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NASA NTRS2002

Surface Temperature Assimilation in the Global Land Data Assimilation System (GLDAS)

The Global Land Data Assimilation System (GLDAS) is a global land parameterization that uses prescribed meteorology as forcing in order to determine regular gridded land surface states (temperature and moisture) and other properties (e.g. water and heat fluxes). In the present experiment, the assimilation of surface skin temperature is incorporated into the land parameterizations. The meteorological forcing was derived from the Goddard Earth Observing System (GEOS-3) Data Assimilation System (DAS) for the full year of 1998 GLDAS can use several land parameterizations, but here we use the Mosaic land surface model and the Common Land Model (CLM). TOVS surface temperature observations are assimilated into GLDAS. The TOVS observations are less frequent that observations used in previous experiments (ISCCP). The purpose of this presentation is to evaluate the impact of the TOVS assimilation on both Mosaic and CLM. We will especially consider the impact of coarse temporal observations on the assimilation and bias correction.

Bosilovich, Michael G.↗

NASA NTRS1977

The effect of oxidation-expanded defects upon MOS parameters

Implantation of Ne ions was chosen as a means of introducing a uniformly distributed quantitatively controllable and reproducible amount of microdefects at the silicon surface. Each wafer was ion-implanted on one half of its surface, the other half remaining as a control. Seven implant fluences from 1 trillion to 5 by 10 to the 14th power Ne ions/sq cm were used. The fluences, as well as the concentrations of defects expanded by the subsequent gate oxidation, were correlated with seven different MOS parameters. For implant fluences of 10 to the 14th power per sq cm and above, increasing stacking-fault densities were found. The oxide defect density associated with time-dependent breakdown increased significantly with Ne dose. The presence of oxidation-expanded defects drastically increases the surface-generation velocity and decreases the bulk lifetime. Slight increases in flatband voltage and surface-state density occurred only for the wafers having the greatest defect concentrations. Oxidation of a P-containing damaged silicon surface results in a greater pileup of P at the surface than occurs for the oxidation of a similar but undamaged surface. It appears that the expanding defects restrain the diffusion of P inward from the surface.

Prussin, S.↗

NASA NTRSDate not supplied

Toward Enhancing the Use of IASI and CrIS Surface-Sensitive Radiances Over Land in the NASA GMAO GEOS Data Assimilation Framework

Assimilating surface-sensitive radiances over land is still challenging for both infrared (IR) and microwave (WV) radiances essentially because of the large uncertainties of the land physical surface emissivity model used in the Community Radiative Transfer Model (CRTM) and the uncertainties of land surface state properties. Currently very few IR radiances are assimilated over land. Large number of IR radiances are rejected by the surface sensitivity checks as well as the cloud detection check. In this study, we identified the appropriate Infrared Atmospheric Sounding Interferometer (IASI) and Cross-track Infrared Sounder (CrIS) surface-sensitive channels to retrieve Land Surface Temperature (LST). Then, we studied the impacts of these retrieved LST and retuned cloud detection on the simulation and assimilation of IASI and CrIS in the NASA GEOS in clear sky conditions. The preliminary results are shown to enhance the rate of IASI and CrIS assimilated channels over land. The impacts on the quality of the resulting analysis and subsequent forecast will be presented at the meeting.

