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Guidance regime for optimal multistage lunar trajectory derived by applying calculus of variations to generalized Bolza problem
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A general first-order dynamic representation for discrete systems with several independent variables is proposed, based on the Dieudonne-Rashevsky form for partial differential equations. This representation does not restrict consideration to causal systems. A minimum principle for such systems is proved, thus extending results known for discrete-time systems to the case of several independent variables. The proof requires only the classical implicit function theorem.
Proper acoustic excitation of a single large-eddy break-up device can increase the resulting drag reduction and, after approximately 40 to 50 delta downstream, provide net drag reduction. Precise optimization of the input time delay, amplitude and response threshold is difficult but possible to achieve. Drag reduction is improved with optimized conditions. The possibility of optimized processing strongly suggests a mechanism which involves interaction of the acoustic waves and large eddies at the trailing edge of the large eddy break-up device. Although the mechanism for spreading of this phenomenon is unknown, it is apparent that the drag reduction effect does tend to spread spanwise as the flow convects downstream. The phenomenon is not unique to a particular blade configuration or flow velocity, although all data have been obtained at relatively low Reynolds numbers. The general repeatibility of the results for small configuration changes serves as verification of the phenomenon.
In friction stir welding (FSW), a rotating threaded pin tool is inserted into a weld seam and literally stirs the edges of the seam together. This environmentally friendly, solid-state technique has been successfully used in the joining of materials that are difficult to fusion weld. To determine optimal processing parameters for producing a defect free weld a better understanding of the resulting metal deformation flow path and velocity is required. In this study the metal flow fields are marked by the use of thin (0.001? tungsten) wires embedded in the weld seam at various locations. X-ray radiographs record the position and segmentation of the wire and are used to elucidate the flow field. Microstructures observed in a FSW cross-section in an aluminum alloy are related to their respective strain-strain rate-temperature histories along their respective flow trajectories. Two kinds of trajectories, each subjecting the weld metal to a distinct thermomechanical process and imparting a distinct microstructure, can be differentiated within the weld structure.
Obtaining uniform mechano-dwarfing of Arabidopsis thaliana (L.) Heynh. seedlings within dense plantings is problematic. Alternative forms of mechano-stimulation were applied to seedlings in effort to obtain uniform growth reduction compared with undisturbed controls in both greenhouse and controlled growth environments. Arabidopsis grown under low photosynthetic photon flux (PPF) artificial light grew upright with limited leaf expansion, which enhanced mechano-responsiveness compared to that of rosette-growing plants under filtered sunlight or high PPF artificial light. Hypocotyls of seedlings grown at PPFs > 60 micromoles m-2 s-1 elongated less and had 6% less sensitivity to mechanical stress than seedlings grown at PPFs < 60 micromoles m-2 s-1. Fluorescent lamps alone (F) or fluorescent plus incandescent (F+I) lamps were compared for seedling responses to mechanical stress. Under F lighting, hypocotyl elongation was reduced 25% to 40% by twice-daily brush or plate treatments, and brushed seedlings exhibited more growth reduction than did plate treatments. Seedlings grown under F+I lamps exhibited similar stress-induced growth reduction compared to seedlings grown under F only, but stressed F+I seedlings lodged to a greater extent due to excessive hypocotyl elongation. Temperature-response studies using standardized F-only lighting indicated increased hypocotyl elongation but decreased leaf expansion, and decreased mechano-responsivity to brushing over the temperature range from 20 to 28 degrees C. Daylength studies indicated similar degrees of mechano-inhibition of hypocotyl elongation over the daylength range of 12, 16, 20, and 24 hours, whereas fresh weight of stressed seedling shoots declined compared to controls. A combination of environmental growth parameters that give repeatable, visual mechanical dwarfing of Arabidopsis include low-PPF fluorescent lighting from 55 to 60 micromoles m-2 s-1, ambient temperatures from 22 to 25 degrees C, and twice-daily brush treatments.
At the NASA Glenn Research Center, we have been training artificial neural networks to interpret the characteristic patterns (see the leftmost image) generated from electronic holograms of vibrating structures. These patterns not only visualize the vibration properties of structures, but small changes in the patterns can indicate structural changes, cracking, or damage. Neural networks detect these small changes well. Our objective has been to adapt the neural-network, electronic-holography combination for inspecting components in Glenn's Spin Rig.
