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At least 1,729 records · Page 96

Theoretical Analysis of Stationary Potential Flows and Boundary Layers at High Speed

The present report consists of two parts. The first part deals with the two-dimensional stationary flow in the presence of local supersonic zones. A numerical method of integration of the equation of gas dynamics is developed. Proceeding from solutions at great distance from the body the flow pattern is calculated step by step. Accordingly the related body form is obtained at the end of the calculation. The second part treats the relationship between the displacement thickness of laminar and turbulent boundary layers and the pressure distribution at high speeds. The stability of the boundary layer is investigated, resulting in basic differences in the behavior of subsonic and supersonic flows. Lastly, the decisive importance of the boundary layer for the pressure distribution, particularly for thin profiles, is demonstrated.

Oswaititsch, K.↗

Experimental Technetium Release from Simulated Salt-stone Cementitious Waste Form - 18419

Experiments are being conducted to evaluate the early release of technetium (Tc) from fresh salt-stone waste forms using dynamic flow-through tests. Salt-stone is a chemically reducing, grout-based waste form used by the U.S. Department of Energy (DOE) to dispose of low-activity salt solutions arising from high-level radioactive waste tank closure activities at the Savannah River Site (SRS). A key safety function of salt-stone is maintaining a low-flow, chemically reducing environment that will attenuate the release of redox-sensitive radioelements such as Tc. Salt-stone also provides a physical barrier due to its low intrinsic permeability, which limits both water and oxygen ingress. These release experiments, conducted to support the U.S. Nuclear Regulatory Commission's monitoring role during tank closure, are designed to provide independent information on how well salt-stone will perform its safety function. The dynamic leach tests were conducted in a Hassler-type core-holder permeameter system that allows an accelerated flow rate of simulated SRS groundwater through an intact cylinder of salt-stone spiked with Tc-99 at a concentration of approximately 2,100 Bq/g (3 ppm). The first salt-stone specimen to be tested (Specimen 2) was prepared with Grade 100 ground granulated blast-furnace slag and aged for 119 days in a temperature-controlled, low-oxygen, high-humidity environment. Before test completion, 9.5 pore volumes (PV) of simulated SRS groundwater were passed through the salt-stone cylinder. After a few PV, apparent saturated hydraulic conductivity (K{sub sat}) values calculated from flow data reached a steady-state value of approximately 1.0 x 10{sup -9} cm/s, which is within the range of previously reported data. Tc-99 concentrations in leachate peaked early during the leach test at 2.0 x 10{sup -7} M and then declined to approximately 4 x 10{sup -8} M after 9.5 PV. The leachate Tc-99 concentration after elution of 9.5 PV is broadly consistent with a Tc solution concentration controlled by the solubility of reduced Tc solids. The range of Tc-99 concentrations is similar to the range reported for a column test that was sponsored by DOE, but the time pattern of release differs. The second salt-stone specimen tested (Specimen 3) was aged for 372 days and it further differed from the first specimen in that its Grade 100 slag component had been finely ground using a mortar and pestle in an attempt to make it more reactive. This second test yielded Tc release behavior broadly similar to that observed during the first test, except that the early Tc peak (at 1.2 x 10{sup -6} M) was six times higher and the concentration after 6.7 PV (8.8 x 10{sup -8} M) was approximately two times higher than in the first test. In addition, the steady-state K{sub sat} was an order of magnitude lower than that of the first specimen. During the second test, the injection pump was intentionally turned off for a period of 11 days (i.e., approximate residence time for 1 PV) and a Tc spike was observed when pumping resumed, suggesting that longer residence times may promote higher Tc effluent concentrations. During a second intentional shut-down of the pump for 25 days (approximate residence time for 2 PV), another Tc spike was observed. An unplanned excursion to higher confining pressure physically affected the specimen, temporarily lowering the apparent K{sub sat} followed by a subsequent increase in both K{sub sat} and Tc effluent concentration. One hypothesis is that the transient spike in confining pressure and resulting salt-stone compression and later decompression may have induced Tc release from otherwise inactive pores. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Rare earth element behavior during groundwater–seawater mixing along the Kona Coast of Hawaii

