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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

Chemistry↗
DOE OSTI2022

MUSE Analysis of Gas around Galaxies (MAGG) – IV. The gaseous environment of z ∼ 3–4 Ly α emitting galaxies

ABSTRACT We study the link between galaxies and H i-selected absorption systems at z ∼ 3–4 in the MUSE Analysis of Gas around Galaxies (MAGG) survey, an ESO large programme consisting of integral field spectroscopic observations of 28 quasar fields hosting 61 strong absorbers with $\rm N_{\rm H\,{\small I}}\gtrsim 10^{16.5}~\rm cm^{-2}$. We identify 127 Ly α emitting galaxies (LAEs) around the absorbers, corresponding to a detection rate of 82 ± 16 per cent. The luminosity function of these LAEs is ≈5 times higher in normalization than the field population and we detect a significant clustering of galaxies with respect to the gas, confirming that high column density absorbers and LAEs trace each other. Between 30 and 40 per cent of the absorbers are associated with multiple LAEs, which lie preferentially along filaments. Galaxies in groups also exhibit a three times higher covering factor of optically thick gas compared to isolated systems. No significant correlations are identified between the emission properties of LAEs and the absorption properties of optically thick gas clouds, except for a weak preference of brighter and multiple galaxies to reside near broad absorbers. Based on the measured impact parameters and the covering factor, we conclude that the near totality of optically thick gas in the Universe can be found in the outer circumgalactic medium (CGM) of LAEs or in the intergalactic medium (IGM) in proximity to these galaxies. Thus, LAEs act as tracers of larger scale structures within which both galaxies and optically thick clouds are embedded. The patchy and inhomogeneous nature of the CGM and IGM explains the lack of correlations between absorption and emission properties. This implies that very large samples are needed to unveil the trends that encode the properties of the baryon cycle.

Astronomy & Astrophysics↗
DOE OSTI2020

Experimental studies of the two-step scheme with an intense radioactive 132 Sn beam for next-generation production of very neutron-rich nuclei

The study of nuclei in the yet-unexplored, very neutron-rich, mid- to heavy-mass region of the nuclear chart, comprising perhaps half of all nuclei predicted to exist, is leading to new and/or upgraded facilities, as well as to research into the underlying production processes. In the present study, the usefulness of the two-step scheme, an alternate method to produce very neutron-rich nuclei, by a combination of an isotope-separation online (ISOL) system as a first step, and in-beam fragmentation of re-accelerated radioactive isotopes (RIs) as a second step, was investigated with a 132 Sn beam. In this work, very neutron-rich RIs around the neutron-rich neutron number N = 82 region were produced from the 278-MeV/nucleon 132 Sn beam impinging on a 5.97-mm Be target, and their production cross sections were measured. Yields were then estimated for the two-step scheme with the 132 Sn beam relative to the ones by a one-step scheme, in-flight fission of a 238 U beam, for 1-MW proton and 238 U beams at respective RI-beam facilities. This comparison suggests that the two-step scheme with the 132 Sn beam provides yields >40-times higher than those with the one-step scheme for the very neutron-rich N = 82 region. Moreover, by using various RI beams over the nuclear chart from ISOL, certain kinds of very neutron-rich RIs around the supernova r-process path can be produced with greater yields than by the one-step approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Experimental and numerical studies of seismic fluid-structure interaction in a base-supported cylindrical vessel

Seismic design and qualification of advanced reactors will rely heavily on the use of verified and validated numerical models capable of capturing the interaction of the vessel, its contained fluid, and the internal equipment: fluid-structure interaction (FSI) analysis. Analytical solutions can be used for preliminary sizing and design of such vessels but their application is limited to simple geometries and boundary conditions, and small amplitude, translational (and rotational) inputs. To validate numerical models for seismic FSI analysis in finite element codes, a comprehensive set of experiments was performed on a liquid-filled cylindrical vessel, using a 6 degree-of-freedom earthquake simulator. Results in terms of sloshing frequency, damping ratio in sloshing modes, and hydrodynamic responses (wave height, hydrodynamic pressure, base shear, and base moment) for multi-directional earthquake simulator inputs are reported and compared with analytical solutions for liquid-filled vessels. The impact of seismic (base) isolation on hydrodynamic responses was studied using earthquake simulator inputs generated using a virtual isolation system. Data from the experiments are used to validate a numerical model of the fluid-filled vessel using the Arbitrary Lagrangian Eulerian (ALE) solver in the commercial finite element program LS-DYNA. Validation studies are presented for multi-directional seismic inputs, including rocking motions. Lagrangian modeling approaches using an elastic material formulation for the fluid are also investigated and their limitations and possible applications are identified. Here, the results are broadly applicable to the seismic response of base supported, liquid-filled vessels.

