Full Equations Research Articles

Establishment of reference intervals for estimated glomerular filtration rate in apparently healthy adults based on the full age spectrum equation: A single-centre study.

Identifying gender and age-related eGFR trends is crucial for precise renal function assessment. This study aims to analyse eGFR distribution with the full age spectrum (FAS) equation and establish reference intervals based on gender and age in a single-centre cohort. Following the inclusion and exclusion criteria outlined in this study, a total of 24,024 reference individuals were ultimately selected. Using the approach recommended by the CLSI C28-A3 guidelines, we assessed the distribution of eGFR across different gender and age groups. The two-sided nonparametric method (P2.5-P97.5) was applied to establish the eGFR reference intervals for a healthy Chinese population. The eGFR levels in healthy adults exhibited a non-normally distributed pattern. Notably, there were significant differences in eGFR levels between males and females, with females showing a notably higher eGFR level than males. Additionally, eGFR levels demonstrated significant variations across different age groups within both male and female cohorts. As age increased, eGFR showed a significant decline, except in individuals aged 20-29 and 30-39 years. Therefore, reference intervals for eGFR were created based on both gender and age. We established the reference interval for eGFR using the FAS equation, drawing from a large sample population at a single centre. This establishes a potential framework for evaluating renal function in healthy individuals and for diagnosing and treating kidney-related diseases.

Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach

Physics-informed neural networks (PINNs) have emerged as a promising approach for simulating nonlinear physical systems, particularly in the field of fluid dynamics and turbulence modelling. Traditional turbulence models often rely on simplifying assumptions or closed numerical models, which simplify the flow, leading to inaccurate flow predictions or long solve times. This study examines solver constraints in a PINNs solver, aiming to generate an understanding of an optimal PINNs solver with reduced constraints compared with the numerically closed models used in traditional computational fluid dynamics (CFD). PINNs were implemented in a periodic hill flow case and compared with a simple data-driven approach to neural network modelling to show the limitations of a data-driven model on a small dataset (as is common in engineering design). A standard full equation PINNs model with predicted first-order stress terms was compared against reduced-boundary models and reduced-order models, with different levels of assumptions made about the flow to monitor the effect on the flow field predictions. The results in all cases showed good agreement against direct numerical simulation (DNS) data, with only boundary conditions provided for training as in numerical modelling. The efficacy of reduced-order models was shown using a continuity only model to accurately predict the flow fields within 0.147 and 2.6 percentage errors for streamwise and transverse velocities, respectively, and a modified mixing length model was used to show the effect of poor assumptions on the model, including poor convergence at the flow boundaries, despite a reduced solve time compared with a numerically closed equation set. The results agree with contemporary literature, indicating that physics-informed neural networks are a significant improvement in solve time compared with a data-driven approach, with a novel proposition of numerically derived unclosed equation sets being a good representation of a turbulent system. In conclusion, it is shown that numerically unclosed systems can be efficiently solved using reduced-order equation sets, potentially leading to a reduced compute requirement compared with traditional solver methods.

Abstract 4137527: Evaluation of 10-Year Atherosclerotic Cardiovascular Risk Prediction Performance using the PREVENT versus Pooled Cohort Equations in a US Integrated Healthcare System

