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A method developed to compute two-body, optimal, N-impulse trajectories was presented. The necessary conditions established define the gradient structure of the primer vector and its derivative for any set of boundary conditions and any number of impulses. Inequality constraints, a conjugate gradient iterator technique, and the use of a penalty function were also discussed.
Described are methods for reducing vibration in helicopter rotor blades by determining optimum sizes and locations of tuning masses through formal mathematical optimization techniques. An optimization procedure is developed which employs the tuning masses and corresponding locations as design variables which are systematically changed to achieve low values of shear without a large mass penalty. The finite-element structural analysis of the blade and the optimization formulation require development of discretized expressions for two performance parameters: modal shaping parameter and modal shear amplitude. Matrix expressions for both quantities and their sensitivity derivatives are developed. Three optimization strategies are developed and tested. The first is based on minimizing the modal shaping parameter which indirectly reduces the modal shear amplitudes corresponding to each harmonic of airload. The second strategy reduces these amplitudes directly, and the third strategy reduces the shear as a function of time during a revolution of the blade. The first strategy works well for reducing the shear for one mode responding to a single harmonic of the airload, but has been found in some cases to be ineffective for more than one mode. The second and third strategies give similar results and show excellent reduction of the shear with a low mass penalty.
Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.
It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.
Deploying energy storage and carbon capture at scale is hindered by the substantial endothermic penalty of decomposing CaCO 3 to CaO and CO 2 , and the rapid loss of CO 2 absorption capacity by CaO sorbent particles due to sintering at the high requisite decomposition temperatures. The decomposition reaction mechanism underlying sorbent deactivation remains unclear at the atomic level and nanoscale due to past reliance on postmortem characterization methods with insufficient spatial and temporal resolution. Thus, elucidating the important CaCO 3 decomposition reaction pathway requires direct observation by time-resolved (sub-)nanoscale methods. Here, chemical and structural dynamics during the decomposition of CaCO 3 nanoparticles to nanoporous CaO particles comprising high-surface-area CaO nanocrystallites are examined. Comparing in situ transmission electron microscopy (TEM) and synchrotron X-ray diffraction experiments gives key insights into the dynamics of nanoparticle calcination, involving anisotropic CaCO 3 thermal distortion before conversion to thermally dilated energetically stable CaO crystallites. Time-resolved TEM uncovered a novel CaO formation mechanism involving heterogeneous nucleation at extended CaCO 3 defects followed by sweeping reaction front motion across the initial CaCO 3 particle. These observations clarify longstanding, yet incomplete, reaction mechanisms and kinetic models lacking accurate information about (sub-)nanoscale dynamics, while also demonstrating calcination of CaCO 3 without sintering through rapid heating and precise temperature control.
An analytical model was developed to predict the noise levels inside propeller-driven aircraft during cruise at M = 0.8. The model was applied to three study aircraft with fuselages of different size (wide body, narrow body and small diameter) in order to determine the noise reductions required to achieve the goal of an A-weighted sound level which does not exceed 80 dB. The model was then used to determine noise control methods which could achieve the required noise reductions. Two classes of noise control treatments were investigated: add-on treatments which can be added to existing structures, and advanced concepts which would require changes to the fuselage primary structure. Only one treatment, a double wall with limp panel, provided the required noise reductions. Weight penalties associated with the treatment were estimated for the three study aircraft.
Here in this paper we consider the possibility and conditions for pair photoemission whereby two incident photons emit pairs of electrons from a candidate material as a novel method to measure and visualize electronic correlations. As opposed to double photoemission - where a single photon precipitates the ejection of a pair electrons via a subsequent electron energy loss scattering process - we show that pair photoemission need not be limited to interference between initial photoelectrons and valence electrons, and moreover, can occur without the energy penalty of two work functions. This enables detection of pairs of electrons at high energy resolution that may be correlated in the same quantum many-body states.
A description is presented of an effective optimality criterion computer design approach for member size selection to improve frequency characteristics for moderately large structure models. It is shown that the implementation of the simultaneous iteration method within a natural frequency structural design optimization provides a method which is more efficient in isolating the lowest natural frequency modes than the frequently applied Stodola method. Additional computational advantages are derived by using previously converged eigenvectors at the start of the iterations during the second and the following design cycles. Vectors with random components can be used at the first design cycle, which, in relation to the entire computer time for the design program, results in only a moderate computational penalty.
