Quadratic Lines Research Articles

Magnetic quadratic nodal lines in half-metallic anode material TiF3: A first-principles study

It is anticipated that nodal line materials may demonstrate unique physical phenomena. The traditional nodal line materials have a linear energy distribution surrounding them. A recent prediction is that systems may similarly stabilize nodal lines with a quadratic or cubic energy dispersion. This work focuses on a half-metal anode material, TiF3, which has already been predicted to host stable ferromagnetism and half-metallicity under Li insertion. Using first-principles calculation, we predicted for the first time that TiF3, a ferromagnetic material, has completely spin-polarized quadratic nodal lines along the Γ-X path. The half-metallic state and the spin-polarized quadratic nodal lines are robust to uniform strains (from −3 to +3 %). TiF3 can be regarded as a promising platform for deepening our comprehension of magnetic quadratic nodal lines in half-metals.

Magnetic quadratic nodal line with spin–orbital coupling in CrSb

Quadratic nodal lines (QNLs) with quadratic band splitting in the Brillouin zone have different properties from conventional linear nodal lines. In this study, based on symmetry analysis and first-principles calculation, we prove that magnetic quadratic nodal line (MQNL) exists in antiferromagnetic configurations of one single realistic solid-state material CrSb with the P63′/m′m′c structure that breaks the time-reversal symmetry. In magnetic systems with the non-negligible spin–orbit coupling effect, we show that nodal lines with a quadratic leading order dispersion can be realized around Fermi level. Moreover, CrSb shows four long Fermi arcs near Fermi energy level resulting from six pairs of Weyl points with opposite chirality. Our results reveal a promising platform for exploring the topological states with intriguing effects. We hope that the proposed realistic material can be viewed as ideal candidate to realize the MQNL in solid-state materials.

Magnetic Weyl and quadratic nodal lines in inverse-Heusler-based fully compensated ferrimagnetic half-metals

Heusler alloys, a class of easily prepared, highly ordered intermetallic compounds, were first reported in 1903. Since then, Heusler alloys have presented various physical phenomena in modern condensed-matter physics. Among Heusler alloys, Heusler-based fully compensated ferrimagnetic half-metals (FCF-HMs) are, particularly, relevant because they host fully spin polarization and have no net magnetic moment, making them have no stray field and less affected by external magnetic fields. Based on first-principles calculations and a tight-binding Hamiltonian model, we provide new insight into inverse-Heusler-based (IHB) FCF-HMs and reveal that they exhibit spin-polarized Weyl and quadratic nodal lines as well as spin-polarized drumheadlike surface states. This paper presents the electron-filling-based design rule and material candidates for IHB FCF-HMs and suggests that IHB FCF-HMs are promising candidates for follow-up investigations in the field of topological spintronics. Subsequent experimental confirmation of the topological states in IHB FCF-HMs is imminent.

Phononic quadratic nodal lines of different types in Li2NaN

The search for new topological states has been shifted from electronic fermionic states to phononic bosonic ones, and topological elements with conventional linear band crossing have also been extended into the high order dispersion field. In this Letter, based on theoretical calculations and effective model analysis, we predicted the quadratic phonon states in the hexagonal compound Li2NaN. Particularly, two quadratic nodal lines are found, which are distributed along the same straight Γ–A path, protected by the C6v point group symmetry. The detailed band surface distribution and effective Hamiltonian construction are elucidated, demonstrating the quadratic order dispersion. These two quadratic nodal lines were further categorized into type-I and type-III, and their surface spectral properties were calculated, in which clear drumhead surface states are observed for both quadratic nodal lines, and they stretched throughout the entire Brillouin zone. Furthermore, the surface states were well separated from the bulk band projection, which is extremely beneficial for experimental detection. Notably, phononic quadratic nodal line states have been rarely studied and, more importantly, a type-III line has even not been reported thus far. Therefore, our work can pave the way for related studies for both quadratic nodal lines and type-III states, and the presented material can serve as an ideal candidate to promote further experimental investigation.