Groundwater and seawater samples were collected from nearshore wells and offshore along the Kona Coast of the Big Island of Hawaii to investigate rare earth element (REE) behavior in local subterranean estuaries. Previously we saw that submarine groundwater discharge (SGD) is the predominant flux of terrestrial waters to the coastal ocean along the arid Kona Coast of Hawaii. Groundwater and seawater samples were filtered through 0.45 μm and 0.02 μm pore-size filters to evaluate the importance of colloidal and soluble (i.e., truly dissolved ionic species and/or low molecular weight [LMW] colloids) fractions of the REEs in the local subterranean estuaries. Mixing experiments using groundwater collected immediately down gradient from a wastewater treatment facility (WWTF) proximal to the Kaloko-Hanokohau National Historic Park, and more “pristine” groundwater from a well constructed in a lava tube at Kiholo Bay, were conducted with local seawater to study the effect of solution composition (i.e., pH, salinity) on the concentrations and fractionation behavior of the REEs as groundwater mixes with seawater in Kona Coast subterranean estuaries. The mixed waters were also filtered through 0.45 or 0.02 μm filters to ascertain the behavior of colloidal and soluble fractions of the REEs across the salinity gradient in each mixing experiment. Concentrations of the REEs were statistically identical (two-tailed Student t-test, 95% confidence) between the sequentially filtered sample aliquots, indicating that the REEs occur as dissolved ionic species and/or LMW colloids in Kona Coast groundwaters. The mixing experiments revealed that the REEs are released to solution from suspended particles or colloids when Kona Coast groundwater waters mix with local seawater. The order of release that accompanies increasing pH and salinity follows light REE (LREE) > middle REE (MREE) > heavy REE (HREE). Release of REEs in the mixing experiments is driven by decreases in the free metal ion activity in solution and the concomitant increase in the amount of each REE that occurs in solution as dicarbonato complexes [i.e., Ln(CO 3 ) 2 - ] as pH increases across the salinity gradient. Input-normalized REE patterns of Kona Coast groundwater and coastal seawater are nearly identical and relatively flat compared to North Pacific seawater, indicating that SGD is the chief source of these trace elements to the ocean along the Kona Coast. Additionally, REE concentrations of the coastal seawater are between 10 and 50 times higher than previously reported open-ocean seawater values from the North Pacific, further demonstrating the importance of SGD fluxes of REEs to these coastal waters. Altogether, these observations indicate that large-scale removal of REEs, which characterizes the behavior of REEs in the low salinity reaches of many surface estuaries, is not a feature of the subterranean estuary along the Kona Coast. A large positive gadolinium (Gd) anomaly characterizes groundwater from the vicinity of the WWTF. The positive Gd anomaly can be traced to the coastal ocean, providing further evidence of the impact of SGD on the coastal waters. Estimates of the SGD fluxes of the REEs to the coastal ocean along the Kona Coast (i.e., 1.3–2.6 mmol Nd day -1 ) are similar to recent estimates of SGD fluxes of REEs along Florida’s east coast and to Rhode Island Sound, all of which points to the importance of SGD as significant flux of REEs to the coastal ocean.

58 GEOSCIENCES↗

Analyzing the Energy and Power Consumption of Remote Memory Accesses in the OpenSHMEM Model

PGAS models like OpenSHMEM provide interfaces to explicitly initiate one-sided remote memory accesses among processes. In addition, the model also provides synchronizing barriers to ensure a consistent view of the distributed memory at different phases of an application. The incorrect use of such interfaces affects the scalability achievable while using a parallel programming model. This study aims at understanding the effects of these constructs on the energy and power consumption behavior of OpenSHMEM applications. Our experiments show that cost incurred in terms of the total energy and power consumed depends on multiple factors across the software and hardware stack. We conclude that there is a significant impact on the power consumed by the CPU and DRAM due to multiple factors including the design of the data transfer patterns within an application, the design of the communication protocols within a middleware, the architectural constraints laid by the interconnect solutions, and also the levels of memory hierarchy within a compute node. This work motivates treating energy and power consumption as important factors while designing compute solutions for current and future distributed systems.