58 GEOSCIENCES↗
NASA NTRS2003

Simulation of Combustion Systems with Realistic g-jitter

In this project a transient, fully three-dimensional computer simulation code was developed to simulate the effects of realistic g-jitter on a number of combustion systems. The simulation code is capable of simulating flame spread on a solid and nonpremixed or premixed gaseous combustion in nonturbulent flow with simple combustion models. Simple combustion models were used to preserve computational efficiency since this is meant to be an engineering code. Also, the use of sophisticated turbulence models was not pursued (a simple Smagorinsky type model can be implemented if deemed appropriate) because if flow velocities are large enough for turbulence to develop in a reduced gravity combustion scenario it is unlikely that g-jitter disturbances (in NASA's reduced gravity facilities) will play an important role in the flame dynamics. Acceleration disturbances of realistic orientation, magnitude, and time dependence can be easily included in the simulation. The simulation algorithm was based on techniques used in an existing large eddy simulation code which has successfully simulated fire dynamics in complex domains. A series of simulations with measured and predicted acceleration disturbances on the International Space Station (ISS) are presented. The results of this series of simulations suggested a passive isolation system and appropriate scheduling of crew activity would provide a sufficiently "quiet" acceleration environment for spherical diffusion flames.

Mell, William E.↗
NASA NTRS2011

Broadband Via-Less Microwave Crossover Using Microstrip-CPW Transitions

The front-to-back interface between microstrip and CPW (coplanar waveguide) typically requires complex fabrication or has high radiation loss. The microwave crossover typically requires a complex fabrication step. The prior art in microstrip-CPW transition requires a physical vias connection between the microstrip and CPW line on a separate layer. The via-less version of this transition was designed empirically and does not have a close form solution. The prior art of the micro wave crossover requires either additional substrate or wire bond as an air bridge to isolate two microwave lines at the crossing junction. The disadvantages are high radiation loss, no analytical solution to the problem, lengthy simulation time, and complex fabrication procedures to generate air bridges or via. The disadvantage of the prior crossover is a complex fabrication procedure, which also affects the device reliability and yield. This microstrip-CPW transition is visualized as two microstrip-slotline transitions combined in a way that the radiation from two slotlines cancels each other out. The invention is designed based on analytical methods; thus, it significantly reduces the development time. The crossover requires no extra layer to cross two microwave signals and has low radiation loss. The invention is simple to fabricate and design. It produces low radiation loss and can be designed with low insertion loss, with some tradeoff with signal isolation. The microstrip-CPW transition is used as an interface to connect between the device and the circuit outside the package. The via-less microwave crossover is used to allow two signals to cross without using an extra layer or fabrication processing step to enable this function. This design allows the solution to be determined entirely though analytical techniques. In addition, a planar via-less microwave crossover using this technique was proposed. The experimental results show that the proposed crossover at 5 GHz has a minimum isolation of 32 dB. It also has low in-band insertion loss and return loss of 1.2 dB and 18 dB, respectively, over more than 44 percent of bandwidth at room temperature. This microstrip-CPW transition requires the microstrip line to be split into two sections. Each section is connected to a microstrip quarter-wavelength openended stub. A slotline is also placed perpendicular to the microstrip section. The slot is connected to a grounded-end quarter-wavelength slotline and generates a microstrip-slotline transition. When two of these sections are placed in parallel and with the microstrip section combined at transition, a microstrip- CPW transition is formed. The slotline radiation is suppressed as two slots are excited with the electric field in an opposite direction, which cancels the radiation in far field. The invention on the crossover consists of the invented microstrip-CPW transitions combined back-to-back and a microstrip low-pass filter. One signal is crossed through to the microstrip layer, while the other signal is crossed through the CPW line located on the ground plane of the microstrip line. The microstrip low-pass filter produces a narrow line at the crossing point to enhance the system isolation. It also produces broadband response in the operating frequency band. The microstrip-CPW transition allows a microwave signal to travel from microstrip line to CPW line with low radiation loss. The crossover allows two microwave signals to cross with minimal parasitic coupling.

