Battelle

Particle-size analysis (PSA) is a measurement of the size distribution of individual particles in a soil sample. The major features of PSA are the destruction or dispersion of soil aggregates into discrete units by chemical, mechanical, or ultrasonic means and the separation of particles according to size limits by sieving and sedimentation. Soils generally contain organic matter and often contain iron oxides and carbonate coatings that bind particles together. Chemical pretreatments are used for removal of these coatings; however, chemical treatment can result in destruction and dissolution of some soil minerals. In addition to sieving and sedimentation procedures, there are numerous techniques for measurement of particle-size distribution that have been developed for powder technology and other applications. These techniques include optical microscopy, transmission electron microscopy (TEM), scanning electron microscopy (SEM), electrical sensory zone (Coulter counter) methods, and light-scattering methods such as laserlight scattering, turbidimeters, holography, and x-ray centrifuges.

The HITRAN database is a compilation of molecular spectroscopic parameters. It was established in the early 1970s and is used by various computer codes to predict and simulate the transmission and emission of light in gaseous media (with an emphasis on terrestrial and planetary atmospheres). The HITRAN compilation is composed of five major components: the line-by-line spectroscopic parameters required for high-resolution radiative-transfer codes, experimental infrared absorption cross-sections (for molecules where it is not yet feasible for representation in a line-by-line form), collision-induced absorption data, aerosol indices of refraction, and general tables (including partition sums) that apply globally to the data. This paper describes the contents of the 2020 quadrennial edition of HITRAN. The HITRAN2020 edition takes advantage of recent experimental and theoretical data that were meticulously validated, in particular, against laboratory and atmospheric spectra. The new edition replaces the previous HITRAN edition of 2016 (including its updates during the intervening years). All five components of HITRAN have undergone major updates. In particular, the extent of the updates in the HITRAN2020 edition range from updating a few lines of specific molecules to complete replacements of the lists, and also the introduction of additional isotopologues and new (to HITRAN) molecules: SO, CH3F, GeH4, CS2, CH3I and NF3. Many new vibrational bands were added, extending the spectral coverage and completeness of the line lists. Also, the accuracy of the parameters for major atmospheric absorbers has been increased substantially, often featuring sub-percent uncertainties. Broadening parameters associated with the ambient pressure of water vapor were introduced to HITRAN for the first time and are now available for several molecules. The HITRAN2020 edition continues to take advantage of the relational structure and efficient interface available at www.hitran.org and the HITRAN Application Programming Interface (HAPI). The functionality of both tools has been extended for the new edition.

1. Introduction. 2. Simple Regression. 3. Multiple Regression. 4. The Special Case of One-Dimensional Location. 5. Algorithms. 6. Outlier Diagnostics. 7. Related Statistical Techniques. References. Table of Data Sets. Index.

This biennial Review summarizes much of particle physics. Using data from previous editions, plus 2658 new measurements from 644 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. Among the 112 reviews are many that are new or heavily revised including those on Heavy-Quark and Soft-Collinear Effective Theory, Neutrino Cross Section Measurements, Monte Carlo Event Generators, Lattice QCD, Heavy Quarkonium Spectroscopy, Top Quark, Dark Matter, ${V}_{\mathit{cb}}$ ${V}_{\mathit{ub}}$, Quantum Chromodynamics, High-Energy Collider Parameters, Astrophysical Constants, Cosmological Parameters, and Dark Matter.A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.lbl.gov/.The 2012 edition of Review of Particle Physics is published for the Particle Data Group as article 010001 in volume 86 of Physical Review D.This edition should be cited as: J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012).