Jana, Siddhartha↗

Experimental and Numerical Investigation on Vibration of Sandwich Plates with Honeycomb Cores Based on Radial Basis Function

The vibration characteristic of the sandwich plate with a honeycomb core was investigated by experimental measurements and numerical calculation based on radial basis function (RBF). RBF method was used not only in the meshless approach but also in the post-processing of the experimental data. During the experiment, amplitude-fluctuation electronic speckle pattern interferometry was applied to access the resonant frequencies and the corresponding vibration mode shapes simultaneously. Then RBF method was used to improve the quality of patterns and reconstruct the out-of-plane vibration amplitude after fringe analysis. As for numerical calculation, the modal parameters were numerically predicted using the first-order shear deformation theory. The computation approach was based on collocation with multi-quadric radial basis function. To understand the influence of the thickness of face sheet on dynamic behaviors, three types of specimens with different thickness were tested and analyzed. Of particular interest was that the vibration modes show veering due to the thickness increment. Furthermore, the numerical predicted results were compared with the experimental measurements for the first five modes. They are in good agreement with each other for resonant frequencies, mode shapes and relative out-of-plane amplitudes.

36 MATERIALS SCIENCE↗

Coalescing Wind Turbine Wakes

A team of researchers from the National Renewable Energy Laboratory and Statoil used large-eddy simulations to numerically investigate the merging wakes from upstream offshore wind turbines. Merging wakes are typical phenomena in wind farm flows in which neighboring turbine wakes consolidate to form complex flow patterns that are as yet not well understood. In the present study, three 6-MW turbines in a row were subjected to a neutrally stable atmospheric boundary layer flow. As a result, the wake from the farthest upstream turbine conjoined the downstream wake, which significantly altered the subsequent velocity deficit structures, turbulence intensity, and the global meandering behavior. The complexity increased even more when the combined wakes from the two upstream turbines mixed with the wake generated by the last turbine, thereby forming a "triplet" structure. Although the influence of the wake generated by the first turbine decayed with downstream distance, the mutated wakes from the second turbine continued to influence the downstream wake. Two mirror-image angles of wind directions that yielded partial wakes impinging on the downstream turbines yielded asymmetric wake profiles that could be attributed to the changing flow directions in the rotor plane induced by the Coriolis force. In conclusion, the turbine wakes persisted for extended distances in the present study, which is a result of low aerodynamic surface roughness typically found in offshore conditions

17 WIND ENERGY↗

Nanoscale dynamics during self-organized ion beam patterning of Si. I. Ar + bombardment

X-ray photon correlation spectroscopy (XPCS) is used to investigate the fluctuation dynamics during self- organized nanopatterning of silicon by Ar + bombardment at 65° polar angle. Rich structure is observed in the development of the correlation dynamics as seen in the evolving correlation time τ(q || ) and fluctuation relaxation exponent n(q || ). Furthermore, on length scales of the ripple structure, local structure becomes ever more long lived as coarsening progresses. In addition, τ (q || ) develops a peak on length scales corresponding to the ripple wavelength. As patterning progresses, correlation times become asymmetric between the positive and negative directions, suggesting the possibility of different dynamics on the slopes facing toward and away from the ion beam. Relaxation exponents show evolution from linear dynamics at early times to compressed exponential relaxation at low wave numbers and stretched exponential relaxation at high wave numbers. Compressed exponential behavior is reminiscent of stress relaxation processes observed in glasses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

CORSAIR: A Framework for Human Mobility Prediction through Visit Characterization and Spatial Behavior Modeling

The rapid advancement of location acquisition technologies has led to the daily collection of vast amounts of mobile trajectory data, facilitating in-depth research on human mobility and enabling more accurate mobility prediction models. However, existing methodologies often fall short in capturing the intricate dynamics of human navigation and spatial behavior. This paper addresses this gap by exploring the multifaceted relationships between individuals and their environments, considering the diverse influences of personal preferences and experiences. Some places hold sentimental value and are visited frequently, while others serve as transient points of passage. To model these differences, we introduce CORSAIR, a novel visit characterization framework that leverages visitation patterns and dwell times to delineate an individual’s relationship with specific places. CORSAIR classifies visits into seven distinct types: casual, occasional, routine, special, anchor, important, and resettling. Also, we show that explicitly recognizing these distinct visit types and incorporating nuanced visit intents into mobility prediction models leads to a substantial improvement in prediction accuracy. This distinction allows for more precise modeling of the individual’s transitions, enhancing the personalization and relevance of location-based services. Our findings suggest that a deeper understanding of the complexities of individual-environment interactions is crucial for developing effective predictive tools in mobility research.

