Random sampling of random processes - Optimum linear interpolation.
Optimum mean square linear interpolation for random sampling, discussing periodic and Poisson sampling
SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Optimum mean square linear interpolation for random sampling, discussing periodic and Poisson sampling
Time-domain and frequency domain statistics for random step-wise sampled data systems
ABSTRACT For the purpose of developing poly(3‐hexylthiophene) (P3HT) based copolymers with deep‐lying highest occupied molecular orbital (HOMO) levels for polymer solar cells with high open‐circuit voltage ( V oc ), we report a combined approach of random incorporation of 3‐cyanothiophene (CNT) and 3‐(2‐ethylhexyl)thiophene (EHT) units into the P3HT backbone. This strategy is designed to overcome CNT content limitations in recently reported P3HT‐CNT copolymers, where incorporation of more than 15% of CNT into the polymer backbone leads to impaired polymer solubility and raises the HOMO level. This new approach allows incorporation of a larger CNT content, reaching even lower‐lying HOMO levels. Importantly, a very low HOMO level of −5.78 eV was obtained, representing one of the lowest HOMO values for exclusively thiophene‐based polymers. Lower HOMO levels result in higher V oc and higher power conversion efficiencies (PCE) compared to the previously reported P3HT‐CNT copolymers containing only 3‐hexylthiophene and CNT units. As a result, solar cells based on P3HT‐CNT‐EHT(15:15) , which contains 70% of P3HT, 15% of CNT and 15% of EHT, yield a V oc of 0.83 V in blends with PC 61 BM while preserving high fill factor (FF) and high short‐circuit current density ( J sc ), resulting in 3.6% PCE. Additionally, we explored the effect of polymer number‐average molecular weight ( M n ) on the optoelectronic properties and solar cell performance for the example of P3HT‐CNT‐EHT(15:15). The organic photovoltaic (OPV) performance improves with polymer M n increasing from 3.4 to 6.7 to 9.6 kDa and then it declines as M n further increases to 9.9 and to 16.2 kDa. The molecular weight study highlights the importance of not only the solar cell optimization, but also the significance of individual polymer properties optimization, in order to fully explore the potential of any given polymer in OPVs. The broader ramification of this study lies in potential application of these high band gap copolymers with low‐lying HOMO level in the development of ternary blend photovoltaics as well as tandem OPV. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54 , 1526–1536
This work experimentally investigated the flow characteristics in a facility with randomly packed spheres at a low-aspect ratio of 4.4. Velocity fields in the near-wall region and in the pores between spheres were obtained by employing the matched-index-of-refraction (MIR) and time-resolved particle image velocimetry (TR-PIV) techniques for Reynolds numbers of 340, 520, and 720. From the obtained TR-PIV velocity vector fields, flow characteristics including first- and second-order statistics, such as mean velocity, root-mean-square fluctuating velocity, and Reynolds stress profiles, were computed. The effects of the wall enclosure and Reynolds numbers on the flow patterns were investigated by comparing the computed flow statistics and evaluating two-point cross correlations of the velocities measured adjacent to and far from the wall. Comparisons of the mean velocities, root-mean-square fluctuating velocities, and Reynolds stress component showed an increase in flow mixing and turbulent intensity in the gaps between spheres in the packed bed. The re-circulation-region sizes, however, were found to be independent from an increase in Reynolds numbers. Finally, flow modal decompositions, such as the proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), were applied to the vorticity fields extracted from sub-regions located near and far from the wall to reveal the most dominant POD and DMD flow structures.
Not provided.
Microphase separation within randomly end-linked copolymer networks (RECNs) provides access to disordered bicontinuous morphologies over a wide composition range of the constituent network strands. Here, we rely on end-linking of telechelic hydroxyl-terminated polystyrene (PS) and poly(D,Llactide) (PLA) chains of equal molecular weight, with a tetrafunctional isocyanate cross-linker in a good solvent for both strands, followed by solvent removal to induce microphase separation, and finally etching of the PLA phase to yield nanoporous materials. Transmission electron microscopy (TEM) tomographic reconstructed 3D images along with gravimetric measurements and small-angle X-ray scattering (SAXS) indicate the formation of highly interconnected structures over a range of ~40-70 vol % of PLA, while N2 adsorption measurements indicate narrowly distributed pore sizes that can be tuned by varying the strand molecular weights. Stretching of the PS/PLA copolymer networks above the glass transition temperatures of both components prior to etching the PLA phase provides a straightforward means to introduce controlled anisotropy into the 3D interconnected porous materials.
