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At least 217 records · Page 12

Mass variation of a thin liquid film driven by an acoustic wave

In this work, we investigate the dynamics of a thin liquid film subjected to an acoustic field in its bounding vapor space. For large acoustic wavelengths, the field imposes a spatially uniform, temporally periodic temperature and pressure at the vapor side of the film interface, which leads to a periodic driving force for mass exchange with the vapor. Neglecting the dynamics of the vapor space, we adopt the “one-sided” model for evaporation/condensation of thin liquid films. In the interest of determining the effect of oscillatory mass exchange on film stability, we consider films in thermodynamic equilibrium with the mean vapor conditions. The effects of oscillatory phase change on both linear stability and nonlinear dynamics are investigated for slightly inclined ceiling films that are destabilized by gravity and subject to thermocapillary effects. At linear order, this mass exchange is not found to alter the band of unstable wave numbers and only marginally affects the growth rates. Additionally, the mass exchanged during evaporation is balanced by condensation so that the total mass of the liquid film is conserved. However, due to nonlinear effects, we find that traveling waves encouraged by the inclination are subject to net mass loss. It is then found that normal thermocapillary effects enhance this loss, and that anomalous thermocapillarity mitigates or even reverses the loss to a mass gain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Framework to predict optimal buffer layer pairing for thin film solar cell absorbers: A case study for tin sulfide/zinc oxysulfide

An outstanding challenge in the development of novel functional materials for optoelectronic devices is identifying suitable charge-carrier contact layers. Herein, we simulate the photovoltaic device performance of various n-type contact material pairings with tin(II) sulfide (SnS), a p-type absorber. The performance of the contacting material, and resulting device efficiency, depend most strongly on two variables: conduction band offset between absorber and contact layer, and doping concentration within the contact layer. By generating a 2D contour plot of device efficiency as a function of these two variables, we create a performance-space plot for contacting layers on a given absorber material. For a simulated high-lifetime SnS absorber, this 2D performance-space illustrates two maxima, one local and one global. The local maximum occurs over a wide range of contact-layer doping concentrations (below 10{sup 16 }cm{sup −3}), but only a narrow range of conduction band offsets (0 to −0.1 eV), and is highly sensitive to interface recombination. This first maximum is ideal for early-stage absorber research because it is more robust to low bulk-minority-carrier lifetime and pinholes (shunts), enabling device efficiencies approaching half the Shockley-Queisser limit, greater than 16%. The global maximum is achieved with contact-layer doping concentrations greater than 10{sup 18 }cm{sup −3}, but for a wider range of band offsets (−0.1 to 0.2 eV), and is insensitive to interface recombination. This second maximum is ideal for high-quality films because it is more robust to interface recombination, enabling device efficiencies approaching the Shockley-Queisser limit, greater than 20%. Band offset measurements using X-ray photoelectron spectroscopy and carrier concentration approximated from resistivity measurements are used to characterize the zinc oxysulfide contacting layers in recent record-efficiency SnS devices. Simulations representative of these present-day devices suggest that record efficiency SnS devices are optimized for the second local maximum, due to low absorber lifetime and relatively well passivated interfaces. By employing contact layers with higher carrier concentrations and lower electron affinities, a higher efficiency ceiling can be enabled.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Review of selective laser melting: Materials and applications

Selective Laser Melting (SLM) is a particular rapid prototyping, 3D printing, or Additive Manufacturing (AM) technique designed to use high power-density laser to melt and fuse metallic powders. A component is built by selectively melting and fusing powders within and between layers. The SLM technique is also commonly known as direct selective laser sintering, LaserCusing, and direct metal laser sintering, and this technique has been proven to produce near net-shape parts up to 99.9% relative density. This enables the process to build near full density functional parts and has viable economic benefits. Recent developments of fibre optics and high-power laser have also enabled SLM to process different metallic materials, such as copper, aluminium, and tungsten. Similarly, this has also opened up research opportunities in SLM of ceramic and composite materials. The review presents the SLM process and some of the common physical phenomena associated with this AM technology. It then focuses on the following areas: (a) applications of SLM materials and (b) mechanical properties of SLM parts achieved in research publications. The review is not meant to put a ceiling on the capabilities of the SLM process but to enable readers to have an overview on the material properties achieved by the SLM process so far. Trends in research of SLM are also elaborated in the last section.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Experimental room temperature hohlraum performance study on the National Ignition Facility [Experimental evidence for improved performance in room temperature hohlraums on the National Ignition Facility]