Obvious Surface States Connecting to the Projected Triple Points in NaCl's Phonon Dispersion.

With the development of computer technology and theoretical chemistry, the speed and accuracy of first-principles calculations have significantly improved. Using first-principles calculations to predict new topological materials is a hot research topic in theoretical and computational chemistry. In this work, we focus on a well-known material, sodium chloride (NaCl), and propose that the triple point (TP), quadratic contact triple point (QCTP), linear and quadratic nodal lines can be found in the phonon dispersion of NaCl with Fm m type structure. More importantly, we propose that the clear surface states connected to the projected TP and QCTP are visible on the (001) surface. It is hoped that further experimental investigation and verification for these properties as mentioned above.

High-order one-dimensional (1D) fermion in ferromagnetic RbFeF3

Nodal line semimetals/metals (NLSMs), hosting band-crossings in one dimension, are expected to exhibit exotic physical phenomena, like drumhead surface states. The conventional NLSMs host a linear energy dispersion around it. Recently, it has been predicted that NLs hosting a high-order energy dispersion may also be stabilized in nonmagnetic systems. However, it still remains challenges to find their counterpart in magnetic systems. Here, based on first-principles calculation and theoretical analysis, we predict for the first-time that RbFeF3, a ferromagnetic material, has a high-order NL without spin-orbital coupling (SOC). We give the symmetry conditions which stabilizes the quadratic nodal lines (QNLs), thus an effective Hamiltonian is constructed to demonstrate its existence. Different from the nonmagnetic nodal lines, they come from the same single spin channel, achieving a 100% spin polarization. Interestingly, it exhibits a “torus” drumhead surface states in the whole Brillouin zone, which is quite different from that of linear NL. Under symmetry breaking, the QNL could be reduced into a pair of linear type-II NLs by tuning the magnetization direction. Our work provides a ideal magnetic material with high-order NL which has not been observed before.

Magnetic higher-order nodal lines

Nodal lines, as one-dimensional band degeneracies in momentum space, usually feature a linear energy splitting. Here, we propose the concept of magnetic higher-order nodal lines, which are nodal lines with higher-order energy splitting and realized in magnetic systems with broken time reversal symmetry. We provide sufficient symmetry conditions for stabilizing magnetic quadratic and cubic nodal lines, based on which concrete lattice models are constructed to demonstrate their existence. Unlike its counterpart in nonmagnetic systems, the magnetic quadratic nodal line can exist as the only band degeneracy at the Fermi level. We show that these nodal lines can be accompanied by torus surface states, which form a surface band that span over the whole surface Brillouin zone. Under symmetry breaking, these magnetic nodal lines can be transformed into a variety of interesting topological states, such as three-dimensional quantum anomalous Hall insulator, multiple linear nodal lines, and magnetic triple-Weyl semimetal. The three-dimensional quantum anomalous Hall insulator features a Hall conductivity $\sigma_{xy}$ quantized in unit of $e^2/(hd)$ where $d$ is the lattice constant normal to the $x$-$y$ plane. Our work reveals previously unknown topological states, and offers guidance to search for them in realistic material systems.

Efficient characterization of optical vortices via diffraction from parabolic-line linear gratings

The diffraction from a linear grating having a quadratic curvature on its lines is proposed for vortex beam characterization. Three types of transmission functions are considered for the gratings, including pure amplitude, pure phase, and hybrid amplitude and phase profiles. The first-order diffraction of the vortex beam through such gratings is only a set of elongated intensity spots. The number of spots determines the value of the topological charge (TC), and the sign of the TC can be distinguished with the elongation (and rotation) direction of the spots. This method is effective because over a given diffraction order, all of the energy of the beam transfers into the bright bar-like spots. Another advantage of the method is its ease of use, because it is not sensitive to the relative location of the beam axis and the grating center. Using a spatial light modulator, we provide different hybrid amplitude and phase linear gratings with a quadratic curvature on their lines and demonstrate the effectiveness of the proposed method experimentally. Also, the same justification was done in the diffraction of vortex beams from printed pure amplitude gratings. We have also investigated the effect of lateral shearing between the amplitude and phase parts of the hybrid grating on the resulted diffraction pattern. It is shown that for given values of lateral shear, one of the first-order diffraction patterns is eliminated, and the intensity of the other one is maximized. Finally, we present the key results of the diffraction of optical vortices from annular amplitude and phase gratings and from phase objects having linearly increasing phase functions along the radial direction. It is shown that the diffraction of optical vortices only from the parabolic-line linear gratings is insensitive to the off-axis value of the beam and grating centers.