Stevenson, Thomas↗
NASA NTRS2016

Qualitative Fault Isolation of Hybrid Systems: A Structural Model Decomposition-Based Approach

Quick and robust fault diagnosis is critical to ensuring safe operation of complex engineering systems. A large number of techniques are available to provide fault diagnosis in systems with continuous dynamics. However, many systems in aerospace and industrial environments are best represented as hybrid systems that consist of discrete behavioral modes, each with its own continuous dynamics. These hybrid dynamics make the on-line fault diagnosis task computationally more complex due to the large number of possible system modes and the existence of autonomous mode transitions. This paper presents a qualitative fault isolation framework for hybrid systems based on structural model decomposition. The fault isolation is performed by analyzing the qualitative information of the residual deviations. However, in hybrid systems this process becomes complex due to possible existence of observation delays, which can cause observed deviations to be inconsistent with the expected deviations for the current mode in the system. The great advantage of structural model decomposition is that (i) it allows to design residuals that respond to only a subset of the faults, and (ii) every time a mode change occurs, only a subset of the residuals will need to be reconfigured, thus reducing the complexity of the reasoning process for isolation purposes. To demonstrate and test the validity of our approach, we use an electric circuit simulation as the case study.

Hybrid Systems Diagnosis↗
NASA NTRS2010

Design and Development of a Model to Simulate 0-G Treadmill Running Using the European Space Agency's Subject Loading System

Develop a model that simulates a human running in 0 G using the European Space Agency s (ESA) Subject Loading System (SLS). The model provides ground reaction forces (GRF) based on speed and pull-down forces (PDF). DESIGN The theoretical basis for the Running Model was based on a simple spring-mass model. The dynamic properties of the spring-mass model express theoretical vertical GRF (GRFv) and shear GRF in the posterior-anterior direction (GRFsh) during running gait. ADAMs VIEW software was used to build the model, which has a pelvis, thigh segment, shank segment, and a spring foot (see Figure 1).the model s movement simulates the joint kinematics of a human running at Earth gravity with the aim of generating GRF data. DEVELOPMENT & VERIFICATION ESA provided parabolic flight data of subjects running while using the SLS, for further characterization of the model s GRF. Peak GRF data were fit to a linear regression line dependent on PDF and speed. Interpolation and extrapolation of the regression equation provided a theoretical data matrix, which is used to drive the model s motion equations. Verification of the model was conducted by running the model at 4 different speeds, with each speed accounting for 3 different PDF. The model s GRF data fell within a 1-standard-deviation boundary derived from the empirical ESA data. CONCLUSION The Running Model aids in conducting various simulations (potential scenarios include a fatigued runner or a powerful runner generating high loads at a fast cadence) to determine limitations for the T2 vibration isolation system (VIS) aboard the International Space Station. This model can predict how running with the ESA SLS affects the T2 VIS and may be used for other exercise analyses in the future.

Caldwell, E. C.↗
NASA NTRS1993

Modeling and new equipment definition for the vibration isolation box equipment system

Our MSAD-funded research project is to provide numerical modeling support for the VIBES (Vibration Isolation Box Experiment System) which is an IML2 flight experiment being built by the Japanese research team of Dr. H. Azuma of the Japanese National Aerospace Laboratory. During this reporting period, the following have been accomplished: A semi-consistent mass finite element projection algorithm for 2D and 3D Boussinesq flows has been implemented on Sun, HP And Cray Platforms. The algorithm has better phase speed accuracy than similar finite difference or lumped mass finite element algorithms, an attribute which is essential for addressing realistic g-jitter effects as well as convectively-dominated transient systems. The projection algorithm has been benchmarked against solutions generated via the commercial code FIDAP. The algorithm appears to be accurate as well as computationally efficient. Optimization and potential parallelization studies are underway. Our implementation to date has focused on execution of the basic algorithm with at most a concern for vectorization. The initial time-varying gravity Boussinesq flow simulation is being set up. The mesh is being designed and the input file is being generated. Some preliminary 'small mesh' cases will be attempted on our HP9000/735 while our request to MSAD for supercomputing resources is being addressed. The Japanese research team for VIBES was visited, the current set up and status of the physical experiment was obtained and ongoing E-Mail communication link was established.