Randomly end-linked copolymer networks (RECNs) provide a robust route to self-assembled cocontinuous nanostructures. Here, we study the orientation of cocontinuous polystyrene/poly(D,L-lactide) (PS/PLA) RECNs induced by uniaxial stretching above the glass transition temperatures of the components. Small-angle X-ray scattering (SAXS) reveals that the domains initially undergo nonaffine stretching at low strain (ε < 0.4), followed by domain rotation at larger strains, yielding a “soft elastic” response and providing a high degree of orientation. Transmission electron microscopy (TEM) tomography confirms that stretching leads to topological changes in the nanostructure, corresponding to reorganization of domain interfaces. The combination of orientation at the molecular and nanostructural levels provides substantial improvements in yield strength, toughness, and stiffness. In addition to possibilities for improving mechanical properties, cocontinuous nanostructures with controlled levels of orientation have potential in a variety of contexts including directional ion transport and energy absorption.
We experimentally demonstrate an extension to coherent diffractive imaging that encodes additional information through the use of a series of randomly coded masks, removing the need for typical object-domain constraints while guaranteeing a unique solution to the phase retrieval problem. Phase retrieval is performed using a numerical convex relaxation routine known as “PhaseCut,” an iterative algorithm known for its stability and for its ability to find the global solution, which can be found efficiently and which is robust to noise. The experiment is performed using a laser diode at 532.2 nm, enabling rapid prototyping for future X-ray synchrotron and even free electron laser experiments.
The accuracy of calculations of atomic Rydberg excitations cannot be judged by the usual measures, such as mean unsigned errors of many transitions. We show how to use quantum defect (QD) theory to (a) separate errors due to approximate ionisation potentials, (b) extract smooth QDs to compare with experiment, and (c) quantify those defects with a few characteristic parameters. The particle–particle random phase approximation (pp-RPA) produces excellent Rydberg transitions that are an order of magnitude more accurate than those of time-dependent density functional theory with standard approximations. Here, we even extract reasonably accurate defects from the lithium Rydberg series, despite the reference being open-shell. Our methodology can be applied to any Rydberg series of excitations with four transitions or more to extract the underlying threshold energy and characteristic QD parameters. Our pp-RPA results set a demanding challenge for other excitation methods to match.
Not Available
Mathematical models of light ray propagation in random media
Relationships between random and nonrandom probabilities corresponding to instantaneous and identical events
Statistical properties of weighted binary random and pseudorandom sequences
Superimposition of fluctuating velocity on steady incompressible channel flow by randomly fluctuating pressure gradients
Most software is contructed on the assumption that the programs and data are stored in random access memory (RAM). Physical limitations on the relative speeds of processor and memory elements lead to a variety of memory organizations that match processor addressing rate with memory service rate. These include interleaved and cached memory. A very high fraction of a processor's address requests can be satified from the cache without reference to the main memory. The cache requests information from main memory in blocks that can be transferred at the full memory speed. Programmers who organize algorithms for locality can realize the highest performance from these computers.
The partition lattice of the set [n] with respect to refinement is studied. Any map ϕ: [n] → [n], is associated with a partition of [n] by taking preimages of the elements. Assume that t partitions p{sub 1}, p{sub 2}, . . . , p{sub t} are chosen independently according to the uniform measure on the set of mappings [n] → [n]. It is shown that the probability for the coarsest refinement of all the partitions pi to be the finest partition {{1}, . . . , {n}} tends to 1 for any t ≥ 3 and to e{sup −1/2} for t = 2. It is also proved that the probability for the finest coarsening of the partitions pi to be the one-block partition tends to 1 as t(n) − log n→∞ and tends to 0 as t(n) − log n→−∞. The size of the maximal block of the finest coarsening of all the pi for a fixed t is also studied.
Abstract not provided.
Abstract not provided.