Singular Properties Research Articles

Compensation and reentrant behaviors in a graphene-like nanoribbon with zigzag and armchair edges

Graphene-like nanoribbon structures (GNRs) in which singular magnetic properties emerge because of the graphene-cutting process, may offer unique opportunities for future technological development such as spintronics. Using the finite cluster approximation, research has been implemented on some magnetic and critical characteristics of a mixed spin-3/2 and spin-1 Ising ferrimagnetic graphene-like nanoribbon with two typical edges, namely armchair, and zigzag. We investigate the influences of such aspects as crystal fields, exchange couplings, and temperature on phase diagrams and magnetizations. Tricritical as well as compensation behaviors have been demonstrated under the effect of the above physical parameters. In particular, only armchair GNR may exhibit double compensation points. Meanwhile, an unexpected reentrant transition has been discovered for both GNRs, which is mainly due to the finite size effect.

Comparison study of fluid thermal boundary-bulk behaviors in the close-to-critical region under different property trends

The high-efficiency energy system based on the utilization of supercritical CO2 has been widely developed in recent years to meet the growing demands of clean energy and the elimination of CO2 emissions. Within this field, the design of the corresponding equipment requires an understanding of the thermodynamic behavior of supercritical fluid affected by the singular thermophysical properties. The analysis of this study is based on the asymptotic expansion of hydrodynamic equations and the thermophysical properties characterized by the exponential trends. The asymptotic model finds the wave and diffusion modes valid within the bulk region in second-order and within the boundary layer region (BLR) in first-order, respectively. Main findings include: (1) The wave mode is found in the bulk region with the wave celerity Γ. When the critical point is approached, Γ decreases from (γ0Mac0/κT0)0.5 = 1 to [(γ0–1)Mac0/κT0]0.5, which; (2) The diffusion mode found in BLR is characterized by non-dimensional diffusion coefficient ζ. This coefficient has the same behavior as thermal diffusivity, which is enlarged by thermal conductivity but weakened by isobaric specific heat. (3) Mass transport from BLR to bulk leads to the generation of the thermal wave, which can be measured by mass transport coefficient Mb=ζβp. Mb also characterizes the magnitude of the thermal wave as u2=Mb(Tb1)z|z=0 (that is, 0.17 mm/s when ϕ=10−4). The behavior of Mb is similar to one of ζ. However, the effect of cp is limited; (4) Two different modes of viscosity are identified. The increase in viscosity leads to the change of viscous stress mode from the second order to the first order, which also leads to a decrease in mass transport.

Complexity=anything: singularity probes

We investigate how the complexity=anything observables proposed by [1, 2] can be used to investigate the interior geometry of AdS black holes. In particular, we illustrate how the flexibility of the complexity=anything approach allows us to systematically probe the geometric properties of black hole singularities. We contrast our results for the AdS Schwarzschild and AdS Reissner-Nordström geometries, i.e., for uncharged and charged black holes, respectively. In the latter case, the holographic complexity observables can only probe the interior up to the inner horizon.

On the visibility of singularities in general relativity and modified gravity theories

We investigate the global causal structure of the end state of a spherically symmetric marginally bound Lemaitre–Tolman–Bondi (LTB) (Lemaitre 1933 Ann. Soc. Sci. Brux. A 53 51, Tolman 1934 Proc. Natl Acad. Sci. USA 20 169–76, Bondi 1947 Mon. Not. Astron. Soc. 107 410) collapsing cloud (which is well studied in general relativity) in the framework of modified gravity having the generalized Lagrangian in the action. Here R is the Ricci scalar, and is a constant. By fixing the functional form of the metric components of the LTB spacetime, using up the available degree of freedom, we realize that the matching surface of the interior and the exterior metric are different for different values of α. This change in the matching surface can alter the causal property of the first central singularity. We depict this by showing a numerical example. Additionally, for a globally naked singularity to have physical relevance, a congruence of null geodesics should escape from such singularity to be visible to an asymptotic observer for infinite time. For this to happen, the first central singularity should be a nodal point. We here give a heuristic method to show that this singularity is a nodal point by considering the above class of theory of gravity, of which general relativity is a particular case.

