Field Geometry Research Articles

Investigation of proton exchange membrane fuel cell stack with inversely phased wavy flow field design

The proton exchange membrane fuel cell stack based on metallic bipolar plate is promising in fuel cell vehicle applications due to its compact design and high power density. As the flow field design is critical to the fuel cell performance, in this work, the novel wavy flow fields designed in metallic bipolar plate with inverse phase for anode and cathode are investigated by both experiment and simulation. Validated by the test of 5-cell short stack with 315 cm2 active area, a three-dimensional non-isothermal model is developed to investigate the multi-physical processes and internal parameter uniformities of the presented stack design. The in-plane parameter distributions of current density, water content and reactant concentrations basically follow the cathode wavy flow field geometry rather than the anode one, while the temperature distribution presents multiple elliptical island shaped patterns according to the intercrossed wavy flow fields. The two-layered intercrossed wavy coolant channels enhance the thermal convection of the coolant which induces interlaminar secondary flow with 25% velocity magnitude of the primary one. The findings of this work are beneficial to understand the internal behavior of the fuel cell stack and optimize the flow field design for enhanced performance and heat dissipation capability.

The effect of discretization on the mean geometry of a 2D random field

The study of the geometry of excursion sets of 2D random fields is a question of interest from both the theoretical and the applied viewpoints. In this paper we are interested in the relationship between the perimeter (resp. the total curvature, related to the Euler characteristic by Gauss-Bonnet Theorem) of the excursion sets of a function and the ones of its discretization. Our approach is a weak framework in which we consider the functions that map the level of the excursion set to the perimeter (resp. the total curvature) of the excursion set. We will be also interested in a stochastic framework in which the sets are the excursion sets of 2D random fields. We show in particular that, in expectation, under some stationarity and isotropy conditions on the random field, the perimeter is always biased (with a 4/π factor), whereas the total curvature is not. We illustrate all our results on different examples of random fields.

Real time display with the ferrolens of homogeneous magnetic fields

In our previous published research we have studied the applications of the ferrolens for the observation and qualitative analysis of non-homogeneous magnetic fields. Latest developments over the last few years of the ferrolens increased multifold the sensitivity of this device allowing it to display magnetic fields as low as 10mT in strength and therefore it is possible now to observe also the homogeneous (i.e. straight parallel magnetic flux lines of uniform density in space) magnetic field existing inside air solenoids and between N-S poles of two attracting separated permanent magnets. We present and analyze herein these novel observations of homogeneous magnetic fields with the ferrolens and as a potential new application of this device. The ferrolens can now display the projected magnetic field on air from a distance without needing to be in physical contact with the field source. Experiments were carried out to demonstrate these new capabilities of the ferrolens as a nanomagnetic flux viewer, real-time physical device and scientific qualitative tool. We compare the geometry of magnetic fields of condensed matter ferromagnets with that of magnetic fields inside electrical air solenoids. Specifically, the homogeneous field between two N-S attracting magnets at a distance as well as inside air solenoids and Helmholtz coils and also the non-homogeneous total field of single dipole permanent magnets were observed using a latest generation very sensitive ferrolens. The unique feature of this magneto optic fluid thin film physical device is that it can display discrete magnetic flux lines of the macroscopic field. Also we show how the ferrolens can be used to detect qualitatively the symmetry center of a non ideal homogeneous magnetic field.

Hexa-μ-acetato-chlorido-(μ-N,2-dioxodo-benzene-1-carboximidato)-μ3-oxido-tetra-iron(III)-water (1/1) and hexa-μ-acetato-(μ-N,2-dioxodo-benzene-1-carboximidato)fluorido-μ3-oxido-tri-pyridine-tetra-iron(III)-pyridine-water (1/1/0.24).

The title compounds, [Fe4(C2H3O2)6(C7H4O3)FO(C5H5N)3]·C5H5N·0.24H2O (1-F) and [Fe4(C2H3O2)6(C7H4O3)ClO(C5H5N)3]·H2O (1-Cl) were synthesized using a self-assembly reaction in methanol and pyridine with stoichiometric addition of salicyl-hydroxamic acid (H3shi), acetic acid (HOAc), and the appropriate ferric halide salt. The compounds crystallize as solvates, where 1-F has one pyridine mol-ecule that is disordered about a twofold axis and one water mol-ecule with an occupancy of 0.24 (2); and 1-Cl has one water mol-ecule that is disordered over two sites with occupancies of 0.71 (1) and 0.29 (1). The space groups for each analog differ as 1-F crystallizes in Fdd2 while 1-Cl crystallizes in P21. The difference in packing is due to changes in the inter-molecular inter-actions involving the different halides. The two mol-ecules are mostly isostructural, differing only by the torsion of the pyrine ligands and slight orientation changes in the acetate ligands. All of the iron(III) ions are in six-coordinate octa-hedral ligand field geometries but each one exhibits a unique coordination environment with various numbers of O (four to six) and N (nought to two) atom donors. Bond-valence sums confirm each iron is trivalent. The hydroximate ligand is bound to three iron(III) ions using a fused chelate motif similar to those in metallacrown compounds.

