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At least 685 records · Page 38

Chemometric analysis for extraction of individual fluorescence spectrum and lifetimes from a target mixture

The present invention is a system for chemometric analysis for the extraction of the individual component fluorescence spectra and fluorescence lifetimes from a target mixture. The present invention combines a processor with an apparatus for generating an excitation signal to transmit at a target mixture and an apparatus for detecting the emitted signal from the target mixture. The present invention extracts the individual fluorescence spectrum and fluorescence lifetime measurements from the frequency and wavelength data acquired from the emitted signal. The present invention uses an iterative solution that first requires the initialization of several decision variables and the initial approximation determinations of intermediate matrices. The iterative solution compares the decision variables for convergence to see if further approximation determinations are necessary. If the solution converges, the present invention then determines the reduced best fit error for the analysis of the individual fluorescence lifetime and the fluorescence spectrum before extracting the individual fluorescence lifetime and fluorescence spectrum from the emitted signal of the target mixture.

Hallidy, William H.↗

Accelerated Monte Carlo Fission Source Convergence with Fission Matrix and Kernel Density Estimators

Accurate solution of the k-eigenvalue form of the Boltzmann radiation transport equation is required in many application areas, including nuclear reactor analysis and criticality safety. Monte Carlo calculations are free of the discretization errors inherent to deterministic methods and therefore offer the most accurate solutions. However, converging the fission source can be difficult for many problems, resulting in either a substantial computational overhead or potential inaccuracies that negate many of the benefits of using Monte Carlo methods. Difficulty in converging the fission source occurs for two distinct reasons. The first is the existence of a high dominance ratio in the problem (i.e. the largest and second largest eigenvalues have approximately the same magnitude). The second difficulty arises due to undersampling of the fission source because an insufficient number of particle histories are simulated. The first difficulty is shared by deterministic solvers when using power iteration, while the second difficulty is unique to Monte Carlo solvers. In practice, both difficulties may be present in the same problem, compounding the difficulty in achieving a converged distribution. In this paper, we consider a new approach to accelerate the convergence of the fission source based on combining the use of fission matrix methods with kernel density estimators (KDEs). It has been observed that deterministic fission matrix methods show the potential to accelerate the convergence of the fission source in Monte Carlo criticality calculations but may introduce significant additional noise for difficult problems. In this paper, we have demonstrated the use of a KDE approach in combination with the fission matrix acceleration. Although the addition of the KDE initially slows the convergence of the fission matrix acceleration, it decreases the magnitude of the noise while still offering significantly improved convergence relative to analog Monte Carlo. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Urban Heat Islands and Summertime Convective Thunderstorms in Atlanta: Three Case Studies

Data from both 27 sites in the Atlanta mesonet surface meteorological network and eight National Weather Service sites were analyzed for the period from 26 July to 3 August 1996. Analysis of the six precipitation events over the city during the period (each on a different day) showed that its urban heat island (UHI) induced a convergence zone that initiated three of the storms at different times of the day, i.e., 0630,0845, and 1445 EDT. Previous analysis has shown that New York City (NYC) effects summer daytime thunderstorm formation and/or movement. That study found that during nearly calm regional flow conditions the NYC UHI initiates convective activity. Moving thunderstorms, however, tended to bifurcate and to move around the city, due to its building barrier effect. The current Atlanta results thus agree with the NYC results with respect to thunderstorm initiation.