In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.
The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.
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The nuclear industry is developing small reactor designs that can target a variety of deployment locations and energy products. Smaller nuclear designs have traditionally struggled to handle the steep trade-offs between size and cost that have historically incentivized large reactors. This motivates computational optimization of small reactors to minimize costs and quantify the trade-off between size and cost. In this paper, the cost/size trade-off for a small fast reactor is derived using a multi-objective genetic algorithm optimization, with steady-state, transient, and cost analysis of the fast reactor being performed. Specifically, the method is demonstrated on a small 10- to 120-MW(thermal) U-Pu-Zr–fueled lead-cooled fast reactor with a 10-year core life for district energy applications, which can have a thermal load compatible with this range. The results reinforced that fast reactor cores at the lower end of this power range suffer cost penalties due to critical mass considerations. It was found that high power density cores with strong reactivity swings and many control rods were favored over designing to minimize reactivity swing. Furthermore, this contrasts with some traditional configurations designed using engineering judgment and demonstrates that optimizers can find nontraditional but realistic solutions, along with demonstrating the value of incorporating cost functions into whole-reactor design optimization.
A method is presented for the estimation of the subsonic-flight-speed characteristics of sharp-lip inlets applicable to supersonic aircraft. The analysis, based on a simple momentum balance consideration, permits the computation of inlet pressure recovery - mass-flow relations and additive-drag coefficients for forward velocities from zero to the speed of sound. The penalties for operation of a sharp-lip inlet at velocity ratios other than 1.0 may be severe; at lower velocity ratios an additive drag is incurred that is not cancelled by lip suction, while at higher velocity ratios, unavoidable losses in inlet total pressure will result. In particular, at the take-off condition, the total pressure and the mass flow for a choked inlet are only 79 percent of the values ideally attainable with a rounded lip. Experimental data obtained at zero speed with a sharp-lip supersonic inlet model were in substantial agreement with the theoretical results.
Radiation shield design is driven by the need to limit radiation risks while optimizing risk reduction with launch mass/expense penalties. Both limitation and optimization objectives require the development of accurate and complete means for evaluating the effectiveness of various shield materials and body-self shielding. For galactic cosmic rays (GCR), biophysical response models indicate that track structure effects lead to substantially different assessments of shielding effectiveness relative to assessments based on LET-dependent quality factors. Methods for assessing risk to the central nervous system (CNS) from heavy ions are poorly understood at this time. High-energy and charge (HZE) ion can produce tissue events resulting in damage to clusters of cells in a columnar fashion, especially for stopping heavy ions. Grahn (1973) and Todd (1986) have discussed a microlesion concept or model of stochastic tissue events in analyzing damage from HZE's. Some tissues, including the CNS, maybe sensitive to microlesion's or stochastic tissue events in a manner not illuminated by either conventional dosimetry or fluence-based risk factors. HZE ions may also produce important lateral damage to adjacent cells. Fluences of high-energy proton and alpha particles in the GCR are many times higher than HZE ions. Behind spacecraft and body self-shielding the ratio of protons, alpha particles, and neutrons to HZE ions increases several-fold from free-space values. Models of GCR damage behind shielding have placed large concern on the role of target fragments produced from tissue atoms. The self-shielding of the brain reduces the number of heavy ions reaching the interior regions by a large amount and the remaining light particle environment (protons, neutrons, deuterons. and alpha particles) may be the greatest concern. Tracks of high-energy proton produce nuclear reactions in tissue, which can deposit doses of more than 1 Gv within 5 - 10 cell layers. Information on rates of cell killing from GCR, including patterns of cell killing from single particle tracks. can provide useful information on expected differences between proton and HZE tracks and clinical experiences with photon irradiation. To model effects on cells in the brain, it is important that transport models accurately describe changes in the GCR due to interactions in the cranium and proximate tissues. We describe calculations of the attenuated GCR particle fluxes at three dose-points in the brain and associated patterns of cell killing using biophysical models. The effects of the brain self-shielding and bone-tissue interface of the skull in modulating the GCR environment are considered. For each brain dose-point, the mass distribution in the surrounding 4(pi) solid angle is characterized using the CAM model to trace 512 rays. The CAM model describes the self-shielding by converting the tissue distribution to mass-equivalent aluminum, and nominal values of spacecraft shielding is considered. Particle transport is performed with the proton, neutron, and heavy-ion transport code HZETRN with the nuclear fragmentation model QMSFRG. The distribution of cells killed along the path of individual GCR ions is modeled using in vitro cell inactivation data for cells with varying sensitivity. Monte Carlo simulations of arrays of inactivated cells are considered for protons and heavy ions and used to describe the absolute number of cell killing events of various magnitude in the brain from the GCR. Included are simulations of positions of inactivated cells from stopping heavy ions and nuclear stars produced by high-energy ions most importantly, protons and neutrons.
