Singularity Structure Research Articles

Nc -insensitivity of QCD2A

The spectrum of two-dimensional adjoint QCD is surprisingly insensitive to the number of colors Nc of its gauge group. It is argued that the cancellation of finite Nc terms is rather natural and ultimately a consequence of the singularity structure of the theory. In short, there are no finite Nc terms, hence effectively there cannot be any finite Nc singular terms, since the former are necessary to guarantee well-behaved principal value integrals. We evaluate and categorize the matrix elements of the theory’s light-cone Hamiltonian to show how terms emerging from finite Nc contributions to the anticommutator cancel against contributions from the purely finite Nc term of the Hamiltonian. The cancellation is not complete; finite terms survive and modify the spectrum, as is known from numerical work. Additionally we show that several parton-number changing finite Nc matrix elements vanish independently of finiteness requirements. In particular, there is only one trace-diagonal finite Nc correction. It seems therefore that considering matrix elements rather than individual contributions can provide substantial simplifications when computing the spectrum of a theory with a large symmetry group. Published by the American Physical Society 2024

Conformal structure of singularities in some varying fundamental constants bimetric cosmologies

In this paper, we explore the conformal structure of singularities arising from varying fundamental constants using the method of Penrose diagrams. We employ a specific type of bimetric model featuring two different metrics. One metric describes the causal structure for matter, while the other characterizes the causal structure for gravitational interactions, which is related to variations in fundamental constants such as the gravitational constant and the speed of light. For this reason, we focused on the gravitational metric to calculate the conformal transformation and compose Penrose diagrams for the singularities arising from the varying fundamental constants. We have shown that, in one case, the parameter such as the scale factor, the density and the pressure resemble those of the finite scale factor singularity (FSF). Despite singularity appears in constant conformal time in our case and in the case of FSF the Misner-Sharp horizon looks different. Our another case is similar to sudden future singularity (SFS), but there are differences in the conformal structures. We have also shown that in our cases the behavior of Misner-Sharp horizon strongly depends on initial conditions. The last analytical solution which we introduced is identical to conformal structure of the standard exotic singularity for the matter.

Dimension two holomorphic distributions on four-dimensional projective space

We study two-dimensional holomorphic distributions on P4. We classify dimension two distributions, of degree at most 2, with either locally free tangent sheaf or locally free conormal sheaf and whose singular scheme has pure dimension one. We show that the corresponding sheaves are split. Next, we investigate the geometry of such distributions, studying from maximally non–integrable to integrable distributions. In the maximally non–integrable case, we show that the distribution is either of Lorentzian type or a push-forward by a rational map of the Cartan prolongation of a singular contact structure on a weighted projective 3-fold. We study distributions of dimension two in P4 whose conormal sheaves are the Horrocks–Mumford sheaves, describing the numerical invariants of their singular schemes which are smooth and connected. Such distributions are maximally non–integrable, uniquely determined by their singular schemes and invariant by a group H5⋊SL(2,Z5)⊂Sp(4,Q), where H5 is the Heisenberg group of level 5. We prove that the moduli spaces of Horrocks–Mumford distributions are irreducible quasi-projective varieties and we determine their dimensions. Finally, we observe that the space of codimension one distributions, of degree d≥6, on P4 has a family of degenerate flat holomorphic Riemannian metrics. Moreover, the degeneracy divisors of such metrics consist of codimension one distributions invariant by H5⋊SL(2,Z5) and singular along a degenerate abelian surface with (1,5)-polarization and level-5-structure.

Emergence of defects-mediated diluted ferromagnetic semiconductor (ZnS: La3+) Quantum Dots: A versatile platform for optoelectronic and spintronic applications

For the first time, La3+ ions incorporated into semiconductor Zinc Sulfide-Quantum Dots (ZnS-QDs), Zn1-xLaxS, were effectively produced via a straightforward co-precipitation approach, with diverse La ratios (0.00 ≤ x ≤ 0.15 at%). The phase analysis of the acquired QDs, conducted through Raman analysis and X-ray diffractometer (XRD), revealed a singular cubic ZnS structure, devoid of any impurities. Morphology studies by HR-TEM showed a nearly spherical particle with a size of approximately 6.4 nm. X-ray photoelectron spectroscope (XPS) investigation disclosed the significant presence of sulfur vacancies, along with the existence of the trivalent oxidation state of lanthanum (La3+) within the ZnS structure. Optical absorbance studies exhibited that all QDs were positioned approximately at the absorption edges of around 270 nm (4.59 eV), surpassing the bulk ZnS energy gap of 337 nm (3.67 eV), harmonically with the quantum confinement effect. Additionally, a pronounced band gap narrowing was observed with increasing the doping level of La ions, on account of the presence of defects that result in the creation of localized states inside the ZnS band structure. The optical results indicated the capability to fine-tune the optical energy gap, dispersion parameters, and enhance the nonlinear optical parameters, which makes these QDs well-suited for use in optoelectronic devices. Furthermore, the photoluminescence (PL) spectra indicated that the La3+-doped ZnS nanocrystals (NCs) exhibited a wide visible emission band (blue emission) at room temperature, influenced by the La-doping concentration. Besides, the La3+-doped ZnS QDs elucidated ferromagnetic behavior at room temperature, which may be accredited to the vacancy-assisted bound magnetic polaron model. Exploring the intriguing magnetic features of ZnS: La3+ QDs could open avenues for developing innovative spintronic devices.