Room temperature or “warm” (273 K) indirect drive hohlraum experiments have been conducted on the National Ignition Facility with laser energies up to 1.26 MJ and compared to similar cryogenic or “cryo” (~20 K) experiments. Warm experiments use neopentane (C 5 H 12 ) as the low pressure hohlraum fill gas instead of helium, and propane (C 3 H 8 ) to replace the cryogenic DT or DHe3 capsule fill. The increased average Z of the hohlraum fill leads to increased inverse bremsstrahlung absorption and an overall hotter hohlraum plasma in simulations. The cross beam energy transfer (CBET) from outer laser beams (pointed toward the laser entrance hole) to inner beams (pointed at the equator) was inferred indirectly from measurements of Stimulated Raman Scattering (SRS). These experiments show that a similar hot spot self-emission shape can be produced with less CBET in warm hohlraums. The measured inner cone SRS reflectivity (as a fraction of incident power neglecting CBET) is ~2.5× less in warm than cryo shots with similar hot spot shapes, due to a less need for CBET. The measured outer-beam stimulated the Brillouin scattering power that was higher in the warm shots, leading to a ceiling on power to avoid the optics damage. These measurements also show that the CBET induced by the flow where the beams cross can be effectively mitigated by a 1.5 Å wavelength shift between the inner and outer beams. A smaller scale direct comparison indicates that warm shots give a more prolate implosion than cryo shots with the same wavelength shift and pulse shape. Lastly, the peak radiation temperature was found to be between 5 and 7 eV higher in the warm than the corresponding cryo experiments after accounting for differences in backscatter.

42 ENGINEERING↗

The fluorescence quantum yield parameter in Förster resonance energy transfer (FRET)—Meaning, misperception, and molecular design

The fluorescence quantum yield parameter in Förster resonance energy transfer (FRET) processes underpins vital phenomena ranging from light harvesting in photosynthesis to design of sensors for monitoring physiological processes. The criteria for choosing a donor for use in FRET processes include chemical features (solubility, bioconjugatability, synthetic accessibility, and stability) as well as photophysical properties pertaining to absorption (wavelength and molar absorption coefficient) and fluorescence (wavelength and fluorescence quantum yield). The value of the donor fluorescence quantum yield (Φf, or emphatically, Φf(D)) alone has sometimes been thought (erroneously) to place a ceiling on the possible quantum yield of energy transfer (Φtrans). A high value of the donor Φf, while attractive, is not at all essential; indeed, many valuable candidates for use as FRET donors have likely been excluded on the basis of this injudiciously applied filter. Such disregard is unwarranted. In this tutorial overview, the equations for FRET are reviewed along with pertinent core concepts in photophysics. An analogy using simple hydraulics provides a pedagogical tool for the non-aficionado to better understand photochemical kinetics. Ten examples are presented of donor–acceptor systems with donors that exhibit a range of Φf values (0.60, 0.59. 0.21, 0.17, 0.12, 0.118, 0.04, 0.018, 0.007, and 0.003; i.e., 60%–0.3%), yet for each corresponding donor–acceptor pair, the value of Φtrans is at least 0.70 and in some cases nearly 1.00 (i.e., 70%–100%). The systems encompass protein, synthetic inorganic, and synthetic organic architectures. The objectives of this illustrative review are to deepen understanding of FRET and to broaden molecular design considerations by enabling selection from among a far richer set of donors for use in FRET processes.