Understanding the impact of extractant functionalization on metal-binding energetics in liquid-liquid extraction is essential to guide the development of better separation processes. Traditionally, computational extractant design uses electronic structure calculations on metal-ligand clusters to determine the metal-binding energy of the lowest energy state. Although highly accurate, this approach does not account for all of the relevant physics encountered under experimental conditions. Such methodologies often neglect entropic contributions such as temperature effects and ligand flexibility, in addition to approximating solvent-extractant interactions with implicit solvent models. In this study, we use classical molecular dynamics simulations with an advanced sampling method, metadynamics, to map out extractant molecule conformational free energies in the condensed phase. Here we generate the complete conformational landscape in solution for a family of bidentate malonamide-based extractants with different functionalizations of the headgroup and the side chains. In particular, we show how such alkyl functionalization reshapes the free energy landscape, affecting the free energy penalty of organizing the extractant into the cis-like metal-binding conformation from the trans-like conformation of the free extractant in solution. Specifically, functionalizing alkyl tails to the center of the headgroup has a greater influence on increasing molecular rigidity and disfavoring the binding conformation than functionalizing side chains. These findings are consistent with trends in metal-binding energetics based on experimentally reported distribution ratios. We also consider a different bidentate extractant molecule, carbamoylmethylphosphine oxide, and show how the choice of solvent can further reshape the conformational energetic landscape. This study demonstrates the feasibility of using molecular dynamics simulations with advanced sampling techniques to investigate extractant conformational energetics in solution, which, more broadly, will enable extractant design that accounts for entropic effects and explicit solvation.
Urban power systems increasingly rely on dense sensing to monitor grid reliability, yet disturbance labels are scarce and events are rare. We present a self-supervised spatio-temporal method that detects, localizes, and characterizes grid frequency disturbances across urban areas using only unlabeled data. Our approach trains a tiny Temporal Graph Convolutional Network (T-GCN) to forecast per-site frequency residuals (deviation from 60 Hz). The sensor graph is constructed directly from signals using pre-event Pearson correlation with a cross-correlation lag penalty without geocoding. At inference, node-level anomalies are the model's forecast errors; region-level alarms arise from connected components of high-score nodes. We estimate disturbance propagation by computing per-node arrival times (first persistent exceedance), then fit a planar or time-of-arrival model to obtain direction, speed, and an epicenter proxy. With only three real events collected at decisecond resolution across U.S. cities, we evaluate the T-GCN and report time-to-detect, footprint size, and propagation consistency. We further show that short-window embeddings from the T-GCN's hidden states enable few-shot event-vs-background recognition via a simple prototypical classifier. Despite minimal data and no labels, our system yields fast, spatially coherent detection and interpretable propagation maps, offering a practical, lightweight pathway to city-scale grid resilience analytics.
RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.
A method is presented for the estimation of the subsonic-flight-speed characteristics of sharp-lip inlets applicable to supersonic aircraft. The analysis, based on a simple momentum balance consideration, permits the computation of inlet-pressure-recovery mass-flow relations and additive-drag coefficients for forward velocities from zero to the speed of sound. The penalties for operation of a sharp-lip inlet at velocity ratios other than 1.0 may be severe; at lower velocity ratios an additive drag is incurred that is not cancelled by lip suction, while at higher velocity ratios, unavoidable losses in inlet total pressure will result. In particular, at the take-off condition, the total pressure and the mass flow for a choked inlet are only 79 percent of the values ideally attainable with a rounded lip. The test specimens were polished and unnotched. The manufacturer of the material, the Aluminum Company of America, has made axial-load tests on 24S-T4 and 75S-T6 rod material. The test techniques used at the three laboratories are described in detail; the test results are presented and are compared with each other and with results obtained on unpolished sheet by the National Bureau of Standards. Experimental data obtained at zero speed with a sharp-lip supersonic inlet model were in substantial agreement with the theoretical results. (author)