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Dataset 3: A National Dataset on Actionable Items in Improving Pooled Rideshare, 2025.

Dataset 3: A National Dataset on Actionable Items in Improving Pooled Rideshare.” 2025. Dataset Description: Pooled Rideshare Acceptance Survey - Phase 3 (2025, N = 8,296). This dataset represents the third and final phase of a national survey aimed at understanding user acceptance and preferences related to pooled rideshare (PR) services in the United States. Building on insights from earlier phases, this phase expands both the sample size and the depth of analysis to support policymaking, transportation planning, and service design for sustainable mobility systems. The Phase 3 survey was administered online to a nationally representative sample of 8,296 U.S. adults. The sample includes a wide range of demographics. The survey retained core questions from previous phases while introducing 77 detailed service features (actionable items) to evaluate potential improvements to PR offerings. Each feature was designed to assess whether a specific improvement, such as enhanced safety measures, real-time ride tracking, or user training would increase participants’ willingness to adopt PR services. In addition, behavioral predictors, current rideshare habits, environmental attitudes, and perceived barriers (e.g., safety, privacy, and comfort) were captured. - Phase_3_Final - The dataset contains rows corresponding to individual respondents and columns representing survey items, demographic characteristics, and response values. The data is available in both .CSV and .SAV formats. - Phase_3_Final_MapFile - Accompanying this dataset is a data dictionary explaining each variable, value range, and coding schema. An .XLSX format of the full survey instrument is included to support interpretation and reuse of the dataset.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Flexible high speed codec

The project's objective is to develop an advanced high speed coding technology that provides substantial coding gains with limited bandwidth expansion for several common modulation types. The resulting technique is applicable to several continuous and burst communication environments. Decoding provides a significant gain with hard decisions alone and can utilize soft decision information when available from the demodulator to increase the coding gain. The hard decision codec will be implemented using a single application specific integrated circuit (ASIC) chip. It will be capable of coding and decoding as well as some formatting and synchronization functions at data rates up to 300 megabits per second (Mb/s). Code rate is a function of the block length and can vary from 7/8 to 15/16. Length of coded bursts can be any multiple of 32 that is greater than or equal to 256 bits. Coding may be switched in or out on a burst by burst basis with no change in the throughput delay. Reliability information in the form of 3-bit (8-level) soft decisions, can be exploited using applique circuitry around the hard decision codec. This applique circuitry will be discrete logic in the present contract. However, ease of transition to LSI is one of the design guidelines. Discussed here is the selected coding technique. Its application to some communication systems is described. Performance with 4, 8, and 16-ary Phase Shift Keying (PSK) modulation is also presented.

Boyd, R. W.↗

Cytoskeletal filament assembly and the control of cell spreading and function by extracellular matrix

This study was undertaken to analyze how cell binding to extracellular matrix produces changes in cell shape. We focused on the initial process of cell spreading that follows cell attachment to matrix and, thus, cell 'shape' changes are defined here in terms of alterations in projected cell areas, as determined by computerized image analysis. Cell spreading kinetics and changes in microtubule and actin microfilament mass were simultaneously quantitated in hepatocytes plated on different extracellular matrix substrata. The initial rate of cell spreading was highly dependent on the matrix coating density and decreased from 740 microns 2/h to 50 microns 2/h as the coating density was lowered from 1000 to 1 ng/cm2. At approximately 4 to 6 hours after plating, this initial rapid spreading rate slowed and became independent of the matrix density regardless of whether laminin, fibronectin, type I collagen or type IV collagen was used for cell attachment. Analysis of F-actin mass revealed that cell adhesion to extracellular matrix resulted in a 20-fold increase in polymerized actin within 30 minutes after plating, before any significant change in cell shape was observed. This was followed by a phase of actin microfilament disassembly which correlated with the most rapid phase of cell extension and ended at about 6 hours; F-actin mass remained relatively constant during the slow matrix-independent spreading phase. Microtubule mass increased more slowly in spreading cells, peaking at 4 hours, the time at which the transition between rapid and slow spreading rates was observed. However, inhibition of this early rise in microtubule mass using either nocodazole or cycloheximide did not prevent this transition. Use of cytochalasin D revealed that microfilament integrity was absolutely required for hepatocyte spreading whereas interference with microtubule assembly (using nocodazole or taxol) or protein synthesis (using cycloheximide) only partially suppressed cell extension. In contrast, cell spreading could be completely inhibited by combining suboptimal doses of cytochalasin D and nocodazole, suggesting that intact microtubules can stabilize cell form when the microfilament lattice is partially compromised. The physiological relevance of the cytoskeleton and cell shape in hepatocyte physiology was highlighted by the finding that a short exposure (6 hour) of cells to nocodazole resulted in production of smaller cells 42 hours later that exhibited enhanced production of a liver-specific product (albumin). These data demonstrate that spreading and flattening of the entire cell body is not driven directly by net polymerization of either microfilaments or microtubules.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Cell Biology↗