Background: The American Heart Association published the new PREVENT equations for estimating atherosclerotic cardiovascular disease (ASCVD) risk. Question: Do the PREVENT equations improve risk prediction for 10-year ASCVD compared with the pooled cohort equations (PCEs) in a large diverse population? Aim: To assess ASCVD risk prediction performance of the two PREVENT equations [PREVENT Base, PREVENT Base plus optional predictors including urine albumin-to-creatinine ratio, glycated hemoglobin, and social deprivation index (PREVENT Full)] compared with the PCEs. Methods: We included adults aged 40-75 years without a history of ASCVD or diabetes from Kaiser Permanente Southern California in 2009 and followed them through 2019. Outcome was incident ASCVD defined as myocardial infarction, fatal coronary heart disease, fatal and nonfatal stroke. We compared model discrimination (Harrell’s C), mean calibration (estimated as the ratio of predicted to observed event rates), and calibration curve among the overall population and stratified by sex and race/ethnicity. Results: Of the 559,111 adults (mean age 54, 11% Black, 32% Hispanic), 10,695 developed an ASCVD event during a median follow-up of 10 years. Harrell’s C among the overall population was 0.741 (95% CI 0.736-0.745) for PREVENT Base, 0.743 (0.738-0.748) for PREVENT Full, and 0.741 (0.736-0.746) for the PCEs ( Table ). Compared with the PCEs, both PREVENT equations improved Harrell’s C in men but not in women, and in Black adults but not in other racial/ethnic groups. Both PREVENT equations were well-calibrated (mean calibration ranged 0.83-1.37; calibration slope ranged 0.71-1.28), while the PCEs overestimated 10-year ASCVD risk (mean calibration ranged 1.80-2.20; calibration slope ranged 0.34-0.45) ( Table & Figure ). Conclusion: Compared with the PCEs, both PREVENT Base and Full equations improved calibration in predicting 10-year ASCVD risk, with minimal improvement in discrimination in men and Black adults only.

Exploring Chemistry Confusions and Misconceptions in Nepalese Secondary Education

This study investigates the confusions and misconceptions in chemistry of ninth and tenth graders in Nepal. The primary objectives were to identify misconceptions in various areas of chemistry, determine their sources, and understand teachers' perceptions of these misconceptions. A concurrent mixed-method research design was employed, utilizing questionnaires and interviews for data collection. A random sample of 120 students from Grades 9 and 10 participated in the study. The findings revealed significant misconceptions in areas such as chemical reactions and stability, chemical equations, acids, bases and salts, and the periodic table. The main sources of these misconceptions were identified as common sense, textbooks, and teachers. The study highlights the importance of addressing these misconceptions to improve chemistry education. It provides valuable insights for future research, aiding in the planning and development of theoretical and conceptual frameworks to better understand and mitigate misconceptions in chemistry education.

Global bifurcation for monotone fronts of elliptic equations

We present two results on global continuation of monotone front-type solutions to elliptic PDEs posed on infinite cylinders. This is done under quite general assumptions, and in particular applies even to fully nonlinear equations as well as quasilinear problems with transmission boundary conditions. Our approach is rooted in the analytic global bifurcation theory of Dancer (1973) and Buffoni–Toland (2003), but extending it to unbounded domains requires contending with new potential limiting behavior relating to loss of compactness. We obtain an exhaustive set of alternatives for the global behavior of the solution curve that is sharp, with each possibility having a direct analogue in the bifurcation theory of second-order ODEs.As a major application of the general theory, we construct global families of internal hydrodynamic bores. These are traveling front solutions of the full two-phase Euler equation in two dimensions. The fluids are confined to a channel that is bounded above and below by rigid walls, with incompressible and irrotational flow in each layer. Small-amplitude fronts for this system have been obtained by several authors. We give the first large-amplitude result in the form of continuous curves of elevation and depression bores. Following the elevation curve to its extreme, we find waves whose interfaces either overturn (develop a vertical tangent) or become exceptionally singular in that the flow in both layers degenerates at a single point on the boundary. For the curve of depression waves, we prove that either the interface overturns or it comes into contact with the upper wall.

In-situ observations of the three-dimensional energy cascade rate and Yaglom flux in the Earth’s magnetosheath

Abstract Measuring the energy cascade rate in space plasmas is a challenging task for several reasons. This quantity is (i) inherently three-dimensional (ii) scale-dependent, (iii) anisotropic in the interplanetary plasma, and (iv) requires measurements of plasma parameters in at least four points. Here, it is shown how three of these problems have been addressed by applying the novel lag polyhedra derivative ensemble (LPDE) technique to the magnetospheric multiscale (MMS) mission in the Earth’s magnetosheath. In particular, this technique solves the full vectorial Yaglom equation, handling problem (i), does not require the assumption of isotropy, solving problem (iii), while the application to MMS addresses constraint (iv).