Niama Boukachaba↗

NASA NTRS2018

Recent Updates in the SMAP Level-4 Soil Moisture Algorithm

The NASA Soil Moisture Active Passive (SMAP) mission generates, among other data sets, the Level-4 Soil Moisture (L4_SM) product. The L4_SM data are published with a mean latency of ~2.5 days from the time of observation and provide global, three-hourly, 9-km resolution estimates of surface and root-zone soil moisture and related land surface states and fluxes. The L4_SM algorithm is based on the assimilation of SMAP radiometer brightness temperature observations into the NASA Catchment land surface model using a spatially distributed ensemble Kalman filter (EnKF). In 2018, the L4_SM algorithm was upgraded from Version 3 to Version 4. Underlying the new version is a revised modeling system that includes improved input parameter datasets for land cover, topography, and vegetation height that are based on recent, high-quality, space-borne remote sensing observations. Additionally, SMAP Level-2 soil moisture retrievals and in situ soil moisture measurements were used to calibrate a particular Catchment model parameter that governs the recharge of surface soil moisture from below under non-equilibrium conditions, which brings the model's surface soil moisture more in line with the SMAP Level-2 and in situ soil moisture. Moreover, the calibration of the assimilated SMAP brightness temperatures changed substantially from Version 3 to Version 4, and the "catchment deficit" model variable was removed from the EnKF state vector to avoid degrading the model's groundwater estimates.Considerable effort went into the version upgrade, creating an expectation that the new version is improved over the old version. Indeed, some aspects of the new version are clearly better. However, other aspects are not. In this presentation we summarize the skill of the new and old versions vs. independent in situ measurements and in terms of data assimilation diagnostics, including, for example, the statistics of the (soil moisture) analysis increments and the observation-minus-forecast (brightness temperatures) residuals. We share our experience with trying to improve to the L4_SM product and the lessons learned from the effort.

Reichle, Rolf H.↗

DOE OSTI2025

Investigation of N 2 /O 2 plasma interaction with Pt-catalyst: effect of metastable adsorbates on product hysteresis

The coupling of catalysts and atmospheric-pressure plasma has the potential to improve the efficiency of certain catalytic reactions. Understanding the changes that the catalyst surface undergoes during exposure to plasma is key to improving plasma–catalytic performance. In this work, long term exposure of Pt–Al 2 O 3 powder catalyst to an Ar/N 2 /O 2 non-equilibrium atmospheric-pressure plasma-jet was investigated. Products produced by the interaction were analyzed downstream with Fourier-transform infrared spectroscopy while surface species were analyzed operandi with diffuse reflectance infrared Fourier transform spectroscopy. During exposure, the catalyst temperature was ramped cyclically between 100 °C and 350 °C to understand how substrate temperature affects the plasma–catalyst interaction. Long-lasting changes were revealed to take place on the catalyst surface during plasma exposure. At low temperatures, Pt–O and Pt–NO accumulate on the surface which react at elevated temperatures to form NO 2 . NO 2 initially appears to spill on to the Al 2 O 3 support as nitrites and nitrates instead of desorbing. Stable surface conditions are only achieved after prolonged plasma exposure, when nitrate sites on the Al 2 O 3 support are filled. By changing the catalyst temperature at various rates, the impact of total plasma species flux to the surface was analyzed. It was found that decreasing the heating rate increased the hysteresis in the pattern of NO 2 formation during thermal cycling. The variation with temperature demonstrates that plasma exposure results in a buildup of surface NO x and oxygen species which react or desorb at high temperatures. The observed changes are discussed from the generic viewpoint that a non-equilibrium plasma interacting with a catalyst at low temperature introduces metastable steady-state surface conditions. Upon heating above a threshold temperature, the introduced surface modifications can change either due to thermal effects, or, for a plasma environment, by additional interaction with the incident plasma species flux. The surface/material changes take place in a highly predictable fashion and after sufficient time above the threshold temperature reach a steady-state condition that is different from the transient behavior that is observed during initial heating. During cooling the plasma-surface interaction exhibits a different behavior than during heating, and this results in hysteresis of diverse observables. The metastability/hysteresis description appears quite generic and analogous to hysteresis behavior seen for different systems. Furthermore, it is expected to be useful for understanding the consequences of plasma–catalyst surface interactions for various systems.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Competition between roughness and strength for scale-dependent surfaces

Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, in this work, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography 𝐶 and yield stress 𝑌 follow power laws as a function of scale 𝜆, such that 𝐶∼𝜆 −𝑚 and 𝑌∼𝜆 −𝑛 , respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as 1−𝑛. We also show that the plasticity is expected to erode the contacts if 𝑚 is lower than 𝑛−3, which corresponds to a Hurst exponent lower than 1−𝑛/2. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.