Amichi, Licia [ORNL] (ORCID:0000000177631394)↗

Emulating Multiple Inheritance in Fortran 2003/2008

Although the high-performance computing (HPC) community increasingly embraces object-oriented programming (OOP), most HPC OOP projects employ the C++ programming language. Until recently, Fortran programmers interested in mining the benefits of OOP had to emulate OOP in Fortran 90/95. The advent of widespread compiler support for Fortran 2003 now facilitates explicitly constructing object-oriented class hierarchies via inheritance and leveraging related class behaviors such as dynamic polymorphism. Although C++ allows a class to inherit from multiple parent classes, Fortran and several other OOP languages restrict or prohibit explicit multiple inheritance relationships in order to circumvent several pitfalls associated with them. Nonetheless, what appears as an intrinsic feature in one language can be modeled as a user-constructed design pattern in another language. The present paper demonstrates how to apply the facade structural design pattern to support a multiple inheritance class relationship in Fortran 2003. The design unleashes the power of the associated class relationships for modeling complicated data structures yet avoids the ambiguities that plague some multiple inheritance scenarios.

97 MATHEMATICS AND COMPUTING↗

A Unified Interpretation of Variability in Precipitation Isotope Ratios

Abstract Several mechanisms have been proposed to explain why the isotope ratios of precipitation vary in space and time and why they correlate with other climate variables like temperature and precipitation. Here, we argue that this behavior is best understood through the lens of radiative transfer, which treats the depletion of atmospheric vapor transport by precipitation as analogous to the attenuation of light by absorption or scattering. Building on earlier work by Siler et al., we introduce a simple model that uses the equations of radiative transfer to approximate the two-dimensional pattern of the oxygen isotope composition of precipitation ( δ p ) from monthly mean hydrologic variables. The model accurately simulates the spatial and seasonal variability in δ p within a state-of-the-art climate model and permits a simple decomposition of δ p variability into contributions from gradients in evaporation and the length scale of vapor transport. Outside the tropics, δ p is mostly controlled by gradients in evaporation, whose dependence on temperature explains the positive correlation between δ p and temperature (i.e., the temperature effect). At low latitudes, δ p is mostly controlled by gradients in the transport length scale, whose inverse relationship with precipitation explains the negative correlation between δ p and precipitation (i.e., the amount effect). This suggests that the temperature and amount effects are both mostly explained by the variability in upstream rainout, but they reflect distinct mechanisms governing rainout at different latitudes. Significance Statement The isotopic composition of precipitation has long been used to make inferences about past climates based on its observed relationship with precipitation in the tropics and with temperature at higher latitudes. These relationships—known as the “amount effect” and “temperature effect,” respectively—have been attributed to many different mechanisms, most of which are thought to operate at either high or low latitudes but not both. Here, we present a unified framework for interpreting the isotope variability that can explain the latitude dependence of the temperature and amount effects despite making no distinction between high and low latitudes. Although our results are generally consistent with certain interpretations of the amount effect, they suggest that the temperature effect is widely misunderstood.

54 ENVIRONMENTAL SCIENCES↗

Evolution of Thyroglobulin Loop Kinetics in EpCAM

Epithelial cell-activating molecule (EpCAM) is an important cancer biomarker and therapeutic target given its elevated expression in epithelial cancers. EpCAM is a type I transmembrane protein that forms cis-dimers along the thyroglobulin type-1A-like domain (TYD) in the extracellular region. The thyroglobulin loop (TY loop) within the TYD is structurally dynamic in the monomer state of human EpCAM, binding reversibly to a TYD site. However, it is not known if this flexibility is prevalent across different species. Here, we conduct over 17 μs of all-atom molecular dynamics simulations to study EpCAM TY loop kinetics of five different species, including human, mouse, chicken, frog, and fish. We find that the TY loop remains dynamic across evolution. In addition to the TYD binding site, we discover a second binding site for the TY loop in the C-terminal domain (CTD). Calculations of the dissociation rate constants from the simulation trajectories suggest a differential binding pattern of fish EpCAM and other organisms. Whereas fish TY loop has comparable binding for both TYD and CTD sites, the TY loops of other species preferably bind the TYD site. A hybrid construct of fish EpCAM with human TY loop restores the TYD binding preference, suggesting robust effects of the TY loop sequence on its dynamic behavior. Our findings provide insights into the structural dynamics of EpCAM and its implication in physiological functions.