Rydberg atom-based microwave electrometry using polarization spectroscopy

Abstract In this study, we investigated Rydberg atom-based microwave (MW) electrometry using polarization spectroscopy in a room-temperature vapor cell. By measuring Autler-Townes splitting in the electromagnetically induced transparency (EIT) spectrum, we determined that the minimum measurable MW electric field is approximately five times lower than conventional EIT techniques. The results are well reproduced by a full optical Bloch equation model, which takes into account all the hyperfine levels involved. Subsequently, the EIT setup was used to characterize a custom MW cylindrical lens, which increases the field at the focus by a factor of three, decreasing the minimum measurable MW electric field by the same amount. Our results indicate that the combination of polarization spectroscopy and a MW lens may enhance MW electrometry, and may allow its use as a secondary standard.

Effective extensional–torsional elasticity and dynamics of helical filaments under distributed loads

We study slender, helical elastic rods subject to distributed forces and moments. Focussing on the case when the helix axis remains straight, we employ the method of multiple scales to systematically derive an ‘equivalent-rod’ theory from the Kirchhoff rod equations: the helical filament is described as a naturally-straight rod (aligned with the helix axis) for which the extensional and torsional deformations are coupled. Importantly, our analysis is asymptotically exact in the limit of a ‘highly-coiled’ filament (i.e., when the helical wavelength is much smaller than the characteristic lengthscale over which the filament bends due to external loading) and is able to account for large, unsteady displacements. In addition, our analysis yields explicit conditions on the external loading that must be satisfied for a straight helix axis. In the small-deformation limit, we exactly recover the coupled wave equations used to describe the free vibrations of helical coil springs, thereby justifying previous equivalent-rod approximations in which linearised stiffness coefficients are assumed to apply locally and dynamically. We then illustrate our theory with two loading scenarios: (I) a heavy helical rod deforming under its own weight; and (II) the dynamics of axial rotation (twirling) in viscous fluid, which may be considered as a simple model for a bacteria flagellar filament. In both scenarios, we demonstrate excellent agreement with solutions of the full Kirchhoff rod equations, even beyond the formal limit of validity of the ‘highly-coiled’ assumption. More broadly, our analysis provides a framework to develop reduced models of helical rods in a wide variety of physical and biological settings, and yields analytical insight into their elastic instabilities. In particular, our analysis indicates that tensile instabilities are a generic phenomenon when helical rods are subject to a combination of distributed forces and moments.

One-step sparse-matrix method for full wave equation depth migration

By completely solving the second-order full-acoustic wave equation, two-way/full wave equation migration generates images up to arbitrary angles in inhomogeneous media. Full wave equation depth migration (FWDM) necessitates less wavefield storage during imaging, generates clearer imaging results, and has more computational flexibility compared with conventional reverse time migration. Conventionally, FWDM uses Runge-Kutta or two explicit one-way operators to extrapolate the data, which involves either a multirecursive process or complex square root computations of the Helmholtz operator, causing implementation complexities and inconveniences. To overcome these challenges, a novel algorithm called the one-step sparse-matrix method for FWDM (OSM-FWDM) is developed and executed. This method involves a straightforward calculation of the full wave equation propagator through a Taylor expansion and using the so-called precise integration method. The computational efficiency can be significantly improved by using sparse-matrix multiplication in the implementation of wavefield extrapolation. Building upon that, the method serves as a basic solution complemented by FWDM, offering straightforward, efficient, and easy coding characteristics. Our OSM-FWDM method is simpler and faster compared with conventional FWDM, all while maintaining imaging accuracy. In addition, a new solution that uses an extended velocity model to remove source-related artifacts in FWDM is developed and illustrated. These improvements are demonstrated through a series of numerical examples and a real data application.