elasticity↗

NASA NTRS1978

Work function measurement of lanthanum-boron compounds

The relationship between emission properties and sample composition is studied for lanthanum-boron compounds. Specifically, the La-B system is considered between 1400 and 2100 K and between LaB(4.24) and LaB(29.2) to determine the phase relationship, chemical activity of the compounds, vapor composition, and vaporization rate. The results indicate that: (1) a blue-colored phase near LaB(9) exists between a purple-colored LaB(6) and elemental boron, (2) vaporization is sufficiently more rapid than diffusion so that great compositional differences exist between the surface and the interior, (3) an activation energy lowers the boron vaporization rate from LaB(6), and (4) a steady-state surface composition between LaB(6.04) and LaB(6.07) exists for freely vaporizing materials as a function of interior composition, purity, and temperature. It is noted that the ultimate life of a thermionic diode is governed by electrode vaporization rate whereas efficiency is governed by the electrode work function.

Jacobson, D. L.↗

NASA NTRS1986

Surface film effects on drop tube undercooling studies

The effects of various gaseous atmospheric constituents on drop-tube solidified samples of elemental metals were examined from a microstructural standpoint. All specimens were prepared from the purest available elements, so effects of impurities should not account for the observed effects. The drop-tube gas has a definite effect on the sample microstructure. Most dramatically, the sample cooling rate is effected. Some samples receive sufficient cooling to solidify in free fall while others do not, splating at the end of the drop tube in the sample catcher. Gases are selectively absorbed into the sample. Upon solidification gas can become less soluble and as a result forms voids within the sample. The general oxidation/reduction characteristics of the gas also affect sample microstructures. In general, under the more favorable experimental conditions including reducing atmospheric conditions and superheatings, examination of sample microstructures indicates that nucleation has been suppressed. This is indicated by underlying uniform dendrite spacings throughout the sample and with a single dendrite orientation through most of the sample. The samples were annealed yielding a few large grains and single or bi-crystal samples were commonly formed. This was especially true of samples that were inadvertently greatly superheated. This is in contrast with results from a previous study in which surface oxides were stable and contained numerous sites of nucleation. The number of nucleation events depends upon the surface state of the specimen as determined by the atmosphere and is consistent with theoretical expectations based upon the thermodynamic stability of surface oxide films. Oxide-free specimens are characterized by shiny surfaces, with no observable features under the scanning electron microscope at 5000X.

Ethridge, E. C.↗

NASA NTRS2010

Towards Global Simulation of Irrigation in a Land Surface Model: Multiple Cropping and Rice Paddy in Southeast Asia

Agricultural land use significantly influences the surface water and energy balances. Effects of irrigation on land surface states and fluxes include repartitioning of latent and sensible heat fluxes, an increase in net radiation, and an increase in soil moisture and runoff. We are working on representing irrigation practices in continental- to global-scale land surface simulation in NASA's Global Land Data Assimilation System (GLDAS). Because agricultural practices across the nations are diverse, and complex, we are attempting to capture the first-order reality of the regional practices before achieving a global implementation. This study focuses on two issues in Southeast Asia: multiple cropping and rice paddy irrigation systems. We first characterize agricultural practices in the region (i.e., crop types, growing seasons, and irrigation) using the Global data set of monthly irrigated and rainfed crop areas around the year 2000 (MIRCA2000) dataset. Rice paddy extent is identified using remote sensing products. Whether irrigated or rainfed, flooded fields need to be represented and treated explicitly. By incorporating these properties and processes into a physically based land surface model, we are able to quantify the impacts on the simulated states and fluxes.