Ketone-based conjugated microporous poly(aniline)s for the ultradeep separation of heavy metal ions

The heavy-metal contamination of aquatic environments presents imminent threat. Herein, we report a class of dual-heteroatomic conjugated microporous poly(aniline)s showing high-affinity separation performance toward heavy metals. The prepared keto-CMPA shows monolayer adsorption capacity for Hg (II) as high as 980 mg g−1 according to the Langmuir model, and ultra-rapid kinetic with h reaching 30.41 mg g−1 that could be described by the pseudo-second-order model. It maintains excellent stability across six reuses under harsh conditions, and furthermore demonstrates ultradeep separation efficiency that could adsorb almost all of heavy metals to ppb level with low usage. For further industrialization, a competent adsorption device was developed to remove heavy metals down to 1 ppb with a remarkable breakthrough over 20,000 BV. Characterizations and DFT calculation showed that the triangular synergistic region formed by the N-O-sites in the singular CMPA structure provided a feasible binding energy to enable the above impressive performance.

Psychometric Properties of the Revised Version of the Prolonged Grief Disorder Scale (PG-13-R): A Methodological Study in the Iranian Population.

Prolonged grief disorder has recently been officially introduced as a new mental disorder. This study aimed to validate the Persian version of the revised Prolonged Grief Scale (PG-13-R). This study was conducted among the general population in Shahroud, Iran, during 2023. Employing face and content validity, along with exploratory and confirmatory factor analyses (EFA), the study validates the PG-13-R. Average variance extracted value showed an acceptable convergent validity. The EFA reveals a singular factor structure explaining 60.541% of the variance in prolonged grief disorder, and the confirmatory factor analysis demonstrates an excellent model fit. Internal consistency, evaluated through Cronbach's alpha and MacDonald's omega, highlights the scale's reliability. The Persian version of PG-13-R had acceptable composite reliability. Stability is confirmed by an intra-class correlation coefficient. In conclusion, the Persian PG-13-R displays satisfactory validity and reliability to assessing prolonged grief symptoms in the Iranian population.

How viscous bubbles collapse: Topological and symmetry-breaking instabilities in curvature-driven hydrodynamics

The duality between deformations of elastic bodies and noninertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly curved liquid film is suddenly forced out of mechanical equilibrium, as occurs, e.g., when the pressure inside a liquid bubble drops rapidly due to rupture or controlled evacuation. In such cases, the film may evolve through a noninertial yet geometrically nonlinear surface dynamics, which has remained largely unexplored. We reveal the driver of such dynamics as temporal variations in the curvature of the evolving surface. Focusing on the prototypical example of a floating bubble that undergoes rapid depressurization, we show that the bubble surface evolves via a topological instability and a subsequent front propagation, whereby a small planar zone that includes a singular flow structure, analogous to a disclination in elastic systems, nucleates spontaneously and expands in the spherically shaped film. This flow pattern brings about hoop compression and triggers another, symmetry-breaking instability to the formation of radial wrinkles that invade the flattening film. Our analysis reveals the dynamics as a nonequilibrium branch of "jellium" physics, whereby a rate-of-change of surface curvature in a viscous film is akin to charge in an electrostatic medium that comprises polarizable and conducting domains. We explain key features underlying recent experiments and highlight a qualitative inconsistency between the prediction of linear stability analysis and the observed "wavelength" of surface wrinkles.