59 BASIC BIOLOGICAL SCIENCES↗

Analysis of severe atmospheric disturbances from airline flight records

Advanced methods were developed to determine time varying winds and turbulence from digital flight data recorders carried aboard modern airliners. Analysis of several cases involving severe clear air turbulence encounters at cruise altitudes has shown that the aircraft encountered vortex arrays generated by destabilized wind shear layers above mountains or thunderstorms. A model was developed to identify the strength, size, and spacing of vortex arrays. This model is used to study the effects of severe wind hazards on operational safety for different types of aircraft. The study demonstrates that small remotely piloted vehicles and executive aircraft exhibit more violent behavior than do large airliners during encounters with high-altitude vortices. Analysis of digital flight data from the accident at Dallas/Ft. Worth in 1985 indicates that the aircraft encountered a microburst with rapidly changing winds embedded in a strong outflow near the ground. A multiple-vortex-ring model was developed to represent the microburst wind pattern. This model can be used in flight simulators to better understand the control problems in severe microburst encounters.

Wingrove, R. C.↗

Analysis of severe atmospheric disturbances from airline flight records

Advanced methods were developed to determine time varying winds and turbulence from digital flight data recorders carried aboard modern airliners. Analysis of several cases involving severe clear air turbulence encounters at cruise altitudes has shown that the aircraft encountered vortex arrays generated by destabilized wind shear layers above mountains or thunderstorms. A model was developed to identify the strength, size, and spacing of vortex arrays. This model is used to study the effects of severe wind hazards on operational safety for different types of aircraft. It is demonstrated that small remotely piloted vehicles and executive aircraft exhibit more violent behavior than do large airliners during encounters with high-altitude vortices. Analysis of digital flight data from the accident at Dallas/Ft. Worth in 1985 indicates that the aircraft encountered a microburst with rapidly changing winds embedded in a strong outflow near the ground. A multiple-vortex-ring model was developed to represent the microburst wind pattern. This model can be used in flight simulators to better understand the control problems in severe microburst encounters.

Wingrove, R. C.↗

Partial melting of apatite-bearing charnockite, granulite, and diorite: Melt compositions, restite mineralogy, and petrologic implications

Melting experiments (P = 6.9 kbar, T = 850-950 deg C, NNO is less than fO2 is less than HM) were done on mafic to felsic charnockites, a dioritic gneiss, and a felsic garnet granulite, all common rock types in the Grenville basement of eastern North America. A graphite-bearing granulite gneiss did not melt. Water (H2O(+) = 0.60 to 2.0 wt %) is bound in low-grade, retrograde metamorphic minerals and is consumed during the earliest stages of melting. Most melts are water-undersaturated. Melt compositions range from metaluminous, silicic granodiorite (diorite starting composition) to peraluminous or weakly metaluminous granites (all others). In general, liquids become more feldspathic, less silicic, and less peraluminous and are enriched in FeO, MgO, and TiO2 with increasing temperature. Residual feldspar mineralogy controls the CaO, K2O, and Na2O contents of the partial melts and the behavior of these elements can be used, particularly if the degree of source melting can be ascertained, to infer some aspects of the feldspar mineralogy of the source. K-feldspar, a common restite phase in the charnockite and granulite (but not the diorite) should control the behavior of Ba and, possibly, Eu in these systems and yield signatures of these elements that can distinguish source regions and, in some cases, bulk versus melt assimilation. Apatite, a common restite phase, is enriched in rare earth elements (REE), especially middle REE. Retention of apatite in the restite will result in steep, light REE-enriched patterns for melts derived from the diorite and charnockites.