Beaudoing, Hiroko Kato↗

DOE OSTI2025

Characterizing Ultrafast Intersystem Crossing Pathways in Molecular Pt Dimers Using Time-Resolved Wide-Angle X-ray Scattering

Vibronic coupling between transition metal charge transfer states is a potential mechanism for enhancing the intersystem crossing (ISC) rate. Vibronic coupling-driven ISC has been observed in Pt(II) dimer complexes, where the trajectory across excited-state pathways is tuned by atomic displacements via Pt–Pt stretching vibrations. Time-resolved wide-angle X-ray scattering (TR-WAXS) was utilized to quantify the Pt–Pt contraction following metal–metal-to-ligand charge transfer (MMLCT) excitation in Pt dimers with different bridging ligands. Both complexes exhibit Pt–Pt bond formation with a decrease in Pt–Pt distance of ∼ 0.25 Å and coherent vibrational wavepackets (CVWPs) encoded in the Pt–Pt contraction of both dimers. However, the complexes exhibit different time-dependent evolution of their CVWPs. Analysis of interference patterns between different CVWPs is used to track the trajectory across the excited-state surfaces. Furthermore, this work demonstrates that the interference between CVWPs in ultrafast TR-WAXS encodes indirect information regarding electronic excited-states to reveal the Pt dimer bridge-dependent ISC mechanism.

Computational chemistry↗

NASA NTRS1977

Semiclassical dynamics on multiple electronic surfaces - Three-dimensional treatment of reactive F + H2

The role of electron transitions in collisions is studied for the F + H2 reaction by combining quasi-classical Monte Carlo trajectories with a semiclassical decoupling approximation for the electron transitions. Attention is directed at the reaction of excited state F atoms reacting to form ground state products; the reactants are initiated in either of two spin-orbit states of the atom with the diatom in the ground vibrational state and the lowest four rotational states, at relative translational energies of 0.1, 0.2 and 0.3 eV. Even if the reactants are initiated on the excited state surface, the reactive cross sections (which are classically forbidden) are significant. The major dynamical effects of the excited state reaction are the flow of reactant electronic energy into product internal energy.

Komornicki, A.↗

DOE OSTI2025

Evidence of Au(111) topological states in a kagome analogue lattice and their robustness beyond ultra-low temperatures and defect-free conditions

The experimental realization of kagome lattices that exhibit the predicted coexistence of topological states with high electron kinetics and non-dispersing quantum states remains challenging. Additionally, the robustness of these states against structural perturbations has rarely been explored. Here, we report on the formation of an analogue kagome structure via the electrostatic self-assembly of 4,7-dibromobenzo[c]-1,2,5-thiadiazole (2Br-BTD) molecules on Au(111). Local spectroscopic measurements, supported by theoretical calculations, reveal that the weak molecular coupling reshapes the topological-induced Shockley surface state of Au(111) by imposing a (7 × 7) periodicity, resulting in new band crossings. The molecular overlayer favours the opening of electron gaps at these positions manifested as sharp peaks in dI/dV spectra and electron localization in either the hexagonal or triangular sublattices of the kagome structure. To explore the robustness of these topological states, we monitored their stability under varied conditions, including different temperatures, the unaltered herringbone reconstruction of the Au(111) surface and local structural relaxation of the molecular assembly. These results demonstrate the degree of topological protection of these states, which holds potential for fundamental and applied research.

Austin, Dave [University of Central Florida, Orlan↗

DOE OSTI2026

Quasi-In-Situ Analysis of Electrode Top Atomic Layers via High-Sensitivity Low-Energy Ion Scattering and Potential-Controlled Sample Transfer