Elevated Uric Acid Prevalence and Clinical Outcomes in Patients with Heart Failure with Preserved Ejection Fraction: Insights from RELAX

PurposeWe aimed to 1) describe characteristics of patients with heart failure with preserved ejection fraction (HFpEF) enrolled in RELAX stratified by normal or elevated baseline serum uric acid (sUA) level; 2) evaluate the association between sUA level and surrogate clinical measures; and 3) assess associations between changes in sUA level over time and changes in surrogate clinical measures. MethodsWe analyzed 212 patients with HFpEF and normal or elevated (>6 mg/dL) baseline sUA measurements from the RELAX trial. Variables examined included clinical characteristics, cardiopulmonary exercise testing, 6-minute walk testing, quality of life, echocardiography, and serum biomarker testing. Baseline characteristics between groups were compared and scatter plots with quadratic regression lines and linear regression modeling were used to assess the relationship between baseline sUA and clinical measures. Kaplan–Meier curves were used to describe composite death or cardiovascular/renal hospitalization. ResultsThe prevalence of elevated baseline sUA was 68.9%. Patients with elevated sUA had more baseline comorbidities and poorer functional status on cardiopulmonary exercise testing than those without. After adjustment, significant associations between baseline sUA levels and cystatin C, N-terminal pro B-type natriuretic peptide, high-sensitivity troponin I, and high-sensitivity C-reactive protein were identified. Higher baseline sUA was also associated with worsening peak VO2, 6-minute walk testing, and left ventricular mass. No significant association was found between baseline sUA levels and the composite of death or cardiovascular/renal hospitalization at 24 weeks. ConclusionsUA is an important marker of comorbidities and functional status in patients with HFpEF. Clinical trials of sUA-lowering therapies in patients with HFpEF are promising.

Bifurcations at a degenerate two-fold singularity and crossing limit cycles

In the 1990s Teixeira studied discontinuous piecewise-smooth (DPWS) dynamical systems in R3, whose state space is divided in two open regions by a plane acting as the switching manifold, and presenting two lines of quadratic tangency, one for each involved vector field. We call T-singularity (Teixeira singularity) the point of transverse intersection of the quadratic tangency lines that are of the invisible type. In this paper, we analyze DPWS systems that present two branches of T-singularities. In our approach we consider the cases where either a pseudo-equilibrium collides to just one of the two T-singularities or the two T-singularities (and also a pseudo-equilibrium between them) collides in a single point. As a consequence of these bifurcations, until now not covered by the literature, we can observe the birth of limit cycles, determine their stability and provide an upper limit for the number of limit cycles that occur in this scenario.

Quadratic and cubic nodal lines stabilized by crystalline symmetry

In electronic band structures, nodal lines may arise when two (or more) bands contact and form a one-dimensional manifold of degeneracy in the Brillouin zone. Around a nodal line, the dispersion for the energy difference between the bands is typically linear in any plane transverse to the line. Here, we perform an exhaustive search over all 230 space groups for nodal lines with higher-order dispersions that can be stabilized by crystalline symmetry in solid state systems with spin-orbit coupling and time reversal symmetry. We find that besides conventional linear nodal lines, only lines with quadratic or cubic dispersions are possible, for which the allowed degeneracy cannot be larger than two. We derive effective Hamiltonians to characterize the novel low-energy fermionic excitations for the quadratic and cubic nodal lines, and explicitly construct minimal lattice models to further demonstrate their existence. Their signatures can manifest in a variety of physical properties such as the (joint) density of states, magneto-response, transport behavior, and topological surface states. Using ab-initio calculations, we also identify possible material candidates that realize these exotic nodal lines.