Bornstein, Robert↗

Uncertainty-Aware Machine Learning for Small-Angle X-ray Scattering Analysis in Autonomous Experimentation

Small-angle X-ray scattering (SAXS) is a powerful high-throughput characterization tool for probing nanoscale structure in native sample environments, providing real-time morphological information such as nanoparticle size and shape during synthesis. However, automated SAXS data analysis for extracting meaningful structural parameters is non-trivial and remains a bottleneck in closed-loop experimentation towards autonomous materials discovery, which demands fast, reliable, and uncertainty-aware data analysis. Here, we develop a machine-learning approach for automated SAXS analysis tailored to closed-loop nanoparticle synthesis. A Random Forest (RF) regression model is trained on 100,000 synthetic SAXS curves generated from polydisperse spherical nanoparticles with realistic background contributions. Using normalized one-dimensional SAXS intensity profiles as input, the RF model directly predicts nanoparticle radius, size polydispersity, and background parameters, while the ensemble standard deviation across trees provides built-in uncertainty quantification (UQ). On synthetic data, we show that combining fit-quality metrics (R 2 , MAE) with thresholds on prediction uncertainty reliably identifies accurate parameter estimates without access to ground truth. We then apply the trained model to 365 experimental SAXS profiles of citrate-reduced gold nanoparticles synthesized using an automated droplet-flow microreactor with in situ SAXS at a synchrotron beamline, classifying the results into high- and low-confidence subsets based on UQ metrics. Finally, we integrate RF-based SAXS analysis into a simulated closed-loop optimization campaign using Gaussian process Bayesian optimization to minimize nanoparticle polydispersity, benchmarking against conventional automated Levenberg–Marquardt fitting. The RF-guided campaign exhibits substantially faster convergence and lower relative opportunity cost (∼0.07 vs ∼0.3), demonstrating that uncertainty-aware machine-learning SAXS analysis significantly enhances the efficiency and robustness of autonomous nanomaterials synthesis workflows.

Bayesian optimization↗

A coarse-grid correction/nonlinear relaxation algorithm for the three-dimensional, compressible Navier-Stokes equations

A combined coarse-grid correction/upwind relaxation strategy to provide rapid convergence for 3D high-speed viscous flowfields is discussed an evaluated. The construction and analysis of a simple two-grid acceleration procedure based on 'hyperbolic' multigrid concepts is presented. Numerical simulations of a 2D compression-corner flowfield, a 3D crossing shock/turbulent boundary layer interaction, and a 3D scramjet inlet flowfield are presented to illustrate the benefits of the approach. Results indicate that the procedure generally converges two or more times faster than the baseline algorithm.

Edwards, Jack R.↗

Crystal structure of the Arabidopsis SPIRAL2 C-terminal domain reveals a p80-Katanin-like domain

Epidermal cells of dark-grown plant seedlings reorient their cortical microtubule arrays in response to blue light from a net lateral orientation to a net longitudinal orientation with respect to the long axis of cells. The molecular mechanism underlying this microtubule array reorientation involves katanin, a microtubule severing enzyme, and a plant-specific microtubule associated protein called SPIRAL2. Katanin preferentially severs longitudinal microtubules, generating seeds that amplify the longitudinal array. Upon severing, SPIRAL2 binds nascent microtubule minus ends and limits their dynamics, thereby stabilizing the longitudinal array while the lateral array undergoes net depolymerization. To date, no experimental structural information is available for SPIRAL2 to help inform its mechanism. To gain insight into SPIRAL2 structure and function, we determined a 1.8 Å resolution crystal structure of the Arabidopsis thaliana SPIRAL2 C-terminal domain. The domain is composed of seven core α-helices, arranged in an α-solenoid. Amino-acid sequence conservation maps primarily to one face of the domain involving helices α1, α3, α5, and an extended loop, the α6-α7 loop. The domain fold is similar to, yet structurally distinct from the C-terminal domain of Ge-1 (an mRNA decapping complex factor involved in P-body localization) and, surprisingly, the C-terminal domain of the katanin p80 regulatory subunit. The katanin p80 C-terminal domain heterodimerizes with the MIT domain of the katanin p60 catalytic subunit, and in metazoans, binds the microtubule minus-end factors CAMSAP3 and ASPM. Structural analysis predicts that SPIRAL2 does not engage katanin p60 in a mode homologous to katanin p80. The SPIRAL2 structure highlights an interesting evolutionary convergence of domain architecture and microtubule minus-end localization between SPIRAL2 and katanin complexes, and establishes a foundation upon which structure-function analysis can be conducted to elucidate the role of this domain in the regulation of plant microtubule arrays.