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4 e , and d -wave charge- 4 e states

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the U⁡(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-4e condensate, which itself can have an underlying s-wave, d x 2 –y 2 -wave, or d xy -wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-4⁢e order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and s-wave charge-4e vestigial states are degenerate. Finally, we discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4⁢e states in material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Experiments on the Capillary Condensation/Evaporation Hysteresis of Pure Fluids and Binary Mixtures in Cylindrical Nanopores

Here, a new experimental method, i.e., isochoric cooling/heating cycle measurement using differential scanning calorimeter (DSC), is applied to investigate the hysteretic phenomenon of pure components and mixtures confined in two different types of cylindrical nanopores (SBA-15 and KIT-6). The capillary condensation/evaporation hysteresis end point (T he ) for a specific system is determined by performing a series of measurements with different densities by increasing initial temperature and pressure. We confirm that for a pure component, T he is lower when confined in smaller nanopores, whereas T he for CH 4 /CO 2 and CH 4 /C 2 H 6 mixtures at the specific composition investigated are higher than that of pure CO 2 and C 2 H 6 , respectively, when confined in the same nanopores. To the best of our knowledge, this is the first time that T he of fluid mixture is experimentally studied, which further demonstrates that binary mixtures behave similarly to pure fluids when confined in nanoporous media. At low temperatures where hysteresis is observed, the shape as well as the duration of the exothermic peak (due to capillary condensation) and endothermic peak (due to capillary evaporation) indicate that capillary condensation, rather than capillary evaporation, takes place at/near a thermodynamic equilibrium. Within the accuracy of the measurements, we find that the total heat of capillary condensation is identical to that of capillary evaporation for all systems examined, regardless of the presence of hysteresis. By comparing the heat per unit volume among different systems, we also find that the heat per unit volume of the phase transition of confined pure fluid is lower than that of bulk, which further demonstrates that the molar density of confined pure liquid is less than that of bulk pure liquid at saturation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cosmic quenching and scaling laws for the evolution of supermassive black holes and host galaxies