Lindsey, Jonathan S. (ORCID:0000000248722040)↗

Challenges and transformative opportunities in superconductor vortex physics

In superconductors, the motion of vortices introduces unwanted dissipation that is disruptive to applications. Fortunately, material defects can immobilize vortices, acting as vortex pinning centers, which engenders dramatic improvements in superconductor material properties and device operation. This has motivated decades of research into developing methods of tailoring the disorder landscape in superconductors to increase the strength of vortex pinning. Yet, efficacious materials engineering still eludes us. The electromagnetic properties of real (disordered) superconducting materials cannot yet be reliably predicted, such that designing superconductors for applications remains a largely inefficient process of trial and error. This is ultimately due to large gaps in our knowledge of vortex dynamics: the field is challenged by the extremely complex interplay between vortex elasticity, vortex-vortex interactions, and material disorder. Here, we review obstacles and recent successes in understanding and controlling vortex dynamics in superconducting materials and devices. We further identify major open questions and discuss opportunities for transformative research in the field. This includes improving our understanding of vortex creep, determining and reaching the ceiling for the critical current, advanced microscopy to garner accurate structure-property relationships, frontiers in predictive simulations and the benefits of artificial intelligence, as well as controlling and exploiting vortices in quantum information applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Crystal structure of human mitochondrial trifunctional protein, a fatty acid β-oxidation metabolon

Membrane-bound mitochondrial trifunctional protein (TFP) catalyzes β-oxidation of long chain fatty acyl-CoAs, employing 2-enoyl-CoA hydratase (ECH), 3-hydroxyl-CoA dehydrogenase (HAD), and 3-ketothiolase (KT) activities consecutively. Inherited deficiency of TFP is a recessive genetic disease, manifesting in hypoketotic hypoglycemia, cardiomyopathy, and sudden death. In this work we have determined the crystal structure of human TFP at 3.6-Å resolution. The biological unit of the protein is α 2 β 2 . The overall structure of the heterotetramer is the same as that observed by cryo-EM methods. The two β-subunits make a tightly bound homodimer at the center, and two α-subunits are bound to each side of the β 2 dimer, creating an arc, which binds on its concave side to the mitochondrial innermembrane. The catalytic residues in all three active sites are arranged similarly to those of the corresponding, soluble monofunctional enzymes. A structure-based, substrate channeling pathway from the ECH active site to the HAD and KT sites is proposed. The passage from the ECH site to the HAD site is similar to those found in the two bacterial TFPs. However, the passage from the HAD site to the KT site is unique in that the acyl-CoA intermediate can be transferred between the two sites by passing along the mitochondrial inner membrane using the hydrophobic nature of the acyl chain. The 3'-AMP-PPi moiety is guided by the positively charged residues located along the “ceiling” of the channel, suggesting that membrane integrity is an essential part of the channel and is required for the activity of the enzyme.

59 BASIC BIOLOGICAL SCIENCES↗

A New 1D Model for Thermal Mixing and Stratification in Advanced Reactor Transients

Thermal mixing and stratification in large pools and enclosures play a critical role in the safety and performance of pool-type nuclear reactors, particularly during transient scenarios involving significant temperature differences between incoming and bulk coolant. Accurate modeling of these phenomena is essential for predicting system behavior and supporting passive safety features such as natural circulation. Here, this paper presents a new 1D model for thermal mixing and stratification, developed and implemented in the SAM code. The model represents a large pool as 1D coolant jet channels and zero-dimensional bulk pool volumes, enabling the simulation of a wide range of flow configurations, including hot and cold jet interactions, stratified layers, and the influence of complex geometries such as ceilings, free surfaces, and internal obstacles. Heat exchange between jet and pool regions is governed by closure relations calibrated against 3D computational fluid dynamics (CFD) simulations. The model improves upon earlier approaches by incorporating time-dependent jet characteristics and capturing the associated delay effects more accurately. Code-to-code comparisons and validation against experimental data from the Thermal Stratification Test Facility demonstrate the model’s accuracy and flexibility. This work offers two key contributions: (1) an efficient and robust method for simulating thermal mixing and stratification at the system level, eliminating the need for external coupling between system analysis codes and CFD, and (2) a significant enhancement of SAM’s capabilities to analyze thermal stratification phenomena in advanced reactor systems.

