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An atmospheric release of hazardous material, whether accidental or intentional, can be catastrophic for those in the path of the plume. Predicting the path of a plume based on characteristics of the release (location, amount, and duration) and meteorological conditions is an active research area highly relevant for emergency and long-term response to these releases. As a result, researchers have developed particle dispersion simulators to provide plume path predictions that incorporate release characteristics and meteorological conditions. However, since release characteristics and meteorological conditions are often unknown, the inverse problem is of great interest, that is, based on all the observations of the plume so far, what can be inferred about the release characteristics? This is the question we seek to answer using plume observations from a controlled release at the Diablo Canyon Nuclear Power Plant in Central California. With access to a large number of evaluations of a computationally expensive particle dispersion simulator that includes continuous and categorical inputs and spatio-temporal output, building a fast statistical surrogate model (or emulator) presents many statistical challenges, but is an essential tool for inverse modeling and sensitivity analysis. We achieve accurate emulation using Bayesian adaptive splines to model weights on empirical orthogonal functions. We use this emulator as well as appropriately identifiable simulator discrepancy and observational error models to calibrate the simulator, thus finding a posterior distribution of characteristics of the release. Since the release was controlled, these characteristics are known, making it possible to compare our findings to the truth. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

An atmospheric release of hazardous material, whether accidental or intentional, can be catastrophic for those in the path of the plume. Predicting the path of a plume based on characteristics of the release (location, amount and duration) and meteorological conditions is an active research area highly relevant for emergency and long-term response to these releases. As a result, researchers have developed particle dispersion simulators to provide plume path predictions that incorporate release characteristics and meteorological conditions. However, since release characteristics and meteorological conditions are often unknown, the inverse problem is of great interest, that is, based on all the observations of the plume so far, what can be inferred about the release characteristics? This is the question we seek to answer using plume observations from a controlled release at the Diablo Canyon Nuclear Power Plant in Central California. With access to a large number of evaluations of a computationally expensive particle dispersion simulator that includes continuous and categorical inputs and spatio-temporal output, building a fast statistical surrogate model (or emulator) presents many statistical challenges, but is an essential tool for inverse modeling and sensitivity analysis. We achieve accurate emulation using Bayesian adaptive splines to model weights on empirical orthogonal functions. Here, we use this emulator as well as appropriately identifiable simulator discrepancy and observational error models to calibrate the simulator, thus finding a posterior distribution of characteristics of the release. Since the release was controlled, these characteristics are known, making it possible to compare our findings to the truth.

Dynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto-correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment-specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.

We study prediction in the functional linear model with functional outputs, Y = SX + ε, where the covariates X and Y belong to some functional space and S is a linear operator. We provide the asymptotic mean square prediction error for a random input with exact constants for our estimator which is based on the functional PCA of X. As a consequence we derive the optimal choice of the dimension kn of the projection space. The rates we obtain are optimal in minimax sense and generalize those found when the output is real. Our main results hold for class of inputs X(·) that may be either very irregular or very smooth. We also prove a central limit theorem for the predictor. We show that, due to the underlying inverse problem, the bare estimate cannot converge in distribution for the norm of the function space.

Background: Grip control is a critical determinant of fencing performance, requiring both stability and precision. Traditional measures of hand strength, such as dynamometry, provide only a global estimate and cannot capture finger-specific load distribution. Yet, upper-extremity overuse syndromes, tendinopathies of the wrist and digital flexors are common in fencers, underscoring the need for more granular assessments that may inform clinical practice, especially in prehension contexts. Methods: This pilot study included eight elite épée fencers from the Polish National Team (age: 23.9 ± 4.9 years; training experience: >10 years) tested using a novel épée handle instrumented with five force-sensitive resistors (FSRs) embedded beneath each finger. Participants performed two 5-s maximal voluntary contractions (MVCs) for each of the three conditions—Pinch (thumb + index), Trio (middle + ring + small), and Whole (all digits). Standard handheld dynamometry was also performed to provide a global reference measure. Results: Maximal grip strength measured with a dynamometer (65.3 ± 11.7 kgf) was substantially higher than finger-specific forces captured with the FSR handle (14.4 ± 4.4 kgf). Isolated Pinch contractions (83.0 ± 29.2 N) were significantly stronger than their integrated contribution within the Whole-hand condition (54.7 ± 16.3 N; Z = 2.52, p = 0.012), whereas Trio forces did not differ significantly (p = 0.263). On average, radial digits (thumb + index) contributed ~39% and ulnar digits (middle, ring, small) ~61% of Whole output, with the thumb and middle finger producing the largest forces. Conclusions: This pilot study demonstrates the feasibility of using an FSR-instrumented épée handle to capture finger-specific grip contributions in elite fencers. Despite limited statistical power (n = 8), the observed effects provide initial quantitative evidence for sport-specific, digit-level assessment, showing potential clinical utility in detecting maladaptive load-transfer mechanisms and informing rehabilitation and injury-prevention programs.

Summary Dynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto-correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment-specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.

We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space–time variational formulation and associated generalized singular value decomposition of the (linearized) Navier–Stokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a ‘data’ space–time norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a ‘solution’ space–time norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected space–time semi-norms; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (Brezzi–Rappaz–Raviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel.

We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a spacetime variational formulation and associated generalized singular value decomposition of the (linearized) NavierStokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a data spacetime norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a solution spacetime norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected spacetime semi-norms; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (BrezziRappazRaviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel.

Predicting the temporal evolution of landslides is typically supported by numerical modelling. Dynamic sensitivity analysis aims at assessing the influence of the landslide properties on the time-dependent predictions (e.g. time series of landslide displacements). Yet, two major difficulties arise: (1) Global sensitivity analysis require running the landslide model a high number of times (>1,000), which may become impracticable when the landslide model has a high computation time cost (>several hours); (2) Landslide model outputs are not scalar, but function of time, that is, they are n -dimensional vectors with n usually ranging from 100 to 1,000. In this article, I explore the use of a basis set expansion, such as principal component analysis, to reduce the output dimensionality to a few components, each of them being interpreted as a dominant mode of variation in the overall structure of the temporal evolution. The computationally intensive calculation of the Sobol’ indices for each of these components are then achieved through meta-modelling, that is, by replacing the landslide model by a “costless-to-evaluate” approximation (e.g. a projection pursuit regression model). The methodology combining “basis set expansion—meta-model—Sobol’ indices” is then applied to the Swiss La Frasse landslide to investigate the dynamic sensitivity analysis of the surface horizontal displacements to the slip surface properties during the pore pressure changes. I show how to extract information on the sensitivity of each main modes of temporal behaviour using a limited number (a few tens) of long-running simulations.

We present a method for Poisson's equation that computes guaranteed upper and lower bounds for the values of piecewise-polynomial linear functional outputs of the exact weak solution of the infinite-dimensional continuum problem with piecewise-polynomial forcing. The method results from exploiting the Lagrangian saddle point property engendered by recasting the output problem as a constrained minimization problem. Localization is achieved by Lagrangian relaxation and the bounds are computed by appeal to a local dual problem. The proposed method computes approximate Lagrange multipliers using traditional finite element approximations to calculate a primal and an adjoint solution along with well-known hybridization techniques to calculate interelement continuity multipliers. The computed bounds hold uniformly for any level of refinement, and in the asymptotic convergence regime of the finite element method, the bound gap decreases at twice the rate of the energy norm measure of the error in the finite element solution. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity that is linear in the number of elements in the finite element discretization. The elemental contributions to the bound gap are always positive and hence lend themselves to be used as adaptive indicators, as we demonstrate with a numerical example.