ABSTRACT Observations suggest a co-evolution of supermassive black holes (SMBHs) and host galaxies. In this paper, we consider the mass and energy flow in a near-equilibrium bulge suffused by gases of varying temperatures. By assuming the rate of energy flow independent of the distance r from the bulge center and the local virial equilibrium for permeated gases on scale r, a key parameter $\varepsilon _b$ was identified that quantifies the mass and energy flow in gases and the efficiency of gas cooling (or the "specific" cooling rate per unit mass), and thus regulates the co-evolution of both SMBHs and hosts. With the help of Illustris simulations and observations, we determined the redshift variation $\varepsilon _b\propto (1+z)^{5/2}$. A higher $\varepsilon _b$ in the early Universe means a higher specific cooling rate that allows rapid evolution of SMBHs and hosts. This simple theory, characterized by a single parameter $\varepsilon _b$, provides the dominant mean cosmic evolution of SMBHs and hosts. All other transient phenomena may only contribute to the dispersion around this mean evolution. Based on this theory and relevant assumptions, scaling laws involving $\varepsilon _b$ were identified for the evolution of SMBHs and hosts. For host galaxies, the mass–size relation $M_b\propto \varepsilon _b^{2/3}r_b^{5/3}G^{-1}$, the dispersion–size relation $\sigma _b^2\propto (\varepsilon _b r_b)^{2/3}\propto (1+z)$, or the mass–dispersion relation $M_b\propto \varepsilon _b^{-1}G^{-1}\sigma _b^5$ were identified, where $r_b\propto (1+z)^{-1}$ is the bulge size. For SMBHs, three evolution phases were found involving an initial rapid growth stage with a rising luminosity $L_B\propto (\varepsilon _b M_{\rm BH})^{4/5}$, a transition stage with a declining $L_B\propto \varepsilon _b^2 M_{\rm BH} \propto (1+z)^5$, and a dormant stage with $L_B\propto (\varepsilon _b M_{\rm BH})^{4/3}$. Our results suggest a rapid initial super-Eddington growth in a short period with a new redshift-dependent luminosity limit $L_X\propto\varepsilon _b^{4/5}M_{\rm BH}^{4/5}G^{-1/5}c$, in contrast to the Eddington limit. Analytical solutions were formulated for the BH mass function $\Phi _{\rm BH}$, active galactic nucleus (AGN) mass function $\Phi _{\rm AGN}$, and duty cycle U that predict $\Phi _L\propto L^{-1/5}$ for the faint-end luminosity function, $\Phi _{\rm AGN}\propto M^{-1/5}$ for small-mass-end AGN mass function $\Phi _L$, and $U\propto M^{-1/5}$ at high redshift.

(galaxies:) quasars: supermassive black holes↗

A Quantum Monte Carlo Study of the Structural, Energetic, and Magnetic Properties of Two-Dimensional H and T Phase VSe 2

Previous works have controversially claimed near-room-temperature ferromagnetism in two-dimensional (2D) VSe 2 , with conflicting results throughout the literature. These discrepancies in magnetic properties between both phases (T and H) of 2D VSe 2 are most likely due to the structural parameters being coupled to the magnetic properties. Specifically, both phases have a close lattice match and similar total energies, which makes it difficult to determine which phase is being observed experimentally. Here, in this study, we used a combination of density functional theory, highly accurate diffusion Monte Carlo (DMC), and a surrogate Hessian line-search optimization technique to resolve the previously reported discrepancy in structural parameters and relative phase stability. With DMC accuracy, we determined the free-standing geometry of both phases and constructed a phase diagram. Our findings demonstrate the successes of the DMC method coupled with the surrogate Hessian structural optimization technique when applied to a 2D magnetic system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural magnetic glassiness in the spin ice Dy 2 Ti 2 O 7

The origin and nature of glassy dynamics presents one of the central enigmas of condensed-matter physics across a broad range of systems ranging from window glass to spin glasses. The spin-ice compound Dy 2 Ti 2 O 7 , which is perhaps best known as hosting a three-dimensional Coulomb spin liquid with magnetically charged monopole excitations, also falls out of equilibrium at low temperature. How and why it does so remains an open question. Based on an analysis of low-temperature diffuse neutron-scattering experiments employing different cooling protocols alongside recent magnetic noise studies, combined with extensive numerical modeling, we argue that upon cooling, the spins freeze into what may be termed a “structural magnetic glass,” without an a priori need for chemical or structural disorder. Specifically, our model indicates the presence of frustration on two levels, first producing a near-degenerate constrained manifold inside which phase ordering kinetics is in turn frustrated. A remarkable feature is that monopoles act as sole annealers of the spin network and their pathways and history encode the development of glass dynamics, allowing the glass formation to be visualized. Our results suggest that spin ice Dy 2 Ti 2 O 7 provides one prototype of magnetic glass formation specifically and a setting for the study of kinetically constrained systems more generally.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Ground-state degeneracy and complex magnetism of geometrically frustrated Gd 2 Ir 0.97 Si 2.97