The Origin of Parity Violation in Polarized Dust Emission and Implications for Cosmic Birefringence

Abstract Recent measurements of Galactic polarized dust emission have found a nonzero TB signal, a correlation between the total intensity and the B-mode polarization component. We present evidence that this parity-odd signal is driven by the relative geometry of the magnetic field and the filamentary interstellar medium in projection. Using neutral hydrogen morphology and Planck polarization data, we find that the angle between intensity structures and the plane-of-sky magnetic field orientation is predictive of the signs of Galactic TB and EB. Our results suggest that magnetically misaligned filamentary dust structures introduce nonzero TB and EB correlations in the dust polarization, and that the intrinsic dust EB can be predicted from measurements of dust TB and TE over the same sky mask. We predict correlations between TE, TB, EB, and EE/BB, and confirm our predictions using synthetic dust polarization maps from magnetohydrodynamic simulations. We introduce and measure a scale-dependent effective magnetic misalignment angle, ψ ℓ dust ∼ 5 ° for 100 ≲ ℓ ≲ 500, and predict a positive intrinsic dust EB with amplitude D ℓ EB ≲ 2.5 μ K CMB 2 for the same multipole range at 353 GHz over our sky mask. Both the sign and amplitude of the Galactic EB signal can change with the sky area considered. Our results imply that searches for parity violation in the cosmic microwave background must account for the nonzero Galactic EB and TB signals, necessitating revision of existing analyses of the evidence for cosmic birefringence.

PRIMARY DISKS AND THEIR OBSERVATIONAL APPEARANCE IN COLLAPSING MAGNETIC ROTATING PROTOSTELLAR CLOUDS

The collapse of the magnetic rotating protostellar cloud with mass of $10\,M_{\odot}$ is numerically studied. The initial ratios of the thermal, magnetic, and rotational energies of the cloud to the modulus of its gravitational energy are 0.3, 0.2 and 0.01, respectively. The emphasis is on the evolution and properties of the quasi-magnetostatic primary disk formed at the isothermal stage of the collapse. Simulations show that the primary disk size and mass increase during evolution from $1500$ au to $7400$ au and from $0.3\,M_{\odot}$ to $5.2\,M_{\odot}$, respectively. Magnetic field is quasi-radial in the cloud envelope and quasi-uniform within the primary disk. A toroidal magnetic field is generated behind the front of the fast shock MHD wave propagating from the primary disk boundary and in the region of the outflow formed near the first hydrostatic core. The hierarchical structure of collapsing protostellar clouds can be revealed in observations in terms of the magnetic field geometry and the angular momentum distribution.

Coherent Emission from QED Cascades in Pulsar Polar Caps

Abstract Pulsar magnetospheres are thought to be filled with electron–positron plasma generated in pair cascades. The driving mechanism of these cascades is the emission of gamma-ray photons and their conversion into pairs via quantum electrodynamics (QED) processes. In this work, we present 2D particle-in-cell simulations of pair cascades in pulsar polar caps with realistic magnetic field geometry that include the relevant QED processes from first principles. Our results show that, due to variation of magnetic field curvature across the polar cap, pair production bursts self-consistently develop an inclination with respect to the local magnetic field that favors the generation of coherent electromagnetic modes with properties consistent with pulsar radio emission. We show that this emission is peaked along the magnetic axis and close to the polar cap edge and may thus offer an explanation for the core and conal components of pulsar radio emission.

Reconstructing magnetic deflections from sets of proton images using differential evolution.