Sani, Robert L.↗
DOE OSTI2023

Smart Droplets Stabilized by Designer Surfactants: From Biomimicry to Active Motion to Materials Healing

The science and technologies of emulsion droplets have been a long‐term focus of extensive research endeavors for their practical utility across a breadth of industries, including pharmaceutical products, oil recovery processes, and the food sciences. However, with advances in materials chemistry and characterization tools, new emerging areas are arising with a focus on “smart droplets”. The versatility of emulsion droplets across is based on their ability to partition and create isolated systems with properties defined by the liquid–liquid interface, while preparative routes allow manipulation of droplet size, stability, and encapsulated contents. As described in this article, significant efforts are being devoted to creating new types of droplets by “activating” this interface through the incorporation of reactive structures that trigger droplet response to applied or environmental stimuli (e.g., pH, temperature, salt, or external fields). Moreover, parallels between droplets and live cells inspire efforts to conceive systems that resemble biological motifs or that can produce cellular behaviors that imitate biology (e.g., swarming, communication, or motion). Here, the authors highlight recent advances in smart droplets, with emphasis on organic, polymer, and/or particle surfactants that give rise to inter‐droplet communication (via aggregation, fusion, division, or mass transfer), droplet vehicles for controlled delivery, autonomous droplet motion, and tunable emulsion inversion. Especially emphasized is the macromolecular design to produce reactive and functional surfactants, which are crucial to responsive droplet behavior and their underlying mechanisms. More generally, the exquisite interplay between materials science and biology inspires the review of this research area that provides unique opportunities for insight and inspiration into the capabilities of new droplet designs.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Impact of ionizing radiation on superconducting qubit coherence

The practical viability of any qubit technology stands on long coherence times and high-fidelity operations with the superconducting qubit modality being an auspicious example, However, superconducting qubit coherence is impacted by broken Cooper pairs referred to as quasiparticles, with a density that is empirically observed to be orders of magnitude greater than the value predicted for thermal equilibrium by the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. Previous work has shown that infrared photons significantly increase the quasiparticle density, yet even in the best isolated systems, it still remains higher than expected, suggesting that another generation mechanism exists. In this Letter, we provide evidence that ionizing radiation from environmental radioactive materials and cosmic rays contributes to this observed difference, leading to an elevated quasiparticle density that would ultimately limit superconducting qubits of the type measured here to coherence times in the millisecond regime. Additionally, we further demonstrate that introducing radiation shielding reduces the flux of ionizing radiation and positively correlates with increased coherence time. Albeit a small effect for today’s qubits, reducing or otherwise mitigating the impact of ionizing radiation will be critical for realizing fault-tolerant superconducting quantum computers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Dynamical topological phase realized in a trapped-ion quantum simulator

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated systems. Here achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work indicates that these capabilities can enable dynamical phases and critical phenomena that show topologically robust methods to create, protect and manipulate quantum entanglement that self-correct against large classes of errors. However, so far, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry-protected topological phase, in a quasiperiodically driven array of ten 171 Yb + hyperfine qubits in Quantinuum’s System Model H1 trapped-ion quantum processor. This phase shows edge qubits that are dynamically protected from control errors, cross-talk and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. Here, this property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient manipulation of quantum information.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Modeling the energetic tail of a dusty plasma's electron energy distribution and its effect on dust grain charge and behavior

A model for a weakly ionized dusty plasma is proposed in which UV or x-ray radiation continuously creates free electrons at high energy, which then cool through collisions with a cold neutral gas before recombining. The transition of a free electron from high energy at birth to low energy at demise implies that the electron energy distribution is not the simple Maxwellian of an isolated system in thermal equilibrium, but instead has a high-energy tail that depends on the recombination time. This tail can have a major effect on dust grain charging because the flux of tail electrons can be substantial even if the density of tail electrons is small. Detailed analytic and numerical calculations of dust grain charging show that situations exist in which a small high-energy tail dominates charge behavior. This implies that dust grain charge in terrestrial and space dusty plasmas may be significantly underestimated if a Maxwellian distribution is assumed and the non-thermal dynamics are neglected.

Physics↗
DOE OSTI2024

Matrix-formation dynamics dictate methyl nitrite conformer abundance

Methyl nitrite has two stable conformational isomers resulting from rotation about the primary C–O–N–O dihedral angle: cis-CH 3 ONO and trans-CH 3 ONO, with cis being more stable by ∼5 kJ/mol. Here, the barrier to rotational interconversion (∼45 kJ/mol) is too large for isomerization to occur under ambient conditions. This paper presents evidence of a change in conformer abundance when dilute CH 3 ONO is deposited onto a cold substrate; the relative population of the freshly deposited cis conformer is seen to increase compared to its gas-phase abundance, measured by in situ infrared spectroscopy. We observe abundance changes depending on the identity of the bath gas (N 2 , Ar, and Xe) and deposition angle. The observations indicate that the surface properties of the growing matrix influence conformer abundance—contrary to the widely held assumption that conformer abundance in matrices reflects gas-phase abundance. We posit that differences in the angle-dependent host-gas deposition dynamics affect the growing surfaces, causing changes in conformer abundances. Quantum chemistry calculations of the binding energies between CH 3 ONO and a single bath-gas component reveal that significant energetic stabilization is not observed in 1:1 complexes of N 2 :CH 3 ONO, Ar:CH 3 ONO, or Xe:CH 3 ONO. From our results, we conclude that the growing surface plays a significant role in trapping cis-CH 3 ONO more effectively than trans-CH 3 ONO, likely because cis-CH 3 ONO is more compact. Taken together, the observations highlight the necessity for careful characterization of conformers in matrix-isolated systems, emphasizing a need for further study into the deposition dynamics and surface structure of chemically inert matrices.

