Single-valued Parameters Research Articles

Radiative acceleration calculation methods and abundance anomalies in Am stars

Atomic diffusion with radiative levitation is a major transport process to consider to explain abundance anomalies in Am stars. Radiative accelerations vary from one species to another, yielding different abundance anomalies at the stellar surface. Radiative accelerations can be computed using different methods: some evolution codes use an analytical approximation, while others calculate them from monochromatic opacities. We compared the abundance evolutions predicted using these various methods. Our models were computed with the Toulouse-Geneva evolution code, in which both an analytical approximation (the single-valued parameter method) and detailed calculations from Opacity Project (OP) atomic data are implemented for the calculation of radiative accelerations. The time evolutions of the surface abundances were computed using macroscopic transport processes that are able to reproduce observed Am star surface abundances in presence of atomic diffusion, namely an ad hoc turbulent model or a global mass loss. The radiative accelerations obtained with the various methods are globally in agreement for all the models below the helium convective zone, but can be much greater between the bottom of the hydrogen convective zone and that of helium. The time evolutions of the surface abundances mostly agree within the observational error, but the abundance of some elements can exceed this error for the least massive mass-loss model. The gain in computing time from using analytical approximations is significant compared to sequential calculations from monochromatic opacities for the turbulence models and for the least massive wind model; the gain is small otherwise. Test calculations of turbulence models with the tabulated OPAL opacities yield quite similar abundances as OP for most elements but in a much shorter time, meaning that determining Am star parameters can be done using a two-step method.

Information transfer rate in BCIs: Towards tightly integrated symbiosis

Objective:The information transmission rate (ITR), or effective bit rate, is a popular and widely used information measurement metric, particularly popularized for SSVEP-based Brain–Computer (BCI) interfaces. By combining speed and accuracy into a single-valued parameter, this metric aids in the evaluation and comparison of various target identification algorithms across different BCI communities. In order to calculate ITR, it is customary to assume a uniform input distribution and an oversimplified channel model that is memoryless, stationary, and symmetrical in nature with discrete alphabet sizes. To accurately depict performance and inspire an end-to-end design for futuristic BCI designs, a more thorough examination and definition of ITR is therefore required. Approach:We model the symbiotic communication medium, hosted by the retinogeniculate visual pathway, as a discrete memoryless channel and use the modified capacity expressions to redefine the ITR. We leverage a result for directed graphs to characterize the relationship between the asymmetry of the transition statistics and the ITR gain due to the new definition, leading to potential bounds on data rate performance. Main Results:On two well-known SSVEP datasets, we compared two cutting-edge target identification methods. Results indicate that the induced DM channel asymmetry has a greater impact on the actual perceived ITR than the change in input distribution. Moreover, it is demonstrated that the ITR gain under the new definition is inversely correlated with the asymmetry in the channel transition statistics. Individual input customizations are further shown to yield perceived ITR performance improvements. Finally, an algorithm is proposed to find the capacity of binary classification and further discussions are given to extend such results to multi-class case through ensemble techniques. Significance:We anticipate that the results of our study will contribute to the characterization of the highly dynamic BCI channel capacities, performance thresholds, and improved BCI stimulus designs for a tighter symbiosis between the human brain and computer systems while ensuring the efficient utilization of the underlying communication resources.

Two-dimensional growth of incompressible and compressible soft biological tissues

Soft tissues have the ability of growth as a response to some especial changes of their environment. The aim of this work is to develop a non-linear finite element formulation for two-dimensional growth of soft tissues. The formulation is derived in Total Lagrangian (TL) framework. Moreover, the growth variable is considered as a single-valued scalar parameter known as growth multiplier. To deal with evolution equation resulting from the growth parameter, an implicit midpoint scheme is employed. Furthermore, a method is presented for compressible hyperelastic material models, and the formulas can be applied to incompressible and compressible, isotropic and anisotropic tissues. Finally, to investigate the performance of the proposed model, some examples are provided and compared to those available in the literature.