Electrocatalytic reactions involve interfacial interactions between the surfaces of electrodes and reactive species at an electrolyte interface. There are presently no universal or unambiguous methods to directly assay the active top atomic layer composition that influences the reactivity of these electrodes under relevant operating conditions. Low-energy ion scattering (LEIS) spectroscopy is a surface characterization technique that yields compositional analysis of the outermost atomic layer of a material, but it must be performed in ultrahigh vacuum (UHV). Application of LEIS measurements to electrochemical materials that are removed from ambient liquid-phase environments thus leaves an open question as to whether the surface that is transferred to UHV is truly the surface that manifested during the electrochemical reaction. Toward the goal of preserving the active surface state, we developed a sample transfer workflow for LEIS enabling air-free removal and drying of an electrode from an electrochemical cell while maintaining control of the potential using an auxiliary electrode. The potential-controlled emersion method was demonstrated to give distinct potential-dependent surface compositions for a Cu−Pd alloy relative to removal after uncontrolled return to open-circuit potential. A Cu-enriched surface was found at anodic potential and a Pd-enriched surface at cathodic potential, suggesting that the approach can be used to retain representative atomic configurations during transfer. Since adsorbates will often persist from the reaction environment, conventional sample pretreatment methods for removal, including atomic O and atomic H exposure, were also contrasted. Both methods were found to differ with results from incidental low-dose depth profiling by the LEIS primary ion source, which removes adventitious species and surface atoms during the course of repeated measurements. These depth profiles were found to be sensitive to sample history and thus qualitatively informative, despite the possible changes induced by ion damage. The results exhibit (i) the need for complete control over the polarization state of the sample at all times (no excursions to open circuit during transfer) and (ii) the utility of low-dose depth profiling to capture changes in the near-surface composition.

Alloys↗

DOE OSTI2024

Characterization of Polyamide Thin Films by Atomic Force Microscopy

This study directly compares the mechanical behavior of novel molecular layer deposition (MLD) and analogous interfacial polymerization (IP) polyamide thin films in environments relevant to reverse osmosis (RO) membrane operation. The elastic modulus of the films was determined using atomic force microscopy (AFM) in dry, hydrated, and chlorinated states. Surface roughness characteristics were also obtained given their potential influence on AFM modulus measurements. The much smoother MLD films demonstrated a statistically higher modulus in all states as compared to their IP counterparts. The MLD films maintained a modulus ~3X and ~5X greater than that of IP films after hydration and chlorination, respectively. Such differences in behavior may be due to the higher density and correspondingly lower void content of the MLD films. Results from this study provide a rationale for future development of MLD for fabrication of polyamide films for incorporation in RO membranes.

atomic force microscopy↗

NASA NTRS1998

Real Time Land-Surface Hydrologic Modeling Over Continental US

The land surface component of the hydrological cycle is fundamental to the overall functioning of the atmospheric and climate processes. Spatially and temporally variable rainfall and available energy, combined with land surface heterogeneity cause complex variations in all processes related to surface hydrology. The characterization of the spatial and temporal variability of water and energy cycles are critical to improve our understanding of land surface-atmosphere interaction and the impact of land surface processes on climate extremes. Because the accurate knowledge of these processes and their variability is important for climate predictions, most Numerical Weather Prediction (NWP) centers have incorporated land surface schemes in their models. However, errors in the NWP forcing accumulate in the surface and energy stores, leading to incorrect surface water and energy partitioning and related processes. This has motivated the NWP to impose ad hoc corrections to the land surface states to prevent this drift. A proposed methodology is to develop Land Data Assimilation schemes (LDAS), which are uncoupled models forced with observations, and not affected by NWP forcing biases. The proposed research is being implemented as a real time operation using an existing Surface Vegetation Atmosphere Transfer Scheme (SVATS) model at a 40 km degree resolution across the United States to evaluate these critical science questions. The model will be forced with real time output from numerical prediction models, satellite data, and radar precipitation measurements. Model parameters will be derived from the existing GIS vegetation and soil coverages. The model results will be aggregated to various scales to assess water and energy balances and these will be validated with various in-situ observations.