Black hole-neutron star mergers in Einstein-scalar-Gauss-Bonnet gravity

Gravitational wave observations of black hole-neutron star binaries, particularly those where the black hole has a lower mass compared to other observed systems, have the potential to place strong constraints on modifications to general relativity that arise at small curvature length scales. Here we study the dynamics of black hole-neutron star mergers in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity, a representative example of such a theory, by numerically evolving the full equations of motion. We consider quasi-circular binaries with different mass-ratios that are consistent with recent gravitational wave observations, including cases with and without tidal disruption of the star, and quantify the impact of varying the coupling controlling deviations from general relativity on the gravitational wave signal and scalar radiation. We find that the main effect on the late inspiral is the accelerated frequency evolution compared to general relativity, and that—even considering Gauss-Bonnet coupling values approaching those where the theory breaks down—the impact on the merger gravitational wave signal is mild, predominately manifesting as a small change in the amplitude of the ringdown. We compare our results to current post-Newtonian calculations and find consistency throughout the inspiral. Published by the American Physical Society 2024

Relations of coping strategies and cognitive emotion regulation to Chinese children's academic achievement goals and academic performance.

Social-emotional skills (e.g., emotion regulation) influence a variety of academic outcomes among children. This study examined the relations of coping strategies and cognitive emotion regulation (CER) to academic achievement goals and academic performance among Chinese children (N = 401, age M = 10.52 years). Full Structural Equation Modeling (SEM) analysis showed that children's use of active coping strategies was positively associated with their endorsement of performance approach and mastery avoidance goals. Avoidant and support-seeking coping strategies were not associated with any outcome variables. Maladaptive CER was positively associated with performance approach, performance avoidance, and mastery avoidance goals and negatively associated with academic performance; adaptive CER was positively associated with mastery approach goals but not associated with other outcome variables. The current study provided some preliminary evidence to indicate that active coping strategies, maladaptive CER, and adaptive CER were associated with academic achievement goals and academic performance among Chinese children. Although maladaptive CER was not used as often as adaptive CER by Chinese children, the more they used maladaptive CER, the more likely they were to have academic achievement goals that focused on things other than learning itself, whereas the more Chinese children used adaptive CER, the more likely they were to set an achievement goal to master the knowledge. Therefore, in teaching practices or intervention planning, decreasing maladaptive CER strategies may be as important as cultivating adaptive CER strategies to facilitate academic success among Chinese children.

Mathematical modeling of bioactive glass degradation

Bioactive glasses (BGs) are promising for bone tissue engineering (BTE). Mathematical modeling is a powerful tool for understanding BTE scaffold degradation. We developed mathematical functions based on chemical reaction equations governing dissolution and diffusion processes to model the degradation of 45S5 BGs. An empirical mathematical model was employed to characterize the formation process of hydroxycarbonate apatite (HCA). Two sets of numerical simulations with BG powder and bulk samples immersed in simulated body fluid were compared with in vitro experiments to validate and parameterize the model. The model could accurately predict BG degradation and HCA formation. Our findings indicate that the proposed parameters K1=2600 mm/(μmol·h), K2=2.0 mm/h and K3=0.001 mm/h are suitable for simulating the degradation of silicate-based BGs, specifically 45S5 BG. The proposed model successfully predicted the degradation behavior and subsequent HCA formation over 21 days. The proposed mathematical model serves as a valuable tool for designing degradable BG-containing scaffolds.

Nonlinear studies of modifications to general relativity: Comparing different approaches

Studying the dynamical, nonlinear regime of modified theories of gravity remains a theoretical challenge that limits our ability to test general relativity. Here we consider two generally applicable, but approximate, methods for treating modifications to full general relativity that have been used to study binary black hole mergers and other phenomena in this regime, and compare solutions obtained by them to those from solving the full equations of motion. The first method evolves corrections to general relativity order by order in a perturbative expansion, while the second method introduces extra dynamical fields in such a way that strong hyperbolicity is recovered. We use shift-symmetric Einstein-scalar-Gauss-Bonnet gravity as a benchmark theory to illustrate the differences between these methods for several spacetimes of physical interest. We study the formation of scalar hair about initially nonspinning black holes, the collision of black holes with scalar charge, and the inspiral and merger of binary black holes. By directly comparing predictions, we assess the extent to which those from the approximate treatments can be meaningfully confronted with gravitational wave observations. We find that the order-by-order approach cannot faithfully track the solutions when the corrections to general relativity are non-negligible. The second approach, however, can provide consistent solutions, provided the timescale over which the dynamical fields are driven to their target values is made short compared to the physical timescales. Published by the American Physical Society 2024