Body mass index and motor coordination: Non-linear relationships in children 6-10 years.

Given the concern for health-related consequences of an elevated body mass index (BMI; obesity), the potential consequences of a low BMI in children are often overlooked. The purpose was to evaluate the relationship between the BMI across its entire spectrum and motor coordination (MC) in children 6-10years. Height, weight, and MC (Körperkoordinationstest für Kinder, KTK test battery) were measured in 1,912 boys and 1,826 girls of 6-10years of age. BMI (kg/m2 ) was calculated. KTK scores for each of the four tests were also converted to a motor quotient (MQ). One-way ANOVA was used to test differences in the BMI, individual test items, and MQ among boys and girls within age groups. Sex-specific quadratic regressions of individual KTK items and the MQ on the BMI were calculated. Girls and boys were also classified into four weight status groups using International Obesity Task Force criteria: thin, normal, overweight, and obese. Differences in specific test items and MQ between weight status groups were evaluated by age group in each sex. Thirty-one percent of the sample was overweight or obese, whereas 5% was thin. On average, normal weight children had the highest MQ in both sexes across the age range with few exceptions. Overweight/obese children had a lower MQ than normal weight and thin children. The quadratic regression lines generally presented an inverted parabolic relationship between the BMI and MC and suggested a decrease in MC with an increase in the BMI. In general, BMI shows a curvilinear, inverted parabolic relationship with MC in children 6-10years.

Wood density as a proxy for vulnerability to cavitation: Size matters

In this study, vulnerability to cavitation, P50 (i.e. the water potential causing 50 % loss of hydraulic conductivity), of Norway spruce trunkwood at different cambial age was related to wood density. Wood density was calculated from mass in the oven dry state related either to volume at the oven-dry state (dry wood density) or to volume at full saturation (basic wood density). Dry wood density and basic wood density were strongly linearly related (r² = 0.99); there was however a shift from the 1:1 reference line with increasing dry wood density. Dry wood density as well as basic wood density had similar high predictive qualities for P50 (r² = 0.85). The quadratic regression lines took however a quite different course below -4 MPa because volume shrinkage increased with increasing dry wood density. For Norway spruce sapwood with high dry wood density, mixing up different wood density traits would thus result in a predicted overestimation or underestimation of vulnerability to cavitation. Gravimetrically wood density measurements at different moisture contents (starting at full saturation) are easily to achieve on standard size specimens and the conversion curves obtained will be of high value for future ecological studies on other species and across species.

A Description of Variability of Pacing in Marathon Distance Running

The purpose of this study was twofold: 1) to describe variability of pacing during a marathon and 2) to determine if there is a relationship between variability of pacing and marathon performance. Publically available personal global positioning system profiles from two marathons (Race 1 n = 116, Race 2 n = 169) were downloaded (http://connect.garmin.com) for analysis. The coefficient of variation of velocity (Velcov) was calculated for each profile. Each profile was categorized as finishing in under 3.9 hours, between 3.9 and 4.6 hours, or longer than 4.6 hours. Linear and quadratic lines of best fit were computed to describe the relationship between marathon finish time and Velcov. A 2 (Race) x 3 (bin) analysis of variance (ANOVA) was used to compare the dependent variable (Velcov) between races and the marathon bin finish times. Velcov was not influenced by the interaction of finish time bin and Race (p>0.05) and was not different between races (Race 1: 16.6 ± 6.4%, Race 2: 16.8 ± 6.6%, p>0.05). Velcov was different between finish time categories (p<0.05) for each race such that Velcov was lower for faster finish times. Using combined data from both races, linear (marathon finish time = marathon finish time = 0.09Velcov + 2.9, R^2 = 0.46) and quadratic (marathon finish time = -0.0006 Velcov 2 + 0.11 Velcov + 2.7, R^2 = 0.46) lines of best fit were significant (p<0.05). Slower marathon finishers had greater variability of pace compared to faster marathoner finishers.

