. Also, the plasma centroid position is estimated using a multi-filament current model. Furthermore, the recent implementation of numerical integrators in the real time ATCA based data acquisition system substantially improved the real time conditioning of the magnetic signals measurements. First results demonstrate that this new approach delivers a more reliable estimation of the plasma current centroid position with noticeable improvement on control performance, which is paramount to the success ratio of the AC plasma current switching.