Singularity properties of timelike circular surfaces in Minkowski 3-space

The approach of the study is on singularity properties of timelike circular surfaces in Minkowski 3-space. A timelike circular surface is a one-parameter set of Lorentzian circles with stationary radius directing a non-null space curve, which acts as the spine curve, and it has symmetrical properties. In this study, we addressed timelike circular surfaces and gained their geometric and singularity properties such as Gaussian and mean curvatures, comparable with those of ruled surfaces. Consequently, we presented timelike roller coaster surfaces as a special class of timelike circular surfaces. Then, the conditions for timelike roller coaster surfaces to be flat or minimal surfaces are obtained. Meanwhile, we supported the results of the approach with some examples.

Efficient design of helical higher-order topological insulators in 3D elastic medium

Topological materials (TMs) are well-known for their topological protected properties. Phononic system has the advantage of direct observation and engineering of topological phenomena on the macroscopic scale. For the inverse design of 3D TMs in continuum medium, however, it would be extremely difficult to classify the topological properties, tackle the computational complexity, and search solutions in an infinite parameter space. This work proposed a systematic design framework for the 3D mechanical higher-order topological insulators (HOTIs) by combining the symmetry indicators (SI) method and the moving morphable components (MMC) method. The 3D unit cells are described by the MMC method with only tens of design variables. By evaluating the inherent singularity properties in the 3D mechanical system, the classic formulas of topological invariants are modified accordingly for elastic waves. Then a mathematical formulation is proposed for designing the helical multipole topological insulators (MTIs) featured corner states and helical energy fluxes, by constraining the corresponding topological invariants and maximizing the width of band gap. Both valley-based and spin-based mechanical helical HOTIs are obtained by this method and verified by full wave simulations. This design paradigm can be further extended to design 3D TMs among different symmetry classes and space groups, and different physical systems.

Alginate/polyacrylamide host-guest supramolecular hydrogels with enhanced adhesion

Although injectable hydrogels with minimally invasive delivery have garnered significant interest, their potential applications have been restricted by a singular property. In this study, a supramolecular hydrogel system with improved adhesion was constructed through host-guest interactions between alginate and polyacrylamide. The maximum tensile adhesion strength between the β-cyclodextrin and dopamine-grafted alginate/adamantane-grafted polyacrylamide (Alg-βCD-DA/PAAm-Ad, namely AβCDPA) hydrogels and pigskin reached 19.2 kPa, which was 76 % stronger than the non-catechol-based control hydrogel (β-cyclodextrin-grafted alginate/adamantane-grafted polyacrylamide, Alg-βCD/PAAm-Ad). Moreover, the hydrogels demonstrated excellent self-healing, shear-thinning, and injectable properties. The required pressure to extrude the AβCDPA2 hydrogel from a 16G needle at a rate of 2.0 mL/min was 67.4 N. As the polymer concentration and adamantane substitution degree increased, the hydrogels exhibited higher modulus, stronger network structure, and lower swelling ratio and degradation rate. Encapsulating and culturing cells within these hydrogels demonstrated good cytocompatibility. Therefore, this hydrogel can serve as a viscosity extender or bioadhesive, and as a carrier material to deliver encapsulated therapeutic substances into the body through minimally invasive injection methods.

Description of the Wild Strain Rhizobium rosettiformans DSM26376, Reclassified under Peteryoungia rosettiformans comb.nov., for Producing Glucuronan.

Glucuronan is a polysaccharide composed of β-(1,4)-linked d-glucuronic acids having intrinsic properties and biological activities recoverable in many fields of application. Currently, the description of Sinorhyzobium meliloti M5N1CS mutant bacterial strain as the sole source of glucuronan makes it relevant to the exploration of new microorganisms producing glucuronan. In this study, the Peteryoungia rosettifformans strain (Rhizobia), was identified as a wild producer of an exopolysaccharide (RhrBR46) related to glucuronan. Structural and biochemical features, using colorimetric assays, Fourier infrared spectroscopy, nuclear magnetic resonance, high pressure size exclusion chromatography coupled to multi-angle light laser scattering, and enzymatic assays allowed the characterization of a polyglucuronic acid, having a molecular mass (Mw¯) of 1.85 × 105 Da, and being partially O-acetylated at C-2 and/or C-3 positions. The concentration of Mg2+ ions in the cultivation medium has been shown to impact the structure of RhrBR46, by reducing drastically its Mw¯ (73%) and increasing its DA (10%). Comparative structural analyses between RhrBR46 and the glucuronan from Sinorhyzobium meliloti M5N1CS strain revealed differences in terms of molecular weight, degree of acetylation (DA), and the distribution of acetylation pattern. These structural divergences of RhrBR46 might contribute to singular properties or biological activities of RhrBR46, offering new perspectives of application.