SAM↗

Design and Implementation of Surface Eroding Thermocouples for Stage-One Modular Divertor Integration at the DIII-D Tokamak

The DIII-D has upgraded its upper divertor to a modular system using copper alloy pedestals to alter the divertor geometry without changing the vessel structure. Six new graphite tiles were designed for the shape and volume rise (SVR) divertor. Here, these new SVR tiles facilitated the formation of a poloidal array of 27 surface eroding thermocouples (SETCs) in the upper divertor region. At one location, a specialized recessed SETC, paired with a standard flush SETC, was installed in one of the ceiling tiles to provide comprehensive heat flux measurements, distinguishing between charged and noncharged particle contributions. Upgrades were made to the SETC system in the small-angle slot (SAS) divertor to improve overall performance. These upgrades included optimizing the feedthrough system to double the thermocouple cable capacity and reallocating cables from the SAS area to the SVR divertor. A compact isolation amplifier system with a fixed gain of 41 was employed to improve the signal level and minimize interference. Additionally, two analog-to-analog fiber systems were implemented for transmitting thermocouple signals over a single fiber, significantly reducing both noise levels and costs. The newly installed SETCs in the SVR divertor successfully completed initial commissioning testing. The SETCs captured the in-out asymmetry in the power distribution between the inner and outer strike points and demonstrated the dependency of the heat flux profile on the outer strike point location. During divertor detachment, heat flux mitigation was noted at the outer strike point location, while significant heat flux contributions from neutral particles were measured in the SVR divertor.

Divertor↗

A CONSTANT LIMITING MASS SCALE FOR FLAT EARLY-TYPE GALAXIES FROM z {approx} 1 TO z = 0: DENSITY EVOLVES BUT SHAPES DO NOT

We measure the evolution in the intrinsic shape distribution of early-type galaxies from z {approx} 1 to z {approx} 0 by analyzing their projected axis-ratio distributions. We extract a low-redshift sample (0.04 < z < 0.08) of early-type galaxies with very low star formation rates from the Sloan Digital Sky Survey, based on a color-color selection scheme and verified through the absence of emission lines in the spectra. The inferred intrinsic shape distribution of these early-type galaxies is strongly mass dependent: the typical short-to-long intrinsic axis ratio of high-mass early-type galaxies (>10{sup 11} M{sub Sun }) is 2:3, whereas at masses below 10{sup 11} M{sub Sun} this ratio narrows to 1:3, or more flattened galaxies. In an entirely analogous manner, we select a high-redshift sample (0.6 < z < 0.8) from two deep-field surveys with multi-wavelength and Hubble Space Telescope/Advanced Camera for Surveys imaging: GEMS and COSMOS. We find a seemingly universal mass of {approx}10{sup 11} M{sub Sun} for highly flattened early-type systems at all redshifts. This implies that the process that grows an early-type galaxy above this ceiling mass, irrespective of cosmic epoch, involves forming round systems. Using both parametric and non-parametric tests, we find no evolution in the projected axis-ratio distribution for galaxies with masses >3 Multiplication-Sign 10{sup 10} M{sub Sun} with redshift. At the same time, our samples imply an increase of 2-3 Multiplication-Sign in comoving number density for early-type galaxies at masses >3 Multiplication-Sign 10{sup 10} M{sub Sun }, in agreement with previous studies. Given the direct connection between the axis-ratio distribution and the underlying bulge-to-disk ratio distribution, our findings imply that the number density evolution of early-type galaxies is not exclusively driven by the emergence of either bulge- or disk-dominated galaxies, but rather by a balanced mix that depends only on the stellar mass of the galaxy. The challenge for galaxy formation models is to reproduce this overall non-evolving ratio of flattened to round early-type galaxies in the context of a continually growing population.

79 ASTRONOMY AND ASTROPHYSICS↗

The magnetohydrodynamical model of kilohertz quasi-periodic oscillations in neutron star low-mass X-ray binaries (II)

We study the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low-mass X-ray binaries (LMXBs) with a new magnetohydrodynamics (MHD) model, in which the compressed magnetosphere is considered. The previous MHD model is reexamined and the relation between the frequencies of the kHz QPOs and the accretion rate in LMXBs is obtained. Our result agrees with the observations of six sources (4U 0614+09, 4U 1636-53, 4U 1608-52, 4U 1915-15, 4U 1728-34, and XTE 1807-294) with measured spins. In this model, the kHz QPOs originate from the MHD waves in the compressed magnetosphere. The single kHz QPOs and twin kHz QPOs are produced in two different parts of the accretion disk and the boundary is close to the corotation radius. The lower QPO frequency in a frequency-accretion rate diagram is cut off at a low accretion rate and the twin kHz QPOs encounter a top ceiling at a high accretion rate due to the restriction of the innermost stable circular orbit.