Proton imaging is a powerful technique for imaging electromagnetic fields within an experimental volume, in which spatial variations in proton fluence are a result of deflections to proton trajectories due to interaction with the fields. When deflections are large, proton trajectories can overlap, and this nonlinearity creates regions of greatly increased proton fluence on the image, known as caustics. The formation of caustics has been a persistent barrier to reconstructing the underlying fields from proton images. We have developed a new method for reconstructing the path-integrated magnetic fields, which begins to address the problem posed by caustics. Our method uses multiple proton images of the same object, each image at a different energy, to fill in the information gaps and provide some uniqueness when reconstructing caustic features. We use a differential evolution algorithm to iteratively estimate the underlying deflection function, which accurately reproduces the observed proton fluence at multiple proton energies simultaneously. We test this reconstruction method using synthetic proton images generated for three different, cylindrically symmetric field geometries at various field amplitudes and levels of proton statistics and present reconstruction results from a set of experimental images. The method we propose requires no assumption of deflection linearity and can reliably solve for fields underlying linear, nonlinear, and caustic proton image features for the selected geometries and is shown to be fairly robust to noise in the input proton intensity.

Demonstration of reduced neoclassical energy transport in Wendelstein 7-X

Research on magnetic confinement of high-temperature plasmas has the ultimate goal of harnessing nuclear fusion for the production of electricity. Although the tokamak1 is the leading toroidal magnetic-confinement concept, it is not without shortcomings and the fusion community has therefore also pursued alternative concepts such as the stellarator. Unlike axisymmetric tokamaks, stellarators possess a three-dimensional (3D) magnetic field geometry. The availability of this additional dimension opens up an extensive configuration space for computational optimization of both the field geometry itself and the current-carrying coils that produce it. Such an optimization was undertaken in designing Wendelstein 7-X (W7-X)2, a large helical-axis advanced stellarator (HELIAS), which began operation in 2015 at Greifswald, Germany. A major drawback of 3D magnetic field geometry, however, is that it introduces a strong temperature dependence into the stellarator’s non-turbulent ‘neoclassical’ energy transport. Indeed, such energy losses will become prohibitive in high-temperature reactor plasmas unless a strong reduction of the geometrical factor associated with this transport can be achieved; such a reduction was therefore a principal goal of the design of W7-X. In spite of the modest heating power currently available, W7-X has already been able to achieve high-temperature plasma conditions during its 2017 and 2018 experimental campaigns, producing record values of the fusion triple product for such stellarator plasmas3,4. The triple product of plasma density, ion temperature and energy confinement time is used in fusion research as a figure of merit, as it must attain a certain threshold value before net-energy-producing operation of a reactor becomes possible1,5. Here we demonstrate that such record values provide evidence for reduced neoclassical energy transport in W7-X, as the plasma profiles that produced these results could not have been obtained in stellarators lacking a comparably high level of neoclassical optimization.

A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows

A variation of moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is developed for solving the compressible Euler equations. The MDG-ICE method, originating from the work of Corrigan et al. [1–4], is based on the space-time DG formulation, where both flow field and grid geometry are considered as independent variables and the conservation laws are enforced both on discrete elements and element interfaces. The element conservation laws are solved in the standard discontinuous solution space to determine conservative quantities, while the interface conservation is enforced using a variational formulation in a continuous space to determine discrete grid geometry. The resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation can then be solved in a least-squares sense, leading to an unconstrained nonlinear least-squares problem that is regularized and solved by Levenberg-Marquardt method. A number of numerical experiments for both 1D unsteady and 2D steady state compressible flow problems are conducted to assess the accuracy and robustness of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to implicitly detect and track all types of discontinuities via interface conservation enforcement and satisfy the conservation law on both elements and interfaces via grid movement and grid management, demonstrating that an exponential rate of convergence for Sod and Lax-Harden shock tube problems can be achieved and highly accurate solutions without overheating to both double-rarefaction wave and Noh problems can be obtained.

Numerical investigation on the improved reactant mass transport with depth-dependent flow fields in polymer electrolyte fuel cell under inhomogeneous gas diffusion layer compression

In this work, a numerical model is developed to analyse the effects of depth-dependent reactant flow field geometry under inhomogeneous gas diffusion layer (GDL) compression on the mass transport process and performance of polymer electrolyte fuel cell (PEFC). The types of depth-dependent flow channels considered in this study are: converging channel (depth continuously decreasing) and diverging channel (depth continuously increasing), and the conventional flow field designs. The model is investigated for local and global inhomogeneity due to GDL compression. The localized inhomogeneity is introduced in the flow-field rib as well as channel regions. The results are compared for reactant concentration, water concentration, local current density, and the polarization curve for different flow channel combinations. It is observed that the availability of reactants is higher in case of converging channel design, which leads to an increase in cell performance at higher currents. However, this is subjected to GDL inhomogeneity in compression. We observe in this study that such inhomogeneity, instead of having a significant impact on cell performance, lead to minimal influence in terms of reduction in cell performance. This we observe is due to improved H2 availability at anode and reduced O2 distribution at cathode that ultimately impacts respective hydrogen oxidation reaction (HOR) and reduction in oxygen reduction reaction (ORR). This study aims to investigate the cases for altered variation in cell performance due to change in depth-dependent flow fields.