Equatorial blowup and polar caps in drop electrohydrodynamics

We illuminate effects of surface-charge convection intrinsic to leaky-dielectric electrohydrodynamics by analyzing the symmetric steady state of a circular drop in an external field at arbitrary electric Reynolds number ReE. In formulating the problem, we identify an exact factorization that reduces the number of dimensionless parameters from four—ReE and the conductivity, permittivity and viscosity ratios—to two: a modified electric Reynolds number Rẽ and a charging parameter ϖ. In the case ϖ<0, where charge relaxation in the drop phase is slower than in the suspending phase, and, as a consequence, the interface polarizes antiparallel to the external field, we find that above a critical Rẽ value the solution exhibits a blowup singularity such that the surface-charge density diverges antisymmetrically with the −1/3 power of distance from the equator. We use local analysis to uncover the structure of that blowup singularity, wherein surface charges are convected by a locally induced flow towards the equator where they annihilate. To study the blowup regime, we devise a numerical scheme encoding that local structure where the blowup prefactor is determined by a global charging-annihilation balance. We also employ asymptotic analysis to construct a universal problem governing the blowup solutions in the regime Rẽ≫1, far beyond the blowup threshold. In the case ϖ>0, where charge relaxation is faster in the drop phase and the interface polarizes parallel to the external field, we numerically observe and asymptotically characterize the formation at large Rẽ of stagnant, perfectly conducting surface-charge caps about the drop poles. The cap size grows and the cap voltage decreases monotonically with increasing conductivity or decreasing permittivity of the drop phase relative to the suspending phase. The flow in this scenario is nonlinearly driven by electrical shear stresses at the complement of the caps. In both polarization scenarios, the flow at large Rẽ scales linearly with the magnitude of the external field, contrasting the familiar quadratic scaling under weak fields. Published by the American Physical Society 2024

Synergistic signal−amplification effect of silver nanowires and bifunctional monomers on molecularly imprinted electrochemical sensor for diuron analysis

Molecularly imprinted polymers (MIP) have been widely owing to their specificity, however, their singular structure imposes limitations on their performance. Current enhancement methods, such as doping with inorganic nanomaterials or introducing various functional monomers, are limited and single, indicating that MIP performances require further advancement. In this work, a dual−modification approach that integrates both conductive inorganic nanomaterials and diverse bifunctional monomers was proposed to develop a multifunctional MIP−based electrochemical (MMIP−EC) sensor for diuron (DU) detection. The MMIP was synthesized through a one−step electrochemical copolymerization of silver nanowires (AgNWs), o−phenylenediamine (O−PD), and 3,4−ethylenedioxythiophene (EDOT). DU molecules could conduct fluent electron transfer within the MMIP layer through the interaction between anchored AgNWs and bifunctional monomers, and the abundant recognition sites and complementary cavity shapes ensured that the imprinted cavities exhibit high specificity. The current intensity amplified by the two modification strategies of MMIP (3.7 times) was significantly higher than the sum of their individual values (3.2 times), exerting a synergistic effect. Furthermore, the adsorption performance of the MMIP was characterized by examining the kinetics and isotherms of the adsorption process. Under optimal conditions, the MMIP−EC sensor exhibits a wide linear range (0.2 ng/mL to 10 μg/mL) for DU detection, with a low detection limit of 89 pg/mL and excellent selectivity (an imprinted factor of 10.4). In summary, the present study affords innovative perspectives for the fabrication of MIP−EC sensor with superior analytical performance.

Two-dimensional bilayer ice in coexistence with three-dimensional ice without confinement

Icing plays an important role in various physical-chemical process. Although the formation of two-dimensional ice requires nanoscale confinement, two-dimensional bilayer ice in coexistence with three-dimensional ice without confinement remains poorly understood. Here, a critical value of a surface energy parameter is identified to characterize the liquid-solid interface interaction, above which two-dimensional and three-dimensional coexisting ice can surprisingly form on the surface. The two-dimensional ice growth mechanisms could be revealed by capturing the growth and merged of the metastable edge structures. The phase diagram about temperature and pressure vs energy parameters is predicted to distinguish liquid water, two-dimensional ice and three-dimensional ice. Furthermore, the deicing characteristics of coexisting ice demonstrate that the ice adhesion strength is linearly related to the ratio of ice-surface interaction energy to ice temperature. In addition, for gas-solid phase transition, the phase diagram about temperature and energy parameters is predicted to distinguish gas, liquid water, two-dimensional ice and three-dimensional ice. This work gives a perspective for studying the singular structure and dynamics of ice in nanoscale and provides a guide for future experimental realization of the coexisting ice.

Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods

As a simple lattice model that exhibits a phase transition, the Ising model plays a fundamental role in statistical and condensed matter physics. The Ising transition is realized by physical systems, such as the liquid-vapor transition. Its continuum limit also furnishes a basic example of interacting quantum field theories and universality classes. Motivated by a recent hybrid bootstrap study of the quantum quartic oscillator, we revisit the conformal bootstrap approach to the 3D Ising model at criticality, without resorting to positivity constraints. We use at most 10 nonperturbative crossing constraints at low derivatives from the Taylor expansion around a crossing symmetric point. The high-lying contributions are approximated by simple analytic formulae deduced from the lightcone singularity structure. Surprisingly, the low-lying properties are determined to good accuracy by this computationally very cheap approach. For instance, the results for the two relevant scaling dimensions (∆σ, ∆ϵ) ≈ (0.518153, 1.41278) are close to the most precise rigorous bounds obtained at a much higher computational cost.

A deformation quantization for non-flat spacetimes and applications to QFT

We provide a deformation quantization, in the sense of Rieffel, for all globally hyperbolic spacetimes with a Poisson structure. The Poisson structures have to satisfy Fedosov type requirements in order for the deformed product to be associative. We apply the novel deformation to quantum field theories and their respective states and we prove that the deformed state (i.e. a state in non-commutative spacetime) has a singularity structure resembling Minkowski, i.e. is Hadamard, if the undeformed state is Hadamard. This proves that the Hadamard condition, and hence the quantum field theoretical implementation of the equivalence principle is a general concept that holds in spacetimes with quantum features (i.e. a non-commutative spacetime).

Homogeneous spacetime with shear viscosity

We study the homogeneous and anisotropic evolution of Bianchi type-Ispacetime driven by perfect fluid with shear viscosity. We obtain exactsolutions by considering the simplest form of the equation of state whereinthe pressure and the shear stress are proportional to the energy densityindividually. A special case of our general solutions represent Bianchitype-VII cosmology. We analyse the singularity structure of the solutionsand its connection with various energy conditions. We find that theinitial singularity can be removed only for the Bianchi type-VII. We alsoanalyse the late-time behaviour of the solutions and find that, comparedto the usual Friedmann universe, the spacetime expands less rapidly andthe energy density drops faster.

Research on compressive strength and thermal conductivity of lightweight phosphogypsum-based composite cementitious materials

Investigation of the mechanical and thermal properties of lightweight phosphogypsum-based cementitious materials can enhance the utilization rate of phosphogypsum-based composites and reduce building energy consumption. In this study, various amounts of hollow glass microspheres (HGMs) are incorporated into phosphogypsum-based composite cementitious materials to investigate their effects on mechanical and thermal insulation properties. Subsequently, comparisons are made between lightweight phosphogypsum-based composite cementitious materials produced by foaming and those with added HGMs. The research findings indicate that HGMs significantly mitigate the loss of compressive strength and notably reduce thermal conductivity, aligning with the development needs of lightweight and high-strength construction materials. Specifically, at a 20 % HGM dosage, the specimen exhibits a thermal conductivity of 0.2512 W·m−1·K−1, marking a 46.0 % decrease compared to specimens without HGMs. Additionally, the compressive strength measures at 25.45 MPa, reflecting a 36.4 % decline relative to specimens without HGMs. However, because of the uncontrolled pore structure and size in lightweight phosphogypsum-based composite cementitious materials produced by direct foaming, the decrease in compressive strength of foamed materials is greater than that of materials with added HGMs when the reduction in the coefficient of thermal conductivity is the same. Moreover, the compressive strength of phosphogypsum-based composite cementitious materials made with HGMs decreases more than that made with the addition of HGMs. This can be attributed to the uniform particle size of HGMs, contributing to a singular and complete pore structure within the phosphogypsum-based cementitious materials, thereby optimizing their performance.

Physical and Thermoelectric Properties of Ternary Semiconducting NiO–V2O5–TeO2 Glasses

Five samples of ternary semiconducting 65V2O5 –xNiO–(35–x) TeO2 glasses, with 5 ≤ x ≤ 25 (x in mol%), were prepared using a press-quenching method from a glass melt. The thermoelectric Power (TEP), density, oxygen molar volume (Vm) and x-ray diffraction (XRD) were analyzed. TEP measurements were conducted within the temperature range of 300 – 506 K for the mentioned glass compositions. Information on the creation of polarons and the disorder energy arising from random fields was gathered. By applying Heikes’ equation and the small polaron model theory to the TEP, the results obtained from experimental data were effectively explained. The study revealed that an increase in the NiO content in the glass led to a rise in density and a consistent decrease in molar volume. All glasses exhibited a singular phase structure.