Hockey, Emily K.↗
DOE OSTI2021

Pharmacokinetics, Metabolite Measurement, and Biomarker Identification of Dermal Exposure to Permethrin Using Accelerator Mass Spectrometry

Impregnating military uniforms and outdoor clothing with the insecticide permethrin is an approach to reduce exposure to insect borne diseases and to repel pests and disease vectors such as mosquitos and sandflies, but the practice exposes wearers to prolonged dermal exposure to the pesticide. Key metabolite(s) from a low dose dermal exposure of permethrin were identified using accelerator mass spectrometry. Metabolite standards were synthesized and a high performance liquide chromatography (HPLC) elution protocol to separate individual metabolites in urine was developed. Six human subjects were exposed dermally on the forearm to 25 mg of permethrin containing 1.0 µCi of 14 C for 8 h. Blood, saliva and urine samples were taken for 7d. Absorption/elimination rates and metabolite concentrations varied by individual. Average absorption was 0.2% of the dose. Serum concentrations rose until 12–24 h postdermal application then rapidly declined reaching predose levels by 72 h. Maximum saliva excretion occurred 6 h postdosing. The maximum urinary excretion rate occurred during 12–24 h; average elimination half-life was 56 h. 3-Phenoxybenzyl alcohol glucuronide was the most abundant metabolite identified when analyzing elution fractions, but most of the radioactivity was in still more polar fractions suggesting extensive degradative metabolism and for which there were no standards. Finally, analyses of archived urine samples with the ultra performance liquid chromatography-accelerator mass spectrometry-mass spectrometry (UPLC-AMS-MS) system isolated a distinct polar metabolite but it was much diminished from the previous analyses a decade earlier.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Majorana Edge Modes in Isolated Wires

Topological superconductors are believed to host exotic quasiparticle excitations known as Majorana zero modes (MZMs), with much of the evidence based on BCS mean-field theory. The direct application of mean-field arguments is tenuous in finite, isolated systems relevant in some experiments. Here, we develop a new correlation-based method for identifying MZMs in interacting, number-conserving systems. Using the density matrix renormalization group, we study fermion number-conserving models with long-range interactions, which under periodic boundary conditions exhibit robust topological and nontopological superconductivity, tuned by the strength of interaction [Ortiz et al., Phys. Rev. Lett. 113, 267002 (2014)]. We find evidence that, on the topological side, Majorana edge modes appear in open chains, manifesting as the vanishing of the energy splitting between odd- and even-parity ground states with increasing system size. Additionally, off-diagonal two-point correlation functions show nonlocal, parity-dependent edge effects. These correlations reveal the spatial structure of Majorana modes in the many-body wave function. We show that the correlation diagnostic applies broadly, including to short-range interacting models, where topological superconductivity is more fragile due to the absence of a bulk excitation gap.

Thomas-Markarian, Jaden↗
DOE OSTI2025

Generic Hilbert space fragmentation in Kogut-Susskind lattice gauge theories

At the heart of quantum many-body physics lies the understanding of mechanisms that avoid quantum thermalization in an isolated system quenched far from equilibrium. A prominent example is Hilbert space fragmentation, which has recently emerged as an ergodicity-breaking mechanism in constrained spin models. Here, we show that Kogut-Susskind formulations of lattice gauge theories in d+1D (d spatial and one temporal dimensions) give rise to Hilbert space fragmentation, and discuss possible implications for understanding continuum physics. Lastly, our findings not only prove that lattice gauge theories are a natural platform for Hilbert space fragmentation, they also serve as a guide to the conditions under which these models can be faithfully used to infer the thermalization properties of quantum chromodynamics.

Eigenstate thermalization↗
DOE OSTI2021

Gauging anomalous unitary operators

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, here we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as C and CP, for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