Simulations of the Isothermal Collapse of Magnetic Rotating Protostellar Clouds

We investigate collapse of magnetic protostellar clouds of mass $10$ and $1 M_{\odot}$. The collapse is simulated numerically using the two-dimensional magnetohydrodynamic (MHD) code `Enlil'. The simulations show that protostellar clouds acquire a hierarchical structure by the end of the isothermal stage of collapse. Under the action of the electromagnetic force, the protostellar cloud takes the form of an oblate envelope with the half-thickness to radius ratio $Z/R \sim (0.20-0.95)$. A geometrically and optically thin primary disk with radius $0.2-0.7 R_0$ and $Z/R \sim (10^{-2}-10^{-1})$ forms inside the envelope, where $R_0$ is the initial radius of the cloud. Primary disks are the structures in magnetostatic equilibrium. They form when the initial magnetic energy of the cloud exceeds $20 \%$ of its gravitational energy. The mass of the primary disk is $30-80 \%$ of the initial mass of the cloud. The first hydrostatic core subsequently forms in the center of the primary disc. We discuss the role of primary disks in the further evolution of clouds, as well as possible observational appearance of the internal hierarchy of the collapsing cloud from the point of view of the features of the magnetic field geometry and the distribution of angular momentum at different levels of the hierarchy

Short-term variations of surface magnetism and prominences of the young sun-like star V530 Per

AbstractV530 Per is a solar-like member of the young open cluster α Persei, with an ultra-short rotation period (P∼0.32d). We report on two spectropolarimetric campaigns using ESPaDOnS, aimed at characterizing the short-term variability of its magnetic activity and large-scale magnetic field. We used time-resolved spectropolarimetric observations obtained in 2006 and 2018 and reconstructed the brightness distribution and large-scale magnetic field geometry of V530 Per through Zeeman-Doppler imaging. Using the same data sets, we also mapped the spatial distribution of prominences through tomography of Hα emission. We reconstruct, at both epochs, a large, dark spot occupying the polar region of V530 Per while smaller (dark and bright) spots were reconstructed at lower latitudes. The maximal field strength reached ∼1 kG. The prominence pattern displayed a stable component that was confined close to the corotation radius. In 2018, we also observed rapidly evolving Hα emitting structures, over timescales ranging from minutes to days. The fast Hα evolution was not linked to any detected photospheric changes in the spot or magnetic coverage.

Dispersion and recovery of solutes and heat under cyclic radial advection

For cyclic injection-extraction wells with various radial flow geometries, we study the transport and recovery of solute and heat. We derive analytical approximations for the recovery efficiency in closed-form elementary functions. The recovery efficiency increases as injection-extraction flow rates increase, dispersion decreases, and spatial dimensionality decreases. In most scenarios, recovery increases as cycle periods increase, but we show numerically and analytically that it varies non-monotonically with cycle period in three-dimensional flow fields, due to competing effects between diffusion and mechanical dispersion. This illustrates essential differences between the spreading mechanisms, and reveals that for a single well it may be impossible to optimize recovery of both solute and heat simultaneously. Whether retardation increases or decreases recovery thus depends on aquifer geometry and the dominant dispersion process. As the dominant dispersion process heavily determines the sensitivity of the recovery efficiency to other parameters, we introduce the dimensionless kinetic dispersion factor ST, to distinguish whether diffusion or mechanical dispersion dominates. We also introduce the geometric dispersion factor G, which is derived from our full solution for the recovery efficiency and improves upon the concept of the area-to-volume ratio (A/V), often used in analysing well problems. Unlike A/V, G accounts for spatio-temporal interactions between dispersion and flow field geometry, and can be applied to determine recovery efficiencies across a wider range of scenarios. It is found that A/V is a special case of G, describing the recovery efficiency only when mechanical dispersion with linear velocity dependence is the sole mechanism of spreading.

Negative Transient Flux in the Near Field of a Subwavelength Source

The emission of waves by a source is often analyzed in the Fourier domain, which hampers the discovery of transient wave phenomena. Based on a fully temporal analysis, the authors observe in acoustic experiments that the energy can flow backward for short durations in the near field of a deep-subwavelength source in a homogenous medium. Through an impedance analysis, this negative transient flux phenomenon is ascribed to the geometry of the outgoing field. This finding is generic and may find applications in emission and scattering scenarios and could be useful for designing time-varying media.