Beard, James S.↗

Training Knowledge Bots for Physics-Based Simulations Using Artificial Neural Networks

Millions of complex physics-based simulations are required for design of an aerospace vehicle. These simulations are usually performed by highly trained and skilled analysts, who execute, monitor, and steer each simulation. Analysts rely heavily on their broad experience that may have taken 20-30 years to accumulate. In addition, the simulation software is complex in nature, requiring significant computational resources. Simulations of system of systems become even more complex and are beyond human capacity to effectively learn their behavior. IBM has developed machines that can learn and compete successfully with a chess grandmaster and most successful jeopardy contestants. These machines are capable of learning some complex problems much faster than humans can learn. In this paper, we propose using artificial neural network to train knowledge bots to identify the idiosyncrasies of simulation software and recognize patterns that can lead to successful simulations. We examine the use of knowledge bots for applications of computational fluid dynamics (CFD), trajectory analysis, commercial finite-element analysis software, and slosh propellant dynamics. We will show that machine learning algorithms can be used to learn the idiosyncrasies of computational simulations and identify regions of instability without including any additional information about their mathematical form or applied discretization approaches.

Samareh, Jamshid A.↗

Analyzing the Energy and Power Consumption of Remote Memory Accesses in the OpenSHMEM Model

PGAS models like OpenSHMEM provide interfaces to explicitly initiate one-sided remote memory accesses among processes. In addition, the model also provides synchronizing barriers to ensure a consistent view of the distributed memory at different phases of an application. The incorrect use of such interfaces affects the scalability achievable while using a parallel programming model. This study aims at understanding the effects of these constructs on the energy and power consumption behavior of OpenSHMEM applications. Our experiments show that cost incurred in terms of the total energy and power consumed depends on multiple factors across the software and hardware stack. We conclude that there is a significant impact on the power consumed by the CPU and DRAM due to multiple factors including the design of the data transfer patterns within an application, the design of the communication protocols within a middleware, the architectural constraints laid by the interconnect solutions, and also the levels of memory hierarchy within a compute node. This work motivates treating energy and power consumption as important factors while designing compute solutions for current and future distributed systems.

Jana, Siddhartha↗

Effects of slope steepness and cross-slope wind speed on fire spreading behavior for various vegetation

Wildland fire behavior is significantly influenced by environmental factors such as slope steepness, wind speed, and fuel type. Understanding these interactions is critical for improving predictive models and fire management. This study explores how slope steepness and cross-slope wind speed influence fire spread dynamics in various fuel bed types. Simulations are conducted using a physics-based wildland fire model, HIGRAD/FIRETEC, across six slope angles (0–50 %), four cross-slope wind speeds (4–10 m s –1 ), and three fuel bed types (grass, shrubland, and forest). Representative cases are additionally compared with FARSITE fireline evolution. Fire behavior is categorized into distinct propagation types based on spread characteristics and analyzed. The fire propagation angle, which indicates deviation from the wind direction, generally increases with steeper slopes and decreases with stronger cross-slope winds. Secondary upslope propagation is observed in shrubland under moderate slopes, while secondary downwind propagation occurs in all fuel beds at higher wind speeds. These findings highlight fire spread characteristics that differ from predictions by traditional models like Rothermel’s. By capturing complex propagation patterns and dynamics, this study demonstrates the value of a physics-based, atmosphere-fire coupled model for accurate wildland fire prediction. Incorporating secondary propagations and the influence of fuel bed complexities into predictive models can improve the accuracy of fire spread forecasts, enabling more effective fire management and risk mitigation efforts.

54 ENVIRONMENTAL SCIENCES↗

Decoding α-MoC 1− x Nanoparticle Formation in Continuous Flow via Machine Learning

Molybdenum carbide nanoparticles (α-MoC 1−x NPs) are promising catalysts that offer noble-metal-like performance at lower cost. We report a mild continuous-flow synthesis of α-MoC 1−x NPs from Mo(CO) 6 , coupled with in-line spectroscopic monitoring and machine learning (ML)-based analysis to quantify precursor conversion and product formation in real time. A multilayer perceptron ML model was found to accurately deconvolute complex, nonlinear spectral patterns, enabling identification of a two-step reaction pathway, involving precursor conversion to an amorphous intermediate followed by intraparticle crystallization to α-MoC 1−x NPs, with the first step being rate limiting. Ex situ small angle X-ray scattering (SAXS) and X-ray diffraction (XRD) validation confirm the predicted concentration profiles and crystallization behavior. This integrated approach showcases how ML can empower insights into NP nucleation and growth, paving the way for self-driving, flow-based platforms for NP synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