59 BASIC BIOLOGICAL SCIENCES↗

Convergence and asymptotical stability of numerical solutions for neutral stochastic delay differential equations driven by G-Brownian motion

There are few numerical analysis results for nonlinear neutral stochastic delay differential equations driven by G-Brownian motion (G-NSDDEs). This paper is concerned with the numerical solutions of the G-NSDDEs to fill this gap. In this paper, we first devote to show that the stochastic theta numerical solution converges to the exact solution for the G-NSDDE. We then prove that the backward Euler–Maruyama numerical solution for the G-NSDDE is asymptotically mean-square stable under suitable conditions. Moreover, a numerical example is demonstrated to illustrate the effectiveness of our obtained results.

97 MATHEMATICS AND COMPUTING↗

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Chen, H. C.↗

A class of efficient difference method for time fractional reaction–diffusion equation

The fractional reaction–diffusion equation has profound physical background and theoretical connotation, and its numerical methods are of great scientific significance and practical value. In this paper, a class of explicit–implicit (E–I) difference method and implicit–explicit (I–E) difference method are proposed for one-dimensional time fractional reaction–diffusion equation. The methods are constructed by combining classical explicit scheme and classical implicit scheme. The existence, uniqueness and convergence of solutions are given for E–I and I–E schemes. Theoretical analysis and numerical experiments show that the E–I and I–E schemes are unconditionally stable, with second-order spatial accuracy and 2−α order temporal accuracy. Compared with the classical implicit difference method with the similar accuracy, the computation time of the presented methods is improved by nearly 41%. It is shown that the E–I difference method and I–E difference method are effective for solving the time fractional reaction–diffusion equation.

97 MATHEMATICS AND COMPUTING↗

Interlaminar stress singularities at a straight free edge in composite laminates

A quasi-three-dimensional finite-element analysis was used to analyze the edge-stress problem in four-ply, composite laminates. The seven laminates that were considered belong to the laminate family where the outer ply angle is between 0 and 90 deg. Systematic convergence studies were made to explore the existence of stress singularities near the free edge. The present analysis appears to confirm the existence of stress singularities at the intersection of the interface and the free edge. The power of the stress singularity was the same for all seven laminates considered.

Raju, I. S.↗

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data

We show the convergence of the zero relaxation limit of $2 \times 2$ systems of hyperbolic balance laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation time tends to zero. The initial data are assumed to depend on finitely many random variables, and the convergence is then proved via the appropriate analogues of the compensated compactness methods used in treating the deterministic case. We also demonstrate the validity of this limit in the case of the semilinear $p$-system; the well-posedness of both the system and its equilibrium approximation is proved, and the convergence is shown with no a priori conditions on solutions. Here, this model serves as a prototype for understanding how asymptotic approximations can be used as control variates for hyperbolic balance laws with uncertainty.

$p$-system↗

The optimization of convergence for Chebyshev polynomial methods in an unbounded domain

Grosch and Orszag (1977) have performed a numerical analysis of the problem of solving differential equations in a semiinfinite or infinite domain using Chebyshev polynomials. The principal limitation of the conducted study was that it was entirely empirical. Various differential equations were solved in different ways and the numbers were compared. The present investigation has the objective to extend the studies conducted by Grosch and Orszag by deriving asymptotic approximations to the Chebyshev coefficients of simple model functions. This approach makes it possible to conduct more systematic comparisons of different methods, extend the range of comparisons, and, perhaps most important, give simple analytic formulas for choosing the optimum domain size or mapping parameter L for various situations.

Boyd, J. P.↗

Postprocessing Mixed Finite Element Methods For Solving Cahn–Hilliard Equation: Methods and Error Analysis

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures.