Convolutional Neural Network Combined With Stochastic Parallel Gradient Descent to Decompose Fiber Modes Based on Far-Field Measurements

Modal decomposition (MD) of fiber modes based on direct far-field measurement combining the convolutional neural network (CNN) with a stochastic parallel gradient descent (SPGD) algorithm is investigated both numerically and experimentally. For obtaining the modal coefficients of fiber modes guided in a large-mode-area fiber, the fiber modes are decomposed into a finite number of Hermite gaussian modes, the initial conditions of the modal coefficients are obtained through the CNN, and further optimization of them are carried out through the SPGD. The ambiguity problem that may happen in the CNN owing to the existence of the pair-beam field is resolved by properly labelling the phase differences with a single-valued parameter set in consideration of the mode-order indices. The feasibility and effectiveness of the proposed MD method is verified both numerical simulations and experimental demonstrations with both recorded image data and online real-time image data. The correlation error incurred by the proposed method is below 6.6×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> and 8.7×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> in the numerical simulations and the experimental demonstrations, respectively. The online real-time operation of the proposed method is also experimentally demonstrated at a decomposing rate of ∼2 Hz.

Single-Flow Batteries Leveraging Multiphase Electrolytes

The share of electricity generated from renewable sources is growing rapidly, and thus grid-scale battery storage is becoming more prevalent. Aqueous redox flow batteries have the potential to provide safe and scalable energy storage, but the high cost of storage, particularly the membrane and balance of plant costs, has inhibited commercialization. The recently developed single-flow battery leveraging a multiphase electrolyte promises a low-cost system [1], as it is membraneless and uses only one tank and flow loop, but suffers from low Coulombic efficiency [1]. To unlock the potential of such a system, the interplay between interphase mass transport, multiphase flow phenomena, and battery performance must be unraveled. Here, we will compare our previously developed theoretical battery model derived from a boundary layer analysis [2,3] to results from a dedicated experimental program [4]. This led to several key findings, including that our battery operates in a regime characterized by a high Stanton number, and that our analytical solutions led to excellent predictions in various operational regimes when using the interphase mass transport coefficient as a single-valued fitting parameter [4]. In other regimes, such as at low electrolyte velocity, results indicate that gravity acting on the denser polybromide phase played a significant role, and progress towards incorporating gravitational effects into models will be discussed [4]. Figure 1: Schematic of a discharging single-flow battery leveraging a multiphase flow electrolyte. The flow consists of a continuous, bromine-poor aqueous phase and dispersed, bromine-rich polybromide phase. Bromine in the polybromide phase is largely electrochemically inactive, thus such an electrolyte enables membraneless operation by limiting the crossover of bromine to the zinc anode.

Quantifying coal rib stability and support requirements using bonded block modeling and reliability analysis based on the random set theory

An apparent flaw in geomechanical analysis of rock structures is the application of single value parameters as input to numerical models. A known but often overlooked characteristic of the rock mass is its inherent strong property variability. In conventional reliability analysis of rock mechanics, subjective assumptions are often made on the probability density function of parameters because, in many cases, the results of geotechnical investigations are set-valued rather than being precise and point-valued. On the other hand, imprecise probability theories such as the Random Set Theory could be considered a possible attractive candidate to employ in these analyses. In this study, the Random Set Theory in combination with the Bonded Block Modeling (RS-BBM) approach is employed to demonstrate its practical applicability in determining coal rib stability and support requirements. Sensitivity analysis of the BBM input parameters is conducted. The uncertainties of the geomechanical parameters of the BBM contacts, which control model behavior, are considered in the reliability analysis model. The analyses were performed in UDEC, and the strength reduction method was used to evaluate rib stability. It is shown that RS-BBM is an efficient tool to determine the most likely bounds of coal rib performance. A method combining the RS-BBM approach with empirical methods is also described to illustrate its practical application.