Sexual dimorphism of adipose tissue distribution across the lifespan: a cross-sectional whole-body magnetic resonance imaging study

BackgroundDespite increasing research and clinical significance, limited information is available on how the visceral and subcutaneous adipose tissue (VAT and SAT) compartments develop during growth and maturation and then vary in volume across the adult lifespan. The present study aimed at exploring how adipose tissue compartments partition across the lifespan.MethodsTotal body VAT and SAT were quantified in an ethnically-diverse cross-sectional sample of healthy subjects ages 5 – 88 yrs [children (5–17 years): males n = 88, BMI percentile (X ± SD), 61.9 ± 27.1; females, n = 59, BMI percentile, 60.0 ± 28.4; adults (≥ 18 yrs): males, n = 164, BMI, 25.6 ± 3.7 kg/m2, and females, n = 188, BMI, 25.5 ± 5.4 kg/m2]. Subjects completed a whole-body magnetic resonance imaging scan and images were then segmented for VAT and SAT; total compartment volumes were calculated from respective slice areas. Sex and age distributions were evaluated by generating quadratic and cubic smoothing lines fitted to the data. Plots were developed with and without adjustment for total adipose tissue, ethnicity, and menopausal status in women. VAT and SAT volumes were both larger with greater age.ResultsIn adulthood, VAT was larger in males than in females with and without adjustment. In contrast, SAT volume was larger in females than in males after entering puberty and sex differences remained, with and without adjustment, across the remaining lifespan.ConclusionBased on observations made in this cross-sectional sample, VAT and SAT volumes were variably larger with greater age across most of the human lifespan, although the relatively small number of children warrants future larger scale studies to validate our observations. Moreover, the pattern and magnitude of adipose tissue "growth" differed between males and females, with the mechanistic basis of this sexual dimorphism only partially understood. These descriptive observations in a large cross-sectional cohort provide an initial foundation for future longitudinal and cohort studies.

Angle Specificity of the Knee Extensor Age-Related Profile in Young Female Athletes

The angle specificity of the knee extensor age-related profile was examined in young females (13-19 yr). Twenty-one track & field jumpers, 20 volleyball players and 20 non-active females were separated into the youngest and the oldest age categories, based on the official competitive age categories. The maximum knee extensor isometric torque (T MAX) was measured at 9 knee angles. The relationships between T MAX at the peak of the torque-angle curve and at the other knee angles (angle-angle relationships) were expressed by R2 (%). Statistics included two-way ANOVA for age category differences and curve fitting to R2 joint angle trend lines. Differences between age categories were significant for the volleyball players and the non-active females (p < 0.05). Age category had an angle specific impact on angle-angle relationships in the athletes, with the youngest ones demonstrating greater R2 decrease at the more extended, or more flexed, knee angles. Significant quadratic R2 joint angle trend lines were found in all track & field jumpers (p < 0.05) and, in the youngest only volleyball players (p < 0.05), but not in the non-active females (p > 0.05). In conclusion, the knee extensor profiles of young female athletes show an age-related angle specificity that should be accounted for when treating athletes within the age range examined.

Prolongation of the QTc interval in African children treated for falciparum malaria.