97 MATHEMATICS AND COMPUTING↗

Stochastic solution of population balance equations for reactor networks

This work presents a sequential modular approach to solve a generic network of reactors with a population balance model using a stochastic numerical method. Full-coupling to the gas-phase is achieved through operator-splitting. The convergence of the stochastic particle algorithm in test networks is evaluated as a function of network size, recycle fraction and numerical parameters. These test cases are used to identify methods through which systematic and statistical error may be reduced, including by use of stochastic weighted algorithms. The optimal algorithm was subsequently used to solve a one-dimensional example of silicon nanoparticle synthesis using a multivariate particle model. This example demonstrated the power of stochastic methods in resolving particle structure by investigating the transient and spatial evolution of primary polydispersity, degree of sintering and TEM-style images. Highlights: •An algorithm is presented to solve reactor networks with a population balance model. •A stochastic method is used to solve the population balance equations. •The convergence and efficiency of the reported algorithms are evaluated. •The algorithm is applied to simulate silicon nanoparticle synthesis in a 1D reactor. •Particle structure is reported as a function of reactor length and time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stability of the discretization of the electron avalanche phenomenon

The numerical simulation of the discharge inception is an active field of applied physics with many industrial applications. In this work we focus on the drift-reaction equation that describes the electron avalanche. This phenomenon is one of the basic building blocks of the streamer model. The main difficulty of the electron avalanche equation lies in the fact that the reaction term is positive when a high electric field is applied. It leads to exponentially growing solutions and this has a major impact on the behavior of numerical schemes. We analyze the stability of a reference finite volume scheme applied to this latter problem. The stability of the method may impose a strict mesh spacing, therefore a proper stabilized scheme, which is stable whatever spacing is used, has been developed. The convergence of the scheme is treated as well as some numerical experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Application of a radial radio-frequency electron gun to waste treatment

Electron-beam irradiation has been shown to be a clean, efficient, and effective technique for treating a variety of contaminants in a variety of media. In particular, the ionizing radiation produced by an electron beam can effectively decontaminate wastewater and aid in removing harmful chemicals from industrial flue gas. In this paper, we investigate a novel technique for waste treatment using an electron-beam system in which an (approximately) annular beam converges radially into the treatment volume. We provide preliminary system-level analysis of the design of a radial electron gun, and we discuss hypothetical system constructs in which a radial electron gun is used for treatment of flue gas and wastewater. We derive dose uniformity, throughput rates, and other important treatment parameters for each application. Our results suggest that a lower-energy system with a large-radius cylindrical treatment volume is preferable for flue gas treatment, whereas a higher-energy system with an annular treatment volume is better-suited for wastewater treatment.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Impact of duration and missing data on the long-term photovoltaic degradation rate estimation

Accurate quantification of photovoltaic (PV) system degradation rate (R D ) is essential for lifetime yield predictions. Although R D is a critical parameter, its estimation lacks a standardized methodology that can be applied on outdoor field data. The purpose of this paper is to investigate the impact of time period duration and missing data on R D by analyzing the performance of different techniques applied to synthetic PV system data at different linear R D patterns and known noise conditions. The analysis includes the application of different techniques to a 10-year synthetic dataset of a crystalline Silicon PV system, with emulated degradation levels and imputed missing data. Here, the analysis demonstrated that the accuracy of ordinary least squares (OLS), year-on-year (YOY), autoregressive integrated moving average (ARIMA) and robust principal component analysis (RPCA) techniques is affected by the evaluation duration with all techniques converging to lower R D deviations over the 10-year evaluation, apart from RPCA at high degradation levels. Moreover, the estimated R D is strongly affected by the amount of missing data. Filtering out the corrupted data yielded more accurate R D results for all techniques. It is proven that the application of a change-point detection stage is necessary and guidelines for accurate R D estimation are provided.

14 SOLAR ENERGY↗