Houser, Paul R.↗

DOE OSTI2025

Noisy Approach to Intrinsically Mixed-State Topological Order

We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed state can display (imTO)—topological order that is not expected to occur in the ground state of 2D local gapped Hamiltonians. Specifically, we show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, is more naturally phrased as, and provides a physical mechanism for, “gauging out” anyons in the original Hilbert space. We find that gauging out anyons generically results in imTO, with the decohered mixed state strongly symmetric under certain anomalous 1-form symmetries. This framework lays bare a striking connection between the decohered density matrix and , which can appear as anomalous surface states of three-dimensional topological orders. Through a series of examples, we show that the decohered state can display a classical memory, encode logical qubits (i.e., exhibit a quantum memory), and even host chiral or nonmodular topological order. We argue that a partial classification of imTO is given in terms of nonmodular braided-fusion categories. Published by the American Physical Society 2025

Sohal, Ramanjit (ORCID:0000000292975715)↗

NASA NTRSDate not supplied

The Land Surface in Current and Planned MERRA Reanalysis Products

Current global atmospheric reanalysis products such as the European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA5), the NASA Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2), and the Japanese Reanalysis for Three Quarters of a Century (JRA-3Q) provide estimates of land surface states and fluxes, including soil moisture, soil temperature, snow mass, latent and sensible heat fluxes, and runoff, that are widely used in research and applications. These land surface estimates are based on land surface process models and, depending on the reanalysis product, on precipitation observations or the assimilation of land surface observations of soil moisture, soil temperature, snow conditions, and screen-level air temperature and humidity from satellite observations and in situ measurements. In this presentation, we review the land surface modeling and data assimilation components of the suite of current and planned MERRA reanalysis products. In addition to MERRA-2, we will discuss the latest NASA reanalysis, MERRA for the 21st century (M21C), which is currently under production, as well as the development and planning of the next version of the MERRA reanalysis, tentatively labeled MERRA-3. In MERRA-2, observations-based precipitation data products are used to correct the precipitation falling on the land surface. Outside of the high-latitudes and Africa, the daily, 0.5-degree, gauge-based Climate Prediction Center (CPC) Unified (CPCU) product is used. In Africa, the pentad, 2.5-degree, satellite- and gauge-based CPC Merged Analysis of Precipitation (CMAP) product is used. Poleward of 62.5 degrees latitude, the land surface sees the precipitation generated by the atmospheric model in the cycling data assimilation system. This configuration provides improved soil moisture estimates compared to those of the original (version 1) MERRA estimates, which did not benefit from the use of precipitation observations. Moreover, the use of precipitation observations facilitates a seamless spin-up of the land surface initial conditions across the MERRA-2 production streams. The use of a gauge-only precipitation product in MERRA-2 across much of the globe, however, adversely impacts the quality of the MERRA-2 land surface estimates in regions with poor gauge coverage, including most of South America and Australia. Therefore, the forthcoming M21C reanalysis uses satellite- and gauge-based precipitation from the Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement Mission (IMERG). This change results in significant improvements in the quality of the M21C soil moisture estimates in the Southern Hemisphere compared to those from MERRA-2. Planning for MERRA-3 focuses on the assimilation of soil moisture observations from the Soil Moisture Active Passive (SMAP) mission and the Advanced Scatterometer (ASCAT), along with snow cover area fraction observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) to further improve the quality of the land surface estimates from the reanalysis. As a first step towards the assimilation of land surface observations in MERRA-3, the offline (land-only) M21C-Land reanalysis is currently under development as a supplemental M21C product that includes the assimilation of SMAP, ASCAT, and MODIS observations. Preliminary results from M21C and M21C-Land will be discussed in the context of MERRA-2 and plans for MERRA-3.

Rolf Reichle↗

NASA NTRS1975

Application of the MOS-C-V technique to determine impurity concentrations and surface parameters on the diffused face of silicon solar cells

The feasibility of using the MOS C-V technique to obtain information regarding impurity and surface state concentrations on the diffused face of silicon solar cells with Ta2O5 coatings is studied. Results indicate that the MOS C-V technique yields useful information concerning surface parameters which contribute to the high, efficiency limiting, surface recombination velocities on the n+ surface of silicon solar cells.

Weinberg, I.↗