Antimalarial drugs can affect the heart and trigger life-threatening arrhythmias. However, little is known about the frequency with which cardiac abnormalities occur during uncomplicated attacks of malaria. Therefore, we have studied the electrocardiograms of 139 Gambian children with uncomplicated falciparum malaria who were treated with co-artemether, pyrimethamine/sulfadoxine, or chloriquine. The QTc intervals were measured on presentation, and four and eight days after treatment. No significant differences in mean QTc or heart rate were found between children in the three treatment groups on days 0, 4, or 8. After adjustment for the type of antimalarial thearapy in an analysis of variance, the mean (SD) QTc intervals on days 0, 4, and 8 were 402 (22.6), 416 (23.1), and 405 (24.3) msec, respectively. The mean QTc on day 4 was significantly longer than the mean QTc on days 0 or 8 (P < 0.01 in both cases). A quadratic line was fitted for QTc against time for each antimalarial therapy. No significant differences were found between the quadratic lines of the three groups. A weak association was found between QTc and the degree of parasitemia (r = 0.17, P = 0.04) and temperature (r = -0.23, P = 0.01) measured on day 0. The QTcs were measured in 18 children who experienced a second episode of malaria. The changes in QTc observed during second episodes were similar to those observed during the first attack. Changes in QTc in five children who developed severe malaria were similar to those found in the remaining children who did not develop severe malaria. This study indicates that the QTc interval changes during the early phase of malaria and this change is independent of the type of antimalarial therapy given.

Coupling electrical and mechanical outputs of human jaw muscles undertaking multidirectional bite-force tasks

Previous studies have identified both linear and curvilinear relations between increasing bite-force magnitude and the integrated electromyogram (EMG) of jaw-closing muscles. In an attempt to explain the discrepancy, bite forces of incrementally increasing magnitude were produced on the right-hand side in five specified directions by eight humans. Linear regression lines were fitted to normalized EMG activities of the left and right masseter and temporalis muscles against increasing bite-force magnitude in each direction. The grand mean of linear correlation coefficients was 0.79 (±0.11 SD), suggesting an overall linear relation. Each set of individual data was fitted with polynomial lines up to the third order. The ‘best’ fit was selected by statistical significance of coefficients and the least-square analysis of the sum of residues for each fitted line; 62% of individual data-sets were best fitted with linear regression lines, 31% with quadratic lines and the remaining 7% with cubic lines. Repeated analysis of residue variance of the pooled data showed that either a linear or quadratic line fitted every data set except one, for which a cubic line had the best fit. Working-side muscles had significantly larger linear correlation coefficients than corresponding balancing-side muscles for most bite-force directions. Analysis of variance of linear correlation coefficients revealed that the degree of linearity often depended upon the roles played by a muscle in producing forces in different directions. It appears that linearity or non-linearity of the EMG-force relation is a determinant, among other variables, of the direction of the resultant force.

On the Distributional Conditions for a Consumption‐oriented Three Moment CAPM

ABSTRACTIn this paper, we develop sufficient conditions on probability distributions for a three moment (mean, variance, and skewness) consumption‐oriented capital asset pricing model (CAPM) to price correctly a subset of assets. The assumptions that individuals in an allocationally efficient capital market have identical probability beliefs and monotone increasing strictly concave utility functions displaying nonincreasing absolute risk aversion imply an aggregate preference function that exhibits preference for expected return, aversion to variance of return, and preference for positive skewness. For otherwise arbitrary preferences, we show that quadratic characteristic lines are sufficient for a subset of assets to be priced according to a three moment consumption‐oriented CAPM.

Equivalent circuits of binomial‐form nonuniform transmission lines and their application

AbstractAmong various nonuniform distributed‐parameter transmission lines, the exponential line and binomial line can be analyzed by obtaining the rigorous solutions of the telegraph equation. The exponential line in which the line parameters change exponentially has been studied in the past, but the binomial line has not yet been studied systematically because the rigorous solutions for the voltage and current distributions differ depending on the characteristic impedance. In this paper, the rigorous solution of the telegraph equation for 2nth‐order binomial lines is derived and its equivalent circuit is constructed by a cascade connection of uniform distributed‐parameter lines, lumped reactance elements and ideal transformers. Further, the binomial line is made equivalent to the exponential line by equating the characteristic impedances of both lines at the input and output terminals and by letting the order n of the binomial line be infinite. Finally, as an application example, the high‐pass filter consisting of the series lumped capacitance and uniform distributed‐parameter line is constructed by the quadratic binomial lines and series lumped capacitances.