We report a new triangular-lattice intermetallic compound Gd 2 Ir 0.97 Si 2.97 was successfully synthesized as single phase by deliberately introducing vacancies. Theoretical analysis suggests that the ground state is competing with several low-energy spin configurations due to magnetic frustration on a nearly ideal triangular lattice. Despite a number of competing magnetic states, the compound exhibits long-range antiferromagnetic order at16K, a long-range ferrimagnetic transition at 6.5 K, and a reentrant cluster-glass transition below T f ~ 3K. The complex magnetism in the compound could be correlated with competing antiferromagnetic and ferrimagnetic structures predicted theoretically.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Autonomous Tools for Attack Surface Reduction (Final Report)

The electric power grid is a complex critical infrastructure that forms the lifeline of modern society, and its secure and reliable operation is of paramount importance to national security and economic wellbeing. However, recent findings documented in authoritative sources indicate the threat of cyber-based attacks growing in numbers and sophistication. However, securing the grid against stealthy cyberattacks is a challenging task due to legacy nature of the infrastructure coupled with dynamic nature of threat landscape and ever-growing sophistication of the adversaries. Additionally, the grid’s attack surface continues to grow with the increased dependence on digital communications and control that now extends to each consumer through smart meters and distributed energy resources. Unfortunately, this expansive surface increases the grid’s vulnerability and further exposes critical control systems in both substations and control centers. To respond to this emerging need, we had successfully assembled an interdisciplinary team with academic- industry partnership to successfully conduct research, development, evaluation, demonstration, and commercialization of attack surface reduction tools, whose goal was to significantly reduce the cyber attack surface in the North American power grid. Our proposed project was a synergistic collaborative effort leveraging the synergistic expertise of the team members across power systems, cyber security and CPS security, testbeds, field deployments and demonstration, and successful commercialization. The following are the specific tasks that have been successfully completed two phases (2016-2020). Phase I: Task 1: Developed and implemented a robust Project Management and Data Management Plan, coupled with a well thought out Risk Mitigation Plan. Task 2.1: Developed a comprehensive framework that continually assesses and autonomously reduces the attack surface for the power grid control environment spanning across substations, control center and the SCADA network to significantly reduce the risks of cyber attacks. Task 2.2: Developed attack surface analysis techniques, metrics, and tools that assess the attack surface at multiple levels including the control center, substations, and the SCADA network. Task 2.3: Developed attack surface reduction techniques and tools that dynamically reduce attack surface and hence increase attacker’s cost without interfering in the critical functions of the system. Task 2.4: Prototyped, implemented, and quantitatively evaluated/validated the techniques and tools on a realistic industrial CPS security testbed environment by leveraging the unique resources of the team. Task 3: Developed Commercialization plan to transition the developed tools into power system industry stakeholders for a broader adoption by leveraging the expertise of our industrial members. Phase II: Task 4: Successfully completed field demonstration, verification, and evaluation of the effectiveness of the attack surface analysis and reduction techniques on a realistic utility testbed environment. This also involved the development of realistic scenarios, sound metrics, data sets, evaluation criteria, and documentation. Technology integration & Field demonstration: The project had significantly advanced the state-of-the-art research and practice in improving the cybersecurity of our nation’s power grid infrastructure against cyber threats. In particular, the proposed, designed, and deployed attack surface analysis and reduction algorithms and tools have contributed to significantly reducing the exposure and risk of the devices, substations, and the integrated SCADA/EMS/ DMS grid environment to cyber threat. Strong demonstration and evaluation techniques have verified the feasibility of the developed techniques on realistic cyber-physical testbeds and utility partner's real grid environment, and collaborative research and evaluation of attack surface reduction techniques (for wide-are monitoring and control) within a vendor (GE) EMS platform. The Attack Host Analyzer (AHA) tool that was developed through this project was made available through GitHub.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Brain-wave measures of workload in advanced cockpits: The transition of technology from laboratory to cockpit simulator, phase 2