Effect of high-temperature annealing on elemental distribution in CSP-produced automotive steel billets

The distribution of C, Si, Mn, P and S in Q&P 980 automotive steel billets produced via the Compact Strip Production (CSP) process was investigated using Electron Probe Microanalysis (EPMA). The segregation ratio of each element was calculated. A diffusion kinetics model was established using the finite element method, and the chemical potential equations of different elements were used as the driving conditions for diffusion. Fick's law was applied to numerically calculate the diffusion behaviour and final concentration distribution of C, Si and Mn during the annealing process at 1100 °C. Results indicate that element segregation in the as-cast billet before annealing decreases gradually from the surface to the core. After annealing, the segregation ratio of elements is reduced, leading to a more homogeneous elemental distribution. It was calculated that the diffusion of C at 1100 °C completes in about 10 s, with micrometer-level long-range diffusion occurring in a shorter period. However, the concentration of Mn does not reach equilibrium at the austenite interface even after 20 h of diffusion at 1100 °C.

Ultrafast superconducting qubit readout with the quarton coupler.

Fast, high-fidelity, and quantum nondemolition (QND) qubit readout is an essential element of quantum information processing. For superconducting qubits, state-of-the-art readout is based on a dispersive cross-Kerr coupling between a qubit and its readout resonator. The resulting readout can be high fidelity and QND, but readout times are currently limited to the order of 50 nanoseconds due to the dispersive cross-Kerr of magnitude 10 megahertz. Here, we present a readout scheme that uses the quarton coupler to facilitate a large (greater than 200 megahertz) cross-Kerr between a transmon qubit and its readout resonator. Full master equation simulations of the coupled system show a 5-nanosecond readout time with greater than 99% readout fidelity and greater than 99.9% QND fidelity. The quartonic readout circuit is experimentally feasible and preserves the coherence properties of the qubit. Our work reveals a path for order of magnitude improvements of superconducting qubit readout by engineering nonlinear light-matter couplings in parameter regimes unreachable by existing designs.

Construction of superconducting dome and emergence of quantum critical region in holography

In this work, we investigate an extended model of holographic superconductor by a nonlinear electrodynamic interaction coupled to a complex scalar field. This nonlinear interaction term can make a quantum phase transition at zero temperature with finite charge carrier density. By solving full equations of motion, we can construct various shapes of the superconducting phase in the phase diagram. With a specific choice of interaction coefficients, we can construct a phase diagram with a superconducting dome. Also, we find a new geometric solution inside the superconducting dome, which turns out to be a Lifshitz-type geometry. This geometry is characterized by a dynamical critical exponent, which plays a crucial role near the quantum critical point. We refer to this region of the phase diagram as a quantum critical region. Published by the American Physical Society 2024

Differentiation of puerarin chelate from salt by phase solubility test

Different from salt, metal chelate is a novel state of drug constructed by more separate coordinate bonds to form a chelating circle. Due to their composition similarity, it is hard to distinguish them except identifying ionic bond (i.e., salt) or coordinate bond (i.e., chelate) in the single crystal structure. In this study, sodium chelate (CDCC No: 1865670) and lithium salt (CDCC No: 2161617) of puerarin (PUE) was prepared. In addition to difference in single crystal structure, it was found that they showed totally different phase solubility behaviors: lithium salt demonstrated a typical inverse proportion curve as other common salts, while sodium chelate exhibited disordered scatters. However, when incorporating the unit PUE-Na complex in solution state and complexation constant K11 in chemical equation, the scatters in phase solubility diagram of chelate could be well fitted and the value of K11 was dramatically higher with orders of magnitude than the dissociation constant Kc; while processing phase solubility curve of lithium salt by incorporating complex item, it could not well match the curve at all. PUE sodium chelate is more likely to be a weak electrolyte with partial dissociation, while PUE lithium salt acted as a strong electrolyte with complete dissociation. The phase solubility test would be served as a surrogate tool for differentiation of chelates from salts when single crystal was not available.