Symplectic period mode decomposition method and its application in fault diagnosis of rolling bearing

The rolling bearing fault signals are accompanied with the specific periodic impulse components in case of fault. Due to the background noise, the periodic impulse component is extremely weak and difficult to be extracted. The periodic segment matrix (PSM) has excellent singular value aggregation property and can accurately separate the periodic impulse components from the signal. Based on this, a symplectic period mode decomposition (SPMD) method is proposed. Firstly, the singular value squared difference ratio (SVSDR) spectrum is defined, and the embedded dimension of PSM is determined. Then, the symplectic geometry component matrix is obtained by symplectic geometry similarity transformation, and the first symplectic geometry period component (SPC) is obtained by periodic impact intensity (PII). Finally, the spectral L2/L1 norm (SNL2/L1) index is used as the termination condition, and the iterative decomposition is terminated when the SNL2/L1 of the residual signal decreases. The emulation and experimental signals results indicate that the SPMD method can extract periodic impulse components accurately and is an effective rolling bearing fault diagnosis method.

Tissue-specific chromatin-binding patterns of Caenorhabditis elegans heterochromatin proteins HPL-1 and HPL-2 reveal differential roles in the regulation of gene expression.

Heterochromatin is characterized by an enrichment of repetitive elements and low gene density and is often maintained in a repressed state across cell division and differentiation. The silencing is mainly regulated by repressive histone marks such as H3K9 and H3K27 methylated forms and the heterochromatin protein 1 (HP1) family. Here, we analyzed in a tissue-specific manner the binding profile of the two HP1 homologs in Caenorhabditis elegans, HPL-1 and HPL-2, at the L4 developmental stage. We identified the genome-wide binding profile of intestinal and hypodermal HPL-2 and intestinal HPL-1 and compared them with heterochromatin marks and other features. HPL-2 associated preferentially to the distal arms of autosomes and correlated positively with the methylated forms of H3K9 and H3K27. HPL-1 was also enriched in regions containing H3K9me3 and H3K27me3 but exhibited a more even distribution between autosome arms and centers. HPL-2 showed a differential tissue-specific enrichment for repetitive elements conversely with HPL-1, which exhibited a poor association. Finally, we found a significant intersection of genomic regions bound by the BLMP-1/PRDM1 transcription factor and intestinal HPL-1, suggesting a corepressive role during cell differentiation. Our study uncovers both shared and singular properties of conserved HP1 proteins, providing information about genomic binding preferences in relation to their role as heterochromatic markers.

Structural, optical and singular magnetic properties of anodized titanium dioxide nanotubes

Highly ordered TiO2 nanotubes with large surface-volume ratios were prepared by anodic oxidation, and the effects of annealing in different atmospheres on their structural, optical and magnetic properties were studied. The as-prepared, air and argon annealed samples all showed low-field ferromagnetism and high-field diamagnetism at room temperature. The unexpected decrease in the band-gap and the enhancement of ferromagnetism in the air-annealed sample provide convincing evidence for the morphology dependence. With decreasing test temperature, low-field ferromagnetism gradually increased, and interestingly, the high-field diamagnetism gradually changed to paramagnetism. Moreover, the argon-annealed sample exhibited significantly enhanced ferromagnetism, which varied with the annealing temperature, reaching a maximum at 400 °C. Important effects of the annealing conditions and the induced morphology changes on the optical and magnetic behavior of the nanotubes were revealed, and the origin of ferromagnetism was explained from a new perspective of hydrogen-like impurities based on the characteristics of localized states associated with oxygen vacancies. Our research will be helpful in expanding the application of TiO2 nanotubes.

All linear fractional derivatives with power functions’ convolution kernel and interpolation properties

Our attempt is an axiomatic approach to find all classes of possible definitions for fractional derivatives with three axioms. In this paper, we consider a special case of linear integro-differential operators with power functions’ convolution kernel a(α)(t−s)b(α) of order α∈(0,1). We determine analytic functions a(α) and b(α) such that when α→0+, the corresponding operator becomes identity operator, and when α→1− the corresponding operator becomes derivative operator. Then, a sequential operator is used to extend the fractional operator to a higher order. Some properties of the sequential operator in this regard also are studied. The singularity properties, Laplace transform and inverse of the new class of fractional derivatives are investigated. Several examples are provided to confirm theoretical achievements. Finally, the solution of the relaxation equation with diverse fractional derivatives is obtained and compared.

