Even though inhalation dosimetry is determined by three factors (i.e., breathing, aerosols, and the respiratory tract), the first two categories have been more widely studied than the last. Both breathing and aerosols are quantitative variables that can be easily changed, while respiratory airway morphologies are difficult to reconstruct, modify, and quantify. Despite several methods are available for model reconstruction and modification, developing an anatomically accurate airway model and morphing it to various physiological conditions remains labor-intensive and technically challenging. The objective of this study is to explore the feasibility of using an adjoint-CFD model to understand airway shape effects on vapor deposition and control vapor flux into the lung. A mouth-throat model was used, with the shape of the mouth and tongue being automatically varied via adjoint morphing, and the vapor transport being simulated using ANSYS Fluent coupled with a wall absorption model. Two chemicals with varying adsorption rates, Acetaldehyde and Benzene, were considered, which exhibited large differences in dosimetry sensitivity to airway shapes. For both chemicals, large shape deformations were explored to find the maximal possible morphing; both the maximal and intermediate deformations were simulated for morphology parametric studies. Results show that changing the mouth-tongue shape can alter the oral filtration by 3.2% for Acetaldehyde and 0.27% for Benzene under a given inhalation condition. This study demonstrates that the hybrid adjoint-CFD approach can be a practical and efficient method to investigate morphology-associated variability in inhalation dosimetry of vapors and nanomedicines.

Mallios and Zafiris emphasize that adjoint functors or adjunctions are not only "ubiquitous" in category theory but characterize the naturality of their approach to physical geometry. Hence in this paper, the history and theory of adjoint functors is investigated. Where do adjoint functors come from mathematically and how did the concepts develop historically?

Numerical optimization methods are widely used for designing turbomachinery components due to the cost and time savings they can provide. In the available literature, shape optimization of radial compressors is mainly focused on improving the impeller alone. However, it is a well-established knowledge that the volute plays a key role in the overall performance of the compressor. The aim of the present paper is to perform the adjoint-based optimization of a volute that is designed for the SRV2-O compressor. The CAD model is first created, using a parametrization of 33 design parameters. Then, a butterfly topology is applied to mesh the computational domain with a multi-block structured grid, and an elliptic smoothing procedure is then used to improve the quality of the fluid grid. A steady-state RANS CFD solver with Spalart-Allmaras turbulence model is used to solve the Navier-Stokes equations, and flow sensitivities are computed with an adjoint solver. The objective function consists in minimizing the loss coefficient of the volute. The optimization is performed to obtain an improved design with 14% losses reduction. Detailed flow and design analysis is carried out to highlight the loss reduction mechanisms followed by the optimizer. Finally, the compressor map of the full stage is compared between the baseline and the optimized volute through CFD simulations using a mixing plane interface. This research demonstrates the successful use of a gradient-based optimization technique to improve the volute of a radial compressor and opens the door towards optimizing simultaneously the wheel and the volute.

There are many criterion to generalize the concept of numerical radius; one of the most recent interesting generalization is what so called the generalized Euclidean operator radius. Simply, it is the numerical radius of multivariable operators. In this work, several new inequalities, refinements and generalizations are established for this kind of numerical radius.

This paper presents a concise mathematical framework for investigating both feed-forward and backward process, during the training to learn model weights, of an artificial neural network (ANN). Inspired from the idea of the two-step rule for backpropagation, we define a notion of F_adjoint which is aimed at a better description of the backpropagation algorithm. In particular, by introducing the notions of F-propagation and F-adjoint through a deep neural network architecture, the backpropagation associated to a cost/loss function is proven to be completely characterized by the F-adjoint of the corresponding F-propagation relatively to the partial derivative, with respect to the inputs, of the cost function.

The licensing of new reactors implies the use of verified and validated neutronics codes. Numerical validation can rely on sensitivity and uncertainty studies but they require repeated execution of time-consuming neutron flux and depletion calculations. The computational costs can be shortened by using perturbation theories. However, Depletion Perturbation Theory is restricted to single integral values such as a nuclide density. Relying on reduced basis approaches, which reconstruct the whole nuclide densities at once, is one way to get around this restriction. Furthermore, the adjoint-based reduced-order model uses the direct and adjoint equations for the projection. For diffusion or transport calculations, Exact-to-Precision Generalized Perturbation Theory has been developed. Still, no models for depletion calculations are readily available. Therefore, this paper describes a novel adjoint-based reduced order model for the Bateman equation. It uses a range-finding algorithm to create the basis and the Depletion Perturbation Theory for the reconstruction of the nuclide densities at first order. Our paper shows that for several perturbed cases, the depletion reduced-order model successfully reconstructs the nuclide densities. As a result, this serves as a proof of concept for our adjoint-based reduced order model which can perform sensitivity and uncertainty burn-up analysis in a shorter time.

In the Formula Student Racing Car, the anti-deformation ability of the frame will affect the four-wheel positioning parameters of the racing car, and then affect the handling and stability performance of the racing car. The quality of the frame directly determines the power and economy of the racing car, so the performance of the frame is very important to the performance of the race. In order to improve the performance of the frame and reduce the total weight of the frame, the research on the lightweight design of the frame is particularly important. In this paper, based on the variable density method, the global topology optimization of the frame is carried out to obtain the distribution of the frame material, realize the efficient use of the material, and improve the torsional stiffness of the frame. Based on the adjoint variable method, the sensitivity analysis of the frame is carried out. According to the sensitivity analysis results, the size of the frame is optimized. The total mass of the frame is reduced by 12.8 %, and the performance of the maximum displacement and maximum stress is improved. The lightweight design of the frame is realized as a whole.

In this work the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions we arrive at the following fourth-order differential equation

This work presents the mathematical framework of the Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “2nd-CASAM-L”), which enables the most efficient computation of exactly obtained mathematical expressions of first- and second-order sensitivities of a generic system response with respect to functions (“features”) of model parameters. Subsequently, the first- and second-order sensitivities with respect to the model’s uncertain parameters, boundaries, and internal interfaces are obtained analytically and exactly, without needing large-scale computations. Within the 2nd-FASAM-L methodology, the number of large-scale computations is proportional to the number of model features (defined as functions of model parameters), as opposed to being proportional to the number of model parameters, which are considerably more than the number of features, being incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities (of any order) with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces. The application of the 2nd-CASAM-L methodology is illustrated using a simplified energy-dependent neutron transport model of fundamental significance in nuclear reactor physics.