Validation of prediction capability of operating space for plasma initiation in MAST-U

Abstract DYON is a plasma initiation modelling code that solves the differential equation system of the full circuit equations (plasma current, active coil currents and eddy currents in full passive structures) and 0D global energy and particle balance equations[1]. In order to test the capability of the full electromagnetic plasma initiation model to predict individual discharges in experiments and thus the operating space in the device, a dedicated experimental database was built in MAST-U by scanning the prefilled gas pressure p0 and the induced loop voltage Vloop . In the experimental operating space of p0 and Vloop the lower and the upper limits of p0 are determined by the plasma breakdown failure and the plasma burn-through failure, respectively. The lower limit of Vloop is determined by the plasma burn-through failure. By directly reading the control room data used in each discharge (i.e. currents in the solenoid, poloidal field coils, and toroidal field coils, p0 , and gas puffing rate), the full electromagnetic DYON consistently predicted the failed breakdown, failed burn-through, and successful plasma initiation discharges in the experimental database, demonstrating its capability to predict the operating space for inductive plasma initiation. The Paschen curve calculated with the effective connection length in MAST-U indicates a much higher p0 required for plasma breakdown than the experimental data, indicating that individual field line evaluation is necessary to calculate the quantitative requirements for Townsend breakdown. The demonstration in this paper shows that the full electromagnetic DYON could be a useful simulation tool to assess the feasibility of inductive plasma initiation and to optimise operating scenarios in future devices. [1] Hyun-Tae Kim 2022 Nuclear Fusion 62 126012

Derivation of full range vapor pressure equation from an arbitrary point

An equation was proposed to obtain the full range of vapor pressures (VPs) for a substance at an arbitrary point of VP data. The basic model is a vapor pressure equation in the form of a reduced Antoine equation derived from the van der Waals equation. Here, Antoine constant C is defined as c by dividing it into gas constant and critical temperature, and is expressed as a polynomial function of reduced temperature. Previously, the exponents were integers, but have been improved to real numbers. Edmister’s formula is a special case in which the Antoine constant C divided by the critical temperature in Chen’s equation is 0. Since this is equivalent to polynomial of c being zero, the intercept can be set to zero. The results, estimated using the derived equation, were compared with VP data for 76 substances. The error rate of the equation using the acentric factor as a variable was 0.49%. This was lower than the 0.50% error rate of the Lee-Kesler method. Meanwhile, by using the correlation between the coefficients, the VP equation can be derived at any one point of VP data other than the acentric factor. For 76 substances, the equation derived from the corresponding VPs at reduced temperatures of 0.25 ∼ 0.95 in increments of 0.05 showed a mean error rate of 0.68%. This can be considered an accuracy equivalent to the Lee-Kesler method, which has the limitation of deriving a VP equation only at the reduced temperature of 0.7.

Random matrix model of the Virasoro minimal string

The model of two dimensional quantum gravity defining the Virasoro minimal string, presented recently by Collier, Eberhardt, Mühlmann, and Rodriguez, was also shown to be perturbatively (in topology) equivalent to a random matrix model. An alternative definition is presented here, in terms of double-scaled orthogonal polynomials, thereby allowing direct access to nonperturbative physics. Already at leading order, the defining string equation’s properties yield valuable information about the nonperturbative fate of the model, confirming that the case (c=25,c^=1) (central charges of spacelike and timelike Liouville sectors) is special, by virtue of sharing certain key features of the N=1 supersymmetric JT gravity string equation. Solutions of the full string equation are constructed using a special limit, and the (Cardy) spectral density is completed to all genus and beyond. The distributions of the underlying discrete spectra are readily accessible too, as is the spectral form factor. Some examples of these are exhibited. Published by the American Physical Society 2024