Modelling of the scandium abundance evolution in AmFm stars

Context. Scandium is a key element of the Am star phenomenon since its surface under-abundance is one of the criteria that characterise such stars. Thanks to the availability of a sufficiently complete set of theoretical atomic data for this element, reliable radiative accelerations for Sc can now be computed, which allows its behaviour under the action of atomic diffusion to be modelled. Aims. We explore the required conditions, in terms of mixing processes or mass loss, for our models to reproduce the observed surface abundances of Sc in Am stars. Methods. The models are computed with the Toulouse-Geneva evolution code, which uses the parametric single-valued parameter method for the calculation of radiative accelerations. Fingering mixing is included, using a prescription that comes from 3D hydrodynamical simulations. Other parameter-dependent turbulent mixing processes are also considered. A global mass loss is also implemented. Results. When no mass loss is considered, the observed abundances of Sc are rather in favour of the models whose superficial layers are fully mixed down to the iron accumulation zone, although other mixing prescriptions are also able to reproduce the observations for the most massive model presented here (2.0 M⊙). The models including mass loss with rates in the range of [10−13; 10−14] M⊙ yr−1 are compatible with some of the observations, while other observations suggest that the mass-loss rate could be lower. The constraints brought by the modelling of Sc are consistent with those derived using other chemical elements.

Single-flow multiphase flow batteries: Experiments

The share of electricity generated from renewable sources is growing rapidly, and thus grid-scale battery storage is becoming more prevalent. Aqueous redox flow batteries have the potential to provide safe and scalable energy storage, but the high cost of storage, particularly the membrane and balance of plant costs, has inhibited commercialization. The recently developed single-flow battery leveraging a multiphase electrolyte promises a low-cost system, as it is membraneless and uses only one tank and flow loop, but suffers from low Coulombic efficiency. To unlock the potential of such a system, the interplay between interphase mass transport, multiphase flow phenomena, and battery performance must be unraveled. Here, we compare our previously developed theoretical battery model derived from a boundary layer analysis to results from a dedicated experimental program. This led to several key findings, including that our battery operates in a regime characterized by a high Stanton number, and that our analytical solutions led to excellent predictions in various operational regimes when using the interphase mass transport coefficient as a single-valued fitting parameter. In other regimes, such as at low electrolyte velocity, results indicate that gravity acting on the denser polybromide phase played a significant role, and thus gravitational effects should be incorporated in future models.

Front Cover: Uncertainty Quantification of Reactivity Scales (ChemPhysChem 8/2022)

The Front Cover image contrasts single-valued reactivity parameters and distributions thereof. The latter allow chemists to better assess relative reactivity and, therefore, support synthesis planning (artwork by Prof. Ricardo A. Mata). More information can be found in the Research Article by Jonny Proppe and Johannes Kircher.

Parameter Estimation Using Adaptive Observations Toward Maximum Total Variance Reduction With Ensemble Adjustment Kalman Filter

In real applications, one common issue of parameter estimation using ensemble-based data assimilation methods is the accumulation of sampling errors when a large number of observations are used to update single-value parameters. In this article, a new parameter estimation method which assimilates a large number of observations to estimate the states while assimilates adaptive observations to update the parameters is introduced. The observations resulting in maximum total variance reduction to the parameter ensembles are identified to perform parameter estimation. To validate this new method, the two-scale Lorenz-96 model is used to generate true states, while a parameterized one-scale Lorenz-96 model is used to perform state and parameter estimation experiments. The comparison between state estimation and parameter estimation with fixed or adaptive observations shows the new method can be more effective in estimating the model parameters and providing more accurate analyses. This method also shows its potential to be used in the data assimilation with large general circulation models to better produce reanalyzes.

Mode I crack growth in paper exhibits three stages of strain evolution in reaching steady-state

The mechanical properties of wood fiber-based, commercial papers and metal foils are qualitatively similar, and their plane stress, Mode I crack growth resistances have not been reliably correlated with single-valued fracture mechanics parameters for centimeter-scale specimens. Experimentally-measured crack tip strain fields of Mode I cracks growing in commercial paper were used to define a three-stage, steady-state crack growth mechanism. Immediately upon loading, the net sections ahead of the cracks yielded. As the cracks began to grow, well-defined zones of (incremental) active plasticity (ZAPs) formed within the yielded ligaments. Cracks transitioned to steady-state growth with an average characteristic stress, σc, of 20.9MPa. In contrast to metallic foils, the characteristic stress in steady-state cracks in paper was offset by 8.3MPa due to a 1.9mm fiber bridging zone that scaled with the average fiber agglomerate (floc) size. The fiber network structure also induced a large, reversed steady-state zone in the crack wakes. While reversed ZAPS were previously predicted by numerical models of plane strain Mode I and III cracks under small-scale yielding conditions, they were never observed experimentally and were neglected. The types and evolution of the cumulative and incremental plastic zones in paper defined appropriate paths for steady-state J-integral calculations.