Sufficient conditions for optimal stochastic control of diffusion processes governed by vector equations satisfying local Lipschitz conditions
Jacobi-type conditions for singular optimization problems obtained by transformation to nonsingular form adaptable to linear quadratic optimal control theory
Hydrogen is pivotal in the transition to sustainable energy systems, playing major roles in power generation and industrial applications. Metal–organic frameworks (MOFs) have emerged as promising mediums for efficient hydrogen storage. However, identifying potential candidates for deployment is challenging due to the vast number of currently available synthesized MOFs. This study integrates molecular simulations, machine learning, and techno-economic analysis to evaluate the performance of MOFs across broad operation conditions for hydrogen storage applications. While previous screenings of MOF databases have predominantly emphasized high hydrogen capacities under cryogenic conditions, this study reveals that optimal temperatures and pressures for cost minimization depend on the raw price of the MOF. Specifically, when MOFs are priced at $15/kg, among the 9720 MOFs tested, 9692 MOFs achieve the lowest cost at temperatures between 170 K and 250 K and a pressure of 150 bar. Under these optimal conditions, 362 MOFs deliver a lower levelized cost of storage than 350 bar compressed gas hydrogen storage. Furthermore, this study reveals key material properties that result in low system cost, such as high surface areas (>3000 m2/g), large void fractions (>0.78), and large pore volumes (>1.1 cm3/g).
A new class of problems was analyzed to estimate an optimal structure of laminated targets fabricated from the specified set of homogeneous materials. An approximate description of the perforation process is based on the model of radial hole extension. The problem is solved by using the needle-type variation technique. The desired optimization conditions and quantitative/qualitative estimations of optimal targets were obtained and are discussed using specific examples.
Necessary conditions for optimality of junctions between singular and nonsingular subarcs for singular optimal control problems
In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.
Electrodeposition is one of the most widely utilized techniques for thin-film production with high yields. Although it is used extensively, this technique still presents several issues limiting its usefulness, including excess thickness and frequent cracking of deposited films. Efforts to improve thin-film production recently undertaken at Oak Ridge Laboratory by the authors have included studying operating conditions and applied electrolytes. Samarium was used as a surrogate material for californium, and yield was compared with different deposition condition. The final procedure from the optimized condition will be applied during production of the californium-252 source for the Californium Rare Isotope Breeder Upgrade (CARIBU) project, and the fission fragment will be analyzed.
Supercritical fluids (SCFs) have attracted significant attention as solvents for chemical reactions due to their unique properties, such as high diffusivity, low viscosity, and tunable solvation properties. These properties profoundly influence reaction kinetics and are often attributed to the formation of molecular clusters within SCFs. To study the effect of supercritical solvent on chemical reactivity and dynamics of reactions, one needs to understand the dynamics of clusters in supercritical fluid. Extensive experiments on the photodissociation and recombination of iodine in supercritical fluids served as a model system for understanding these effects. Experimental studies have been complemented by theoretical and computational investigations, which mostly employ Monte Carlo or empirical molecular dynamics simulations. However, computational studies using non-reactive force fields and ab initio approaches present challenges in capturing reactive processes at larger scales within supercritical fluids. Here, in this work, we developed the ReaxFF parameters by training against quantum mechanics data. ReaxFF reactive force field based molecular dynamics simulations were performed, studying the dynamics of a xenon solvent and cage effect at different thermodynamic conditions for the iodine recombination reaction. We show that the conditions near the critical point are the optimal conditions to study the cage effect. We show that the average lifetime of xenon clusters ranging between 5 and 11 ps is comparable to iodine geminate recombination. Our simulation results of iodine recombination in xenon solvent demonstrate the higher probability of iodine molecule formation in the presence of xenon clusters. Finally, we show that the supercritical condition exhibits the highest recombination rate for iodine atoms.
Since the prebiotic atmosphere was anaerobic, if not reducing, a useful function of primordial photosynthesis would have been to photooxidize reduced substrates such as Fe(+2), S(-2) or reduced organic molecules and to emit hydrogen. Experiments have shown that the early biogenic pigments uroporphyrin and coproporphyrin do photooxidize organic compounds and emit hydrogen in the presence of a platinum catalyst. These experiments were carried out in dilute aqueous solution near neutral pH under anaerobic atmosphere, and quantum yields near 10-2 were obtained. Thus relevant prebiotic conditions were maintained. Rather then to further optimize conditions, attempts were made to replace the platinum catalyst by a more prebiotically suitable catalyst. Trials with an Fe4S4(SR)4 cluster, in analogy to the present hydrogenase and nitrogenase, were not successful. However, experiments using cobalt complexes to catalyze the formation of hydrogen are promising. In analogy with biological photosynthetic systems which group pigments, electron transfer molecules and enzymes in clusters for efficiency, it was found that binding the biogenic porphyrins to the polyvinyl alcohol used to support the platinum catalyst did increase the quantum yield of the reaction. It was also found that ultraviolet light can serve to photo-oxidize porphyrinogens to porphyrins under anaerobic conditions. Thus the formation of the colorless porphyriogens by the extraordinarily simple biosynthetic pathway would not be a problem because of the prevalence of UV light in the prebiotic, anoxic atmosphere.
Computation difficulty in optimal control law for dynamical system, noting three optimal conditions.