Longitudinal evolution from scalar to vector beams assembled from all-dielectric metasurfaces.

Vector vortex beams (VVBs) with non-uniform polarization states have a wide range of applications, from particle capture to quantum information. Here, we theoretically demonstrate a generic design for all-dielectric metasurfaces operating in the terahertz (THz) band, characterized as a longitudinal evolution from scalar vortices carrying homogeneous polarization states to inhomogeneous vector vortices with polarization singularities. The order of the converted VVBs can be arbitrarily tailored by manipulating the topological charge embedded in two orthogonal circular polarization channels. The introduction of the extended focal length and the initial phase difference effectively guarantees the smoothness of the longitudinal switchable behavior. A generic design approach based on vector-generated metasurfaces can assist in the exploration of new singular properties of THz optical fields.

On (contra)pedals and (anti)orthotomics of frontals in de Sitter 2‐space

In this paper, we mainly investigate (contra)pedals and (anti)orthotomics of frontals in the de Sitter 2‐space from the viewpoint of singularity theory and differential geometry. We utilize the de Sitter Legendrian Frenet frames to provide parametric representations of (contra)pedal curves of spacelike and timelike frontals in the de Sitter 2‐space and to investigate the geometric and singularity properties of these (contra)pedal curves. We then introduce orthotomics of frontals in the de Sitter 2‐space and explain these orthotomics as wavefronts from the viewpoint of Legendrian singularity theory. Furthermore, we generalize these methods to study antiorthotomics of frontals in the de Sitter 2‐space.

Cancer stem cell-derived extracellular vesicles preferentially target MHC-II-macrophages and PD1+ T cells in the tumor microenvironment.

Immunotherapy is an approved treatment option for head and neck squamous cell carcinoma (HNSCC). However, the response rate to immune checkpoint blockade is only 13% for recurrent HNSCC, highlighting the urgent need to better understand tumor-immune interplay, with the ultimate goal of improving patient outcomes. HNSCC present high local recurrence rates and therapy resistance that can be attributed to the presence of cancer stem cells (CSC) within tumors. CSC exhibit singular properties that enable them to avoid immune detection and eradication. How CSC communicate with immune cells and which immune cell types are preferentially found within the CSC niche are still open questions. Here, we used genetic approaches to specifically label CSC-derived extracellular vesicles (EVs) and to perform Sortase-mediated in vivo proximity labeling of CSC niche cells. We identified specific immune cell subsets that were selectively targeted by EVCSC and that were found in the CSC niche. Native EVCSC preferentially targeted MHC-II-macrophages and PD1+ T cells in the tumor microenvironment, which were the same immune cell subsets enriched within the CSC niche. These observations indicate that the use of genetic technologies able to track EVs without in vitro isolation are a valuable tool to unveil the biology of native EVCSC.

Employing Topological Properties of Phase Singularities for Designing Supercavity Systems with Tailored Excitation

AbstractTrapping electromagnetic waves in high‐index resonators with extreme quality factors (Q‐factor) can be achieved by exciting supercavity (quasi‐bound states in the continuum, quasi‐BIC) modes with minimal radiation loss. Conventionally, the quasi‐BICs are achieved by tuning the resonator dimensions to promote destructive interference between two modes in the cavity. In this work, an enhanced Q‐factor is achieved by manipulating the structure of a near‐field excitation source and tailoring the excitation strength of individual multipolar modes. A pair of concentric rings with strong mutual coupling is used in contrast to a simple single‐ring case. We show that adding the second passive ring enables additional degrees of freedom to manipulate the multipolar content exited in the cavity. The multipole decomposition of the cavity modes is performed using full‐wave numerical simulations to support these claims. Experimental validation with a double‐ring fed supercavity demonstrates the highest measured Q‐factor of ≈310 or ≈2× the quality factor of a design without supercavity, which is consistent with a numerical model predicting up to 3× enhanced Q‐factor. We show that, analyses of polarization singularities and multipolar decomposition can be used to understand, characterize, and design such systems, employing their topological properties not broadly explored before.

A Novel Strategy for Eliminating the Boundary Layer Effect in the Regularized Integral Identity in PIES for 2D Potential Problem

The paper presents a new strategy for improving the accuracy of solutions near the boundary in the integral identity associated with the parametric integral equation system (PIES) for two-dimensional (2D) potential problems. A significant reduction in accuracy in the zone close to the boundary, also known as the boundary layer effect, is directly associated with the nearly singular properties of kernels present in the integral identity. The paper shows that these singularities can be efficiently eliminated by regularizing the integral identity with the help of the so-called regularizing function with appropriate coefficients. The analyzed examples demonstrate a significant improvement in accuracy, where all integrals of the regularized integral identity are accurately calculated using low-order standard Gauss–Legendre quadrature. The proposed regularization algorithm is independent of the actual boundary shape, its representation and assumed boundary conditions.