Quantifying Distributions of Parameters for Cardiac Action Potential Models Using the Hamiltonian Monte Carlo Method.

Cardiac action potential (AP) models are typically given with a single set of parameter values; however, this approach does not consider variability and uncertainty across individuals and experimental conditions. As an alternative to single-value parameter fitting, we sought to use a Bayesian approach, the Hamiltonian Monte Carlo (HMC) algorithm, to find distributions of physiological parameter values for cardiac AP models across a range of cycle lengths (CLs) and dynamics. To assess HMC's accuracy for cardiac data, we applied it to synthetic APs from the Mitchell-Shaeffer (MS) and Fenton-Karma (FK) models with added noise over a range of physiological CLs, some of which included alternans. To show the applicability of HMC to experimental data, we calculated parameter distributions for both models using micro-electrode recordings of zebrafish APs from a range of CLs. For synthetic APs generated from three CLs using the MS (FK) models, HMC produced unimodal quasi-symmetric distributions for all five (13) parameters. APs generated by setting all parameters in the MS (FK) model to the modes of their corresponding marginal distributions yielded errors in voltage traces below 5.0% (0.6%). We also obtained distributions for the MS (FK) model parameters using zebrafish data to construct the first minimal model of the zebrafish AP, with voltage trace errors below 4.8% (3.4%). We have shown that HMC can identify not only a single set of parameter values but also viable distributions for cardiac AP model parameters using synthetic and experimental data. Because HMC generates samples from the parameter distributions based on input data, it can produce families of parameterizations that can be used in population-based modeling approaches without the need for rejecting a large number of randomly generated candidate parameterizations. HMC also has the potential to provide quantitative measures of spatial/individual variability and uncertainty.

Riemann–Hilbert approach for a Schrödinger-type equation with nonzero boundary conditions

In this paper, we focus on investigating a nonlinear Schrödinger-type equation with nonzero boundary at infinity. An appropriate two-sheeted Riemann surface is introduced to map the original spectral parameter [Formula: see text] into a single-valued parameter [Formula: see text]. Starting from the Lax pair of the Schrödinger-type equation, we derive its Jost solutions with nonzero boundary conditions, and further analyze the asymptotic behaviors, analyticity, the symmetries of the Jost solutions and the corresponding spectral matrix. An associated matrix Riemann–Hilbert (RH) problem associated with the problem of nonzero boundary conditions is subsequently presented, and a formulae of [Formula: see text]-soliton solutions for the Schrödinger-type equation by solving the matrix RH problem. As an application of the [Formula: see text]-soliton formulae, we present two kinds of one-soliton solutions and three kinds of two-soliton solutions according to different distributions of spectral parameters, and dynamical features of those solutions are also further analyzed.