Using isometries for computational design and fabrication

We solve the task of representing free forms by an arrangement of panels that are manufacturable by precise isometric bending of surfaces made from a small number of molds. In fact we manage to solve the paneling task with surfaces of constant Gaussian curvature alone. This includes the case of developable surfaces which exhibit zero curvature. Our computations are based on an existing discrete model of isometric mappings between surfaces which for this occasion has been refined to obtain higher numerical accuracy. Further topics are interesting connections of the paneling problem with the geometry of Killing vector fields, designing and actuating isometries, curved folding in the double-curved case, and quad meshes with rigid faces that are nevertheless flexible.

On the geometry of numerical ranges over finite fields

Numerical ranges over a certain family of finite fields were classified in 2016 by a team including our fifth author [5]. Soon afterward Ballico generalized these results to all finite fields and published some new results about the cardinality of the finite field numerical range [1,2]. In this paper we study the geometry of these finite fields using the boundary generating curve, first introduced by Kippenhahn in 1951 [8,9]. We restrict our study to square matrices of dimension 2, with at least one eigenvalue in Fq2.

Tuning the Magnetic Anisotropy of Lanthanides on a Metal Substrate by Metal-Organic Coordination.

Taming the magnetic anisotropy of lanthanides through coordination environments is crucial to take advantage of the lanthanides properties in thermally robust nanomaterials. In this work, the electronic and magnetic properties of Dy-carboxylate metal-organic networks on Cu(111) based on an eightfold coordination between Dy and ditopic linkers are inspected. This surface science study based on scanning probe microscopy and X-ray magnetic circular dichroism, complemented with density functional theory and multiplet calculations, reveals that the magnetic anisotropy landscape of the system is complex. Surface-supported metal-organic coordination is able to induce a change in the orientation of the easy magnetization axis of the Dy coordinative centers as compared to isolated Dy atoms and Dy clusters, and significantly increases the magnetic anisotropy. Surprisingly, Dy atoms coordinated in the metallosupramolecular networks display a nearly in-plane easy magnetization axis despite the out-of-plane symmetry axis of the coordinative molecular lattice. Multiplet calculations highlight the decisive role of the metal-organic coordination, revealing that the tilted orientation is the result of a very delicate balance between the interaction of Dy with O atoms and the precise geometry of the crystal field. This study opens new avenues to tailor the magnetic anisotropy and magnetic moments of lanthanide elements on surfaces.

Anisotropic Helmholtz decomposition for controlled fluid simulation

The combination of fluids and tensors has been explored in recent works to constrain the fluid flow along specific directions for simulation applications. Such an approach points towards the necessity to model flows using anisotropic fluid dynamics. The formalism behind anisotropic Helmholtz decomposition plays a central role given the foundations to model directional constraints. In this paper, we apply the anisotropic Helmholtz theory to obtain a divergent free velocity field that respects the constraints of a symmetric positive tensor field. A major contribution is a well-defined anisotropic projection method suitable for anisotropic transport. An anisotropic projection is paramount for stable incompressible advection in anisotropic medium. Aiming to show how to benefit from the anisotropic projection, we customize the Navier-Stokes equations to use tensor information for locally modifying fluid momentum and material advection. Besides, we develop a stable numerical method to integrate the obtained system of partial differential equations and a methodology to optimize the tensor field to reduce numerical errors. Experiments show that tensor fields with different anisotropic features can provide distinct projected divergence-free vector fields. Our results also show that the proposed method forms a basis for fluid flow simulation following meaningful paths induced by the tensor field geometry and topology.

Leveling Transient and Spatial Gradients in Planar Solid Oxide Cells Using Spatially Varied Microstructures: A Numerical Study

Spatial and transient gradients of temperature, current density, and gas species concentrations are expected to occur within large area planar solid oxide cells. These gradients can be detrimental to cell performance and stability. Such gradients are inherent to the geometry of the flow fields and interconnects between cells, especially at high current densities and fuel/steam utilizations in fuel cell/electrolysis modes, respectively. To reduce the extent of these gradients, additive manufacturing techniques could be employed to level the electrochemical reaction rates in the electrodes by purposefully designing the electrode active layer to have engineered property distributions. The purpose of this study is to investigate the effects of applied microstructural property gradients on spatial and transient gradients under extreme operating conditions. Modeling results suggest that by strategically varying the volume fractions of composite electrode materials, it is possible to modulate temperature, species, and current density gradients in planar solid oxide cells.