The present Phase 2 small business innovation research study was designed to address issues related to scalp-recorded event-related potential (ERP) indices of mental workload and to transition this technology from the laboratory to cockpit simulator environments for use as a systems engineering tool. The project involved five main tasks: (1) Two laboratory studies confirmed the generality of the ERP indices of workload obtained in the Phase 1 study and revealed two additional ERP components related to workload. (2) A task analysis' of flight scenarios and pilot tasks in the Advanced Concepts Flight Simulator (ACFS) defined cockpit events (i.e., displays, messages, alarms) that would be expected to elicit ERPs related to workload. (3) Software was developed to support ERP data analysis. An existing ARD-proprietary package of ERP data analysis routines was upgraded, new graphics routines were developed to enhance interactive data analysis, and routines were developed to compare alternative single-trial analysis techniques using simulated ERP data. (4) Working in conjunction with NASA Langley research scientists and simulator engineers, preparations were made for an ACFS validation study of ERP measures of workload. (5) A design specification was developed for a general purpose, computerized, workload assessment system that can function in simulators such as the ACFS.

Horst, Richard L.↗

Chemical transitions for interstellar C2 and CN in cloud envelopes

Observations were made of absorption from CH, C2, and CN toward moderately reddened stars in Sco, OB2, Ceo OB3, and Taurus/Auriga. For these directions, most of the reddening is associated with a single cloud complex, for example, the rho Ophiuchus molecular cloud, and as a result, the observations probe moderately dense material. When combined with avaliable data for nearby directions, the survey provides the basis for a comprehensive analysis of the chemistry for these species. The chemical transitions affecting C2 and CN in cloud envelopes were analyzed. The depth into a cloud at which a transition takes place was characterized by tau(sub uv), the grain optical depth at 1000 A. One transition at tau(sub uv) approx. = 2, which arises from, the conversion of C(+) into CO, affects the chemistries for both molecules because of the key role this ion plays. A second one involving production terms in the CN chemistry occurs at tau(sub uv) of approx. = 3; neutral reactions which C2 and CH is more important at larger values for tau(sub uv). The transition from photodissociation to chemical destruction takes place at tau(sub uv) approx. = 4.5 for C2 and CN. The observational data for stars in Sco OB2, Cep OB3, and Taurus/Auriga were studied with chemical rate equations containing the most important production and destruction mechanisms. Because the sample of stars in Sco OB2 includes sight lines with A(sub v) ranging from 1-4 mag, sight lines dominated by photochemistry could be analyzed separately from those controlled by gas-phase destruction. The analysis yielded values for two poorly known rate constants for reactions involved in the production of CN; the reactions are C2 + N yields CN + C and C(+) + NH yields all products. The other directions were analyzed with the inferred values. The predicted column densities for C2 and CN agree with the observed values to better than 50%, and in most instances 20%. When combining the estimates for density and temperature derived from chemical modeling and molecular excitation for a specific cloud, such as the rho Ophiuchus molecular cloud, the portion of the cloud envelope probed by C2 and CN absorption was found to be in pressure equilibrium.

Federman, S. R.↗

Overview of the Medium and High Frequency Telescopes of the LiteBIRD Satellite Mission

LiteBIRD is a JAXA-led Strategic Large-Class mission designed to search for the existence of the primordial gravitational waves produced during the inflationary phase of the Universe, through the measurements of their imprint onto the polarization of the cosmic microwave background (CMB). These measurements, requiring unprecedented sensitivity, will be performed over the full sky, at large angular scales, and over 15 frequency bands from 34 GHz to 448 GHz. The LiteBIRD instruments consist of three telescopes, namely the Low-, Medium- and High-Frequency Telescope (respectively LFT, MFT and HFT). We present in this paper an overview of the design of the Medium-Frequency Telescope (89–224 GHz) and the High-Frequency Telescope (166–448 GHz), the so-called MHFT, under European responsibility, which are two cryogenic refractive telescopes cooled down to 5 K. They include a continuous rotating half-wave plate as the first optical element, two high-density polyethylene (HDPE) lenses and more than three thousand transition-edge sensor (TES) detectors cooled to 100 mK. We provide an overview of the concept design and the remaining specific challenges that we have to face in order to achieve the scientific goals of LiteBIRD.