Boosting photoelectrochemical performance through appling magnetic field in manganese-doped cobalt ferrite photoanodes

An efficient photoelectrochemical water-splitting process is of paramount importance as it provides a sustainable and clean method for generating hydrogen fuel, which is crucial for addressing the world’s growing energy needs while mitigating environmental concerns. Herein, the effects of applying a magnetic field on the photoelectrochemical performance of photoanodes composed of Cobalt ferrite (CoFe2O4) and Manganese (Mn)-doped CoFe2O4 are investigated. The CoMnxFe2-xO4 nanoparticles were synthesized using a sol–gel method, with varying values of x (0.0, 0.1, 0.3, and 0.5). X-ray diffraction analysis consistently reveals a singular cubic spinel structure for all four samples. Magnetic analyses demonstrate an enhancement in magnetic characteristics, including saturation magnetization, coercivity, and anisotropy field in the CoMn0.3Fe1.7O4 sample compared to the other three samples. Photoelectrochemical (PEC) measurements indicate that the photocurrent increases in all four samples when a static magnetic field is applied. However, the CoMn0.3Fe1.7O4 sample shows a more pronounced enhancement. Specifically, the dark current density increases by more than 115 % when a magnetic field of 190 ± 20 mT is applied. Additionally, it rises by 387 % under light illumination with the magnetic field. This enhancement in PEC performance is attributed to electron spin polarization adjusted through the external magnetic field.

Delay Painlevé-I equation, associated polynomials and Masur-Veech volumes

We study a delay-differential analogue of the first Painlevé equation obtained as a delay periodic reduction of Shabat's dressing chain. We construct formal entire solutions to this equation and introduce a new family of polynomials (called Bernoulli-Catalan polynomials), which are defined by a nonlinear recurrence of Catalan type, and which share properties with Bernoulli and Euler polynomials. We also discuss meromorphic solutions and describe the singularity structure of this delay Painlevé-I equation in terms of an affine Weyl group of type A1(1). As an application we demonstrate the link with the problem of calculation of the Masur-Veech volumes of the moduli spaces of meromorphic quadratic differentials by re-deriving some of the known formulas.

Porcospino Flex: A Bio-Inspired Single-Track Robot with a 3D-Printed, Flexible, Compliant Vertebral Column

This paper is focused on the design and development of the Porcospino Flex, a single-track robot inspired by nature and featuring a meta-material structure. In the earlier version of the Porcospino, the main body was composed of a chain of vertebrae and two end sections linked by flexible joints, but the excessive use of materials in 3D printing and the resulting weight of the robot posed challenges, ultimately leading to a decrease in its overall efficiency and performance. The Porcospino Flex is manufactured through the fused deposition modeling process using acrylonitrile butadiene styrene and thermoplastic polyurethane, featuring a singular meta-material structure vertebral column. The adoption of a lattice structure in the main body of the Porcospino Flex leads to a substantial increase in performance, reducing its weight from 4200 g to 3600 g. Furthermore, the decrease in weight leads to a reduction in material usage and waste, making a substantial contribution to the sustainability of the robot. The discussion focuses on the testing results of the Porcospino Flex prototype, highlighting the enhancements observed compared to its prior version.

The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements [formula omitted] and [formula omitted]

The non-first-order-factorizable contributions1 to the unpolarized and polarized massive operator matrix elements to three-loop order, AQg(3) and ΔAQg(3), are calculated in the single-mass case. For the F12-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to O(ε5) in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable x∈]0,∞[ using highly precise series expansions to obtain the imaginary part of the physical amplitude for x∈]0,1] at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-x region. We also derive expansions in the region of small and large values of x. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.

Microstructure and properties of laser-melted FeCoCrNiSiMox high-entropy alloy coatings

In this research, FeCoCrNiSiMox high-entropy alloy coatings were created using laser cladding technology on 45 steel surfaces in order to provide a coating with high hardness and strong abrasion resistance. The present study aims to evaluate the effects of including Mo elements on the tissue, structure, and mechanical characteristics of FeCoCrNiSiMox high mercury alloy coatings under optimal laser melting process conditions. Through the regulation of Mo element incorporation, it has been observed that for values of x less than or equal to 0.2, the coating exhibits a singular FCC structure. However, for values of x greater than 0.2, a phase transition occurs in the coating’s structure, resulting in the appearance of a second phase. Consequently, the alloy primarily comprises a solid solution phase combined with the FCC phase and the Mo-rich phase. The introduction of the Mo element results in a steady reduction in the microstructure of the coating, which predominantly consists of dendritic structures. Additionally, the average hardness of the coating exhibits an increase, accompanied by an enhancement in its wear resistance.