Spacelike Circular Surfaces in Minkowski 3-Space

The approach of the paper is on spacelike circular surfaces in the Minkowski 3-space. A spacelike circular surface is a one-parameter family of Lorentzian circles with a fixed radius regarding a non-null curve, which acts as the spine curve, and it has symmetrical properties. In the study, we have parametrized spacelike circular surfaces and have provided their geometric and singularity properties such as Gaussian and mean curvatures, comparing them with those of ruled surfaces and the classification of singularities. Furthermore, the conditions for spacelike roller coaster surfaces to be flat or minimal surfaces are obtained. Meanwhile, we support the results of the approach with some examples.

Soliton Waves with the (3+1)-Dimensional Kadomtsev–Petviashvili–Boussinesq Equation in Water Wave Dynamics

We examined the (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-B) equation, which arises not only in fluid dynamics, superfluids, physics, and plasma physics but also in the construction of connections between the hydrodynamic and optical model fields. Moreover, unlike the Kadomtsev–Petviashvili equation (KPE), the KP-B equation allows the modeling of waves traveling in both directions and does not require the zero-mass assumption, which is necessary for many scientific applications. Considering these properties enables researchers to obtain more precise results in many physics and engineering applications, especially in research on the dynamics of water waves. We used the modified extended tanh function method (METFM) and Kudryashov’s method, which are easily applicable, do not require further mathematical manipulations, and give effective results to investigate the physical properties of the KP-B equation and its soliton solutions. As the output of the work, we obtained some new singular soliton solutions to the governed equation and simulated them with 3D and 2D graphs for the reader to understand clearly. These results and graphs describe the single and singular soliton properties of the (3+1)-dimensional KP-B equation that have not been studied and presented in the literature before, and the methods can also help in obtaining the solution to the evolution equations and understanding wave propagation in water wave dynamics.

Solid oxide electrolysis cells – Interplay between operating conditions, fuel electrode overpotential and degradation

With the integration of increased share of energy from renewable, but fluctuating, energy sources there will be an increased demand for large-scale flexible conversion of electrical energy into easily storable chemical fuels. Electrolysis will be a key component in the future of energy conversion and storage solutions. Solid oxide cells (SOC) can provide the most efficient electrolysis technology. Furthermore, solid oxide electrolysis cell (SOEC) technology has improved tremendously in terms of initial performance, long-term durability, and up-scaling of cell and stack sizes; and with respect to commissioning and operation of SOEC plants. Nevertheless, it is evident that further improvement of electrochemical performance and especially long-term durability is crucial for the coming up-scaling and integrated SOEC systems as part of our energy grid. This calls for research within 1) thorough mapping of degradation mechanisms, 2) determination of thresholds for the onset of irreversible degradation processes, 3) safe operating conditions and means to mitigate known degradation processes, etc. However, degradation is not a simple singular property and there is often a puzzling interplay between parameters such as: the chosen electro-catalysts, the manufacturing of cell components, obtained microstructures, the resulting initial electrochemical performance, operating conditions, and the nature and extent of different degradation processes. This work will present11This work has been presented as invited keynote speak at symposium E01.07 as part of the 23rd International Conference on Solid State Ionics, MRS Meeting, Boston (US), July 2022. an overview of the puzzling interplay between initial electrochemical performance and long-term durability. It will then provide examples of multiple complementary characterization techniques applied for the analyses of these features and processes (e.g., SEM, TEM, Raman spectroscopy and electrochemical impedance spectroscopy). Furthermore, strategies to mitigate and/or limit specific degradation processes and insight into data required to establish degradation wise safe operating conditions are discussed. The present work will touch upon multiple performance characteristics and degradation processes: 1) triple-phase-boundaries (TPB) and critical micro/nano-structural parameters of the porous nickel/yttria-stabilized-zirconia (Ni/YSZ) electrode; 2) the perception of electrode overpotential and why this parameter is more important than the set current density or operating cell/stack voltage, 3) the effect of impurities, 4) the interplay between impurities and carbon deposition and 5) the degradation caused by Ni migration and actions to mitigate this degradation process.