Riemann–Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions

The modified nonlinear Schrödinger (NLS) equation was proposed to describe the nonlinear propagation of the Alfven waves and the femtosecond optical pulses in a nonlinear single-mode optical fiber. In this paper, we present the inverse scattering transform for the modified NLS equation iut+uxx+2|u|2u+i1α(|u|2u)x=0,α>0,with nonvanishing boundary values at infinity u(x,t)∼u±e−4iα2t+2iαx,x→±∞.An appropriate two-sheeted Riemann surface is introduced to map the original spectral parameter k into a single-valued parameter z. The direct scattering problem is shown to be well posed for potentials u such that u−u±∈L1,2(R±), for which existence and analyticity properties of eigenfunctions and scattering data are established. Their asymptotic behaviors and the symmetries are analyzed in details based on the Lax pair for the modified NLS equation. Then the inverse scattering problem is formulated as a Riemann–Hilbert (RH) problem associated with the problem of nonzero boundary conditions. The existence and uniqueness of solution for the mixed RH problem for t>0 are strictly proved by decomposing it into a pure RH problem and a scattering RH problem. The N-soliton solutions for the modified NLS equation are obtained via a reconstruction formulae between solution of the modified NLS equation and the solution of above mixed RH problem. As an illustrate example of N-soliton formula, for N=1 and N=2, two kinds of one-soliton solutions and three kinds of two-soliton solutions are explicitly presented, respectively according to different distribution of the spectrum. The dynamical feature of those solutions are characterized in the particular case with a quartet of discrete eigenvalues. It is shown that distribution of the spectrum and non-vanishing boundary also affect feature of soliton solutions. Finally, we analyze the differences between our results and those on zero boundary case.

2D fourier transform for global analysis and classification of meibomian gland images

In recent years, significant progress has been made in the Meibography technique resulting from the use of advanced image analysis methods allowing a quantitative description of the Meibomian gland structures. Many objective measures of gland distortion were previously proposed allowing for user-independent classification of acquired gland images. However, due to the complicated nature of gland deformation, none of the single-valued parameters can fully describe the analyzed gland images. There is a need to increase the number of descriptive factors, selectively sensitive to different gland features. Here we show that global 2D Fourier transform analysis of infra-red gland images provides values of two new such parameters: mean gland frequency and anisotropy in gland periodicity. We show that their values correlate with gland dysfunction and can be used to automatically categorize the images into the three subjective classes (healthy, intermediate and unhealthy). We also demonstrated that classification performance can be improved by dimensionality reduction approach using principal component analysis.

Inverse scattering transform for the Gerdjikov–Ivanov equation with nonzero boundary conditions

In this article, we focus on the inverse scattering transform for the Gerdjikov–Ivanov equation with nonzero boundary at infinity. An appropriate two-sheeted Riemann surface is introduced to map the original spectral parameter k into a single-valued parameter z. Based on the Lax pair of the Gerdjikov–Ivanov equation, we derive its Jost solutions with nonzero boundary. Further asymptotic behaviors, analyticity and the symmetries of the Jost solutions and the spectral matrix are in detail derived. The formula of N-soliton solutions is obtained via transforming the problem of nonzero boundary into the corresponding matrix Riemann–Hilbert problem. As examples of N-soliton formula, for $$N=1$$ and $$N=2$$ , respectively, different kinds of soliton solutions and breather solutions are explicitly presented according to different distributions of the spectrum. The dynamical features of those solutions are characterized in the particular case with a quartet of discrete eigenvalues. It is shown that distribution of the spectrum and non-vanishing boundary also affect feature of soliton solutions.

An improved parametric method for evaluating radiative accelerations in stellar interiors

ABSTRACT The single-valued parameter (SVP) method is a parametric method that offers the possibility of computing radiative accelerations in stellar interiors much faster than other methods. It has been implemented in a few stellar evolution numerical codes for about a decade. In this paper, we describe improvements we have recently brought in the process of preparing, from atomic/opacity data bases, the SVP tables that are needed to use the method, and their extension to a larger stellar mass domain (from 1 to 10 solar mass) on the main sequence. We discuss the validity domain of the method. We also present the website from where new tables and codes can be freely accessed and implemented in stellar evolution codes.

The Riemann–Hilbert approach to focusing Kundu–Eckhaus equation with non-zero boundary conditions

In this paper, we investigate the focusing Kundu–Eckhaus equation with non-zero boundary conditions. An appropriate two-sheeted Riemann surface is introduced to map the spectral parameter [Formula: see text] into a single-valued parameter [Formula: see text]. Starting from the Lax pair of Kundu–Eckhaus equation, two kinds of Jost solutions are constructed. Further, their asymptotic, analyticity, symmetries as well as spectral matrix are analyzed in detail. It is shown that the solution of the Kundu–Eckhaus equation with non-zero boundary conditions can be characterized with a matrix Riemann–Hilbert problem. Then a formula of [Formula: see text]-soliton solutions is derived by solving the Riemann–Hilbert problem. As applications of the [Formula: see text]-soliton formula, the first-order explicit soliton solutions with different dynamical features are obtained and analyzed.