LiteBIRD↗

Optimizing Li‐Excess Cation‐Disordered Rocksalt Cathode Design Through Partial Li Deficiency

Li-excess disordered rocksalts (DRXs) are emerging as promising cathode materials for Li-ion batteries due to their ability to use earth-abundant transition metals. In this work, a new strategy based on partial Li deficiency engineering is introduced to optimize the overall electrochemical performance of DRX cathodes. Specifically, by using Mn-based DRX as a proof-of-concept, it is demonstrated that the introduction of cation vacancies during synthesis (e.g., Li 1.3-x Mn 2+ 0.4-x Mn 3+ x Nb 0.3 O 1.6 F 0.4 , x = 0, 0.2, and 0.4) improves both the discharge capacity and rate performance due to the more favored short-range order in the presence of Mn3+. Density functional theory calculations and Monte Carlo simulations, in combination with spectroscopic tools, reveal that introducing 10% vacancies (Li 1.1 Mn 2+ 0.2 Mn 3+ 0.2 Nb 0.3 O 1.6 F 0.4 ) enables both Mn 2+ /Mn 3+ redox and excellent Li percolation. However, a more aggressive vacancy doping (e.g., 20% vacancies in Li 0.9 Mn 3+ 0.4 Nb 0.3 O 1.6 F 0.4 ) impairs performance because it induces phase separation between an Mn-rich and a Li-rich phase.

25 ENERGY STORAGE↗

Synchrotron-based techniques for characterizing STCH water-splitting materials

Understanding the role of oxygen vacancy–induced atomic and electronic structural changes to complex metal oxides during water-splitting processes is paramount to advancing the field of solar thermochemical hydrogen production (STCH). The formulation and confirmation of a mechanism for these types of chemical reactions necessitate a multifaceted experimental approach, featuring advanced structural characterization methods. Synchrotron X-ray techniques are essential to the rapidly advancing field of STCH in part due to properties such as high brilliance, high coherence, and variable energy that provide sensitivity, resolution, and rapid data acquisition times required for the characterization of complex metal oxides during water-splitting cycles. X-ray diffraction (XRD) is commonly used for determining the structures and phase purity of new materials synthesized by solid-state techniques and monitoring the structural integrity of oxides during water-splitting processes (e.g., oxygen vacancy–induced lattice expansion). X-ray absorption spectroscopy (XAS) is an element-specific technique and is sensitive to local atomic and electronic changes encountered around metal coordination centers during redox. While in operando measurements are desirable, the experimental conditions required for such measurements (high temperatures, controlled oxygen partial pressures, and H 2 O) practically necessitate in situ measurements that do not meet all operating conditions or ex situ measurements. Here, we highlight the application of synchrotron X-ray scattering and spectroscopic techniques using both in situ and ex situ measurements, emphasizing the advantages and limitations of each method as they relate to water-splitting processes. The best practices are discussed for preparing quenched states of reduction and performing synchrotron measurements, which focus on XRD and XAS at soft (e.g., oxygen K-edge, transition metal L-edges, and lanthanide M-edges) and hard (e.g., transition metal K-edges and lanthanide L-edges) X-ray energies. The X-ray absorption spectra of these complex oxides are a convolution of multiple contributions with accurate interpretation being contingent on computational methods. The state-of-the-art methods are discussed that enable peak positions and intensities to be related to material electronic and structural properties. Through careful experimental design, these studies can elucidate complex structure–property relationships as they pertain to nonstoichiometric water splitting. A survey of modern approaches for the evaluation of water-splitting materials at synchrotron sources under various experimental conditions is provided, and available software for data analysis is discussed.

08 HYDROGEN↗

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