79 ASTRONOMY AND ASTROPHYSICS↗

Impact of β n and spectrum of n = 1 applied fields on fast ion losses in DIII-D

Abstract The effect of n = 1 magnetic perturbations (MPs) on prompt fast ion losses in DIII-D has been investigated using the light ion beam probe technique. The effect of normalized beta, β n , and the plasma response to the MPs is studied for several MP spectra. Magnetics data show a strong dependence of plasma response to β n that depends on the phase difference in perturbation coils, Δ ϕ U L . For most phases, the response increases with β n , however, the response is suppressed for phases between 180 ∘ and 240 ∘ . Experimental data from scintillator based fast ion loss detectors shows that relative fluctuation of lost ions (20%–30% of the steady signal) does not diminish across the L- to H-mode transition for Δ ϕ U L = 240 ∘ , despite the 34% decrease in radial response field and 50% decrease in poloidal response field. Simulations of the DIII-D discharges using M3D-C1 and ASCOT5 find that prompt losses from neutral beam injection in each investigated case hit the first wall at several concentrated locations: the vessel floor, midplane diagnostic ports, vessel ceiling, and inner wall. Simulated losses from co-injection neutral beams are born outside the last closed flux surface, corresponding to radial orbit displacements of 3–6 cm due to the MPs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Implementation and optimization of the PTOLEMY transverse drift electromagnetic filter

The PTOLEMY transverse drift filter is a new concept to enable precision analysis of the energy spectrum of electrons near the tritium β-decay endpoint. Here, we detail the implementation and optimization methods for successful operation of the filter for electrons with a known pitch angle. We present the first demonstrator that produces the required magnetic field properties with an iron return-flux magnet. Two methods for the setting of filter electrode voltages are detailed. The challenges of low-energy electron transport in cases of low field are discussed, such as the growth of the cyclotron radius with decreasing magnetic field, which puts a ceiling on filter performance relative to fixed filter dimensions. Additionally, low pitch angle trajectories are dominated by motion parallel to the magnetic field lines and introduce non-adiabatic conditions and curvature drift. To minimize these effects and maximize electron acceptance into the filter, we present a three-potential-well design to simultaneously drain the parallel and transverse kinetic energies throughout the length of the filter. These optimizations are shown, in simulation, to achieve low-energy electron transport from a 1 T iron core (or 3 T superconducting) starting field with initial kinetic energy of 18.6 keV drained to < 10 eV (< 1 eV) in about 80 cm. This result for low field operation paves the way for the first demonstrator of the PTOLEMY spectrometer for measurement of electrons near the tritium endpoint to be constructed at the Gran Sasso National Laboratory (LNGS) in Italy.

47 OTHER INSTRUMENTATION↗

Quasi-static magnetic compression of field-reversed configuration plasma: amended scalings and limits from two-dimensional MHD equilibrium

In this work, several key scaling laws of the quasi-static magnetic compression of field reversed configuration (FRC) plasma (Spencer et al 1983 Phys. Fluids 26 1564) are amended from a series of two-dimensional FRC MHD equilibriums numerically obtained using the Grad–Shafranov equation solver NIMEQ. Based on the new scaling for the elongation and the magnetic fields at the separatrix and the wall, the empirically stable limits for the compression ratio, the fusion gain, and the neutron yield are evaluated, which may serve as a more accurate estimate for the upper ceiling of performance from the magnetic compression of FRC plasma as a potential fusion energy as well as neutron source devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Model BOSS and eBOSS luminous red galaxies at 0.2< z<1.0 using SubHalo Abundance Matching with three parameters