Describing the Failure Characteristics of Concrete Derived from Standard ASTM Testing—An Illustration of Full-Field Measurement Using 3D Digital Image Correlation

Abstract Concrete is one of the most recognized materials in civil infrastructure with a long history of applications, but its nonhomogeneous nature and complex multi-phase interactions across different dimensional scale levels have always presented a challenge for describing its behavior. In practice, it is assumed that the bulk material is approximately homogeneous while the behavior can be described using empirical models developed based on series of experimental tests. Over time, most of these experimental methods have been standardized, with most yielding a single-value parameter to define the overall response characteristic of the materials. However, the majority of these methods are not well suited to characterize local features, which often govern the failure characteristics of such brittle material. Recent advances in noncontact full-field measurement technologies, such as digital image correlation (DIC), have provided the opportunity to revisit this complex behavior and comprehensively characterize the behavior of concrete at specimen scale level. In this manuscript, 3D-DIC is used to evaluate the behavior of two conventional concrete mixes tested according to a series of ASTM standard tests. The experimental study consisted of a series of concrete tests including compression, modulus of elasticity, split tensile, and flexural tests. Results from this investigation demonstrated the suitability of the DIC technique for characterizing the full-field behavior of concrete subjected to various states of stresses and providing a mechanism to understand the linkage between local behavioral features and corresponding failure characteristics. Comparisons of experimental results to those obtained from theoretical predictions also highlighted the shortcomings associated with these existing theoretical approaches in describing the brittle nature of concrete. Results from this investigation provided a foundation for improving the current knowledge base regarding the behavioral features of conventional concrete materials and provides a framework for efficiently describing the behavior of the next generations of innovative high-performance cementitious composites.

Basic Features of the Analysis of Germination Data with Generalized Linear Mixed Models

Germination data are discrete and binomial. Although analysis of variance (ANOVA) has long been used for the statistical analysis of these data, generalized linear mixed models (GzLMMs) provide a more consistent theoretical framework. GzLMMs are suitable for final germination percentages (FGP) as well as longitudinal studies of germination time-courses. Germination indices (i.e., single-value parameters summarizing the results of a germination assay by combining the level and rapidity of germination) and other data with a Gaussian error distribution can be analyzed too. There are, however, different kinds of GzLMMs: Conditional (i.e., random effects are modeled as deviations from the general intercept with a specific covariance structure), marginal (i.e., random effects are modeled solely as a variance/covariance structure of the error terms), and quasi-marginal (some random effects are modeled as deviations from the intercept and some are modeled as a covariance structure of the error terms) models can be applied to the same data. It is shown that: (a) For germination data, conditional, marginal, and quasi-marginal GzLMMs tend to converge to a similar inference; (b) conditional models are the first choice for FGP; (c) marginal or quasi-marginal models are more suited for longitudinal studies, although conditional models lead to a congruent inference; (d) in general, common random factors are better dealt with as random intercepts, whereas serial correlation is easier to model in terms of the covariance structure of the error terms; (e) germination indices are not binomial and can be easier to analyze with a marginal model; (f) in boundary conditions (when some means approach 0% or 100%), conditional models with an integral approximation of true likelihood are more appropriate; in non-boundary conditions, (g) germination data can be fitted with default pseudo-likelihood estimation techniques, on the basis of the SAS-based code templates provided here; (h) GzLMMs are remarkably good for the analysis of germination data except if some means are 0% or 100%. In this case, alternative statistical approaches may be used, such as survival analysis or linear mixed models (LMMs) with transformed data, unless an ad hoc data adjustment in estimates of limit means is considered, either experimentally or computationally. This review is intended as a basic tutorial for the application of GzLMMs, and is, therefore, of interest primarily to researchers in the agricultural sciences.