SubHalo Abundance Matching (SHAM) is an empirical method for constructing galaxy catalogues based on high-resolution N-body simulations. Here, we apply SHAM on the UNIT simulation to simulate SDSS BOSS/eBOSS luminous red galaxies (LRGs) within a wide redshift range of 0.2 < $z$ < 1.0. Besides the typical SHAM scatter parameter σ, we include $v$ smear and V ceil to take into account the redshift uncertainty and the galaxy incompleteness, respectively. These two additional parameters are critical for reproducing the observed 2PCF multipoles on 5–25$\, h^{-1}\, {\rm Mpc}$. The redshift uncertainties obtained from the best-fitting $v$ smear agree with those measured from repeat observations for all SDSS LRGs except for the LOWZ sample. We explore several potential systematics but none of them can explain the discrepancy found in LOWZ. Our explanation is that the LOWZ galaxies might contain another type of galaxies that needs to be treated differently. The evolution of the measured σ and Vceil also reveals that the incompleteness of eBOSS galaxies decreases with the redshift. This is the consequence of the magnitude lower limit applied in eBOSS LRG target selection. Our SHAM also set upper limits for the intrinsic scatter of the galaxy–halo relation, given a complete galaxy sample: σ int < 0.31 for LOWZ at 0.2 < $z$ < 0.33, σ int < 0.36 for LOWZ at 0.33 < $z$ < 0.43, and σ int < 0.46 for CMASS at 0.43 < $z$ < 0.51. The projected 2PCFs of our SHAM galaxies also agree with the observational ones on the 2PCF fitting range.

79 ASTRONOMY AND ASTROPHYSICS↗

Setup and Characterization of a 137 CS Dosimetry Calibration Source in a Space-constrained Environment

Proper characterization of 137 Cs sources used for dosimeter calibration and performance testing is crucial for accurate and precise knowledge of air kerma rate and delivered dose. A 269 GBq 137 Cs source was relocated to a new facility, which had a footprint of approximately 2.8 m × 3.6 m and a 3.4 m high ceiling. A small room size, such as in the new facility, may significantly increase backscatter from the walls or room return. Due to the limited source strength, a relatively close irradiation position of 1.00 m from the source was selected to decrease required exposure times. Proximity to the small but cylindrical source has the potential to alter the 1/r 2 relationship (inverse square law) of air kerma rate with distance associated with point sources. Practical tutorials concerning dosimetry irradiation facilities are largely absent from the archival literature. For those reasons, standard characterization experiments were repeated multiple times, great care was taken with positioning, several experiments were added to the standard ones, an ion chamber and dosimeters were used rather than film for greater accuracy and precision, and practical details of the process were recorded. The impacts of room size and finite source dimensions were quantified and mitigated by the efforts reported here. Finally, recommendations for simple but thorough facility characterization, beam calibration, and quality control resulted.

42 ENGINEERING↗

Intercomparison of Commercially Available Active Radon Measurement Devices in a Discovered Radon Chamber

An unventilated 70 m 3 underground space, with 2.1 m high ceilings and an inner set of concrete walls to damp vibrations, was discovered to have relatively stable radon levels of ~1,080 Bq m -3 over a 1-y period. The addition of radium sources was not required to achieve high and somewhat variable radon levels, as these arise naturally in the space. Several active radon monitoring devices designed for homeowners, radon screeners, radon mitigation professionals, and researchers were tested in the space. These devices were variable in both cost and intended user sophistication. Data were collected at specific time intervals that varied for each device. A cellphone was deployed with an available camera application to periodically capture photographs of the displays of devices not enabled for automatic temporal recording. Attempts were made to alter the radon concentration using fans, radium-laden objects, and radon impermeable sheets. Statistical methods were employed to compare the device's performance under the minor radon transients produced by the addition of 226 Ra sources during the test period. The evaluation of the overall accuracy, noise, and response to transients revealed highly affordable devices that may be useful for future research applications.While unsuitable for precise calibrations at stable radon levels, the space was determined to be adequate as a radon chamber for general research purposes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Geometric pumping and dephasing at topological phase transition

A measure-preserving formalism (MPF) is constructed and applied to spin/band models, which yield observations about pumping. It occurs at the topological phase transition, i.e., a Z 2 flip, suggesting that Z 2 can imply bulk effects. The model's asymptotic behavior is analytically solved via MPF. The pumping probability is geometric, fractional, and has a ceiling of $\frac{1}{2}$. Intriguingly, theorems are proved about occurrence conditions, which are linked to the system's dimension and the distinction between rational and irrational numbers. Finally, experimental detection is discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