Abstract An analysis is described for the rapid determination of nitrate‐N in plant extracts. The complex formed by nitration of salicylic acid under highly acidic conditions absorbs maximally at 410 nm in basic (pH>12) solutions. Absorbance of the chromophore is directly proportional to the amount of nitrate‐N present. Ammonium, nitrite, and chloride ions do not interfere. Key words: nitrosalicylic acidnitrate determination Notes Cooperative Investigation, Agricultural Research Service, U.S. Department of Agriculture, and the Agricultural Experiment Station, University of Wisconsin‐Madison. Research supported by the College of Agricultural and Life Sciences, University of Wisconsin‐Madison, by USDA Cooperative Agreement 12–14–100–10,888, and by an award from the UN Graduate School Research Committee. Mention of a trademark or proprietary product does not constitute a guarantee or warranty of the product by the U.S. Department of Agriculture and does not imply its approval to the exclusion of other products that may also be suitable. Former Postdoctoral Fellow, Graduate Research Assistant, Associate Professor of Agronomy, and Research Chemist, U.S. Department of Agriculture. (VLY is also Associate Professor of Agronomy). Present address of DAC: Battelle, Pacific Northwest Laboratories, Ecosystems Department, Richland, Washington 99352.

We present an overview of the current status of transition-state theory and its generalizations. We emphasize (i) recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, (ii) progress in the theory and application of transition-state theory to condensed-phase reactions, and (iii) insight into the relation of transition-state theory to accurate quantum dynamics and tests of its accuracy via comparisons with both experimental and other theoretical dynamical approximations.

Contracted [5s3p] and [5s4p] Gaussian basis sets for the first-row atoms are derived from the (10s6p) primitive basis sets of Huzinaga. Contracted [2s] and [3s] sets for the hydrogen atom obtained from primitive sets ranging in size from (4s) to (6s) are also examined. Calculations on the water and nitrogen molecules indicate that such basis sets when augmented with suitable polarization functions should yield wavefunctions near the Hartree–Fock limit.

Hollow carbon nanowires (HCNWs) were prepared through pyrolyzation of a hollow polyaniline nanowire precursor. The HCNWs used as anode material for Na-ion batteries deliver a high reversible capacity of 251 mAh g(-1) and 82.2% capacity retention over 400 charge-discharge cycles between 1.2 and 0.01 V (vs Na(+)/Na) at a constant current of 50 mA g(-1) (0.2 C). Excellent cycling stability is also observed at an even higher charge-discharge rate. A high reversible capacity of 149 mAh g(-1) also can be obtained at a current rate of 500 mA g(-1) (2C). The good Na-ion insertion property is attributed to the short diffusion distance in the HCNWs and the large interlayer distance (0.37 nm) between the graphitic sheets, which agrees with the interlayered distance predicted by theoretical calculations to enable Na-ion insertion in carbon materials.

This report updates the 2020-21 recommendations of the Advisory Committee on Immunization Practices (ACIP) regarding the use of seasonal influenza vaccines in the United States (MMWR Recomm Rep 2020;69[No. RR-8]). Routine annual influenza vaccination is recommended for all persons aged ≥6 months who do not have contraindications. For each recipient, a licensed and age-appropriate vaccine should be used. ACIP makes no preferential recommendation for a specific vaccine when more than one licensed, recommended, and age-appropriate vaccine is available. During the 2021-22 influenza season, the following types of vaccines are expected to be available: inactivated influenza vaccines (IIV4s), recombinant influenza vaccine (RIV4), and live attenuated influenza vaccine (LAIV4).The 2021-22 influenza season is expected to coincide with continued circulation of SARS-CoV-2, the virus that causes COVID-19. Influenza vaccination of persons aged ≥6 months to reduce prevalence of illness caused by influenza will reduce symptoms that might be confused with those of COVID-19. Prevention of and reduction in the severity of influenza illness and reduction of outpatient visits, hospitalizations, and intensive care unit admissions through influenza vaccination also could alleviate stress on the U.S. health care system. Guidance for vaccine planning during the pandemic is available at https://www.cdc.gov/vaccines/pandemic-guidance/index.html. Recommendations for the use of COVID-19 vaccines are available at https://www.cdc.gov/vaccines/hcp/acip-recs/vacc-specific/covid-19.html, and additional clinical guidance is available at https://www.cdc.gov/vaccines/covid-19/clinical-considerations/covid-19-vaccines-us.html.Updates described in this report reflect discussions during public meetings of ACIP that were held on October 28, 2020; February 25, 2021; and June 24, 2021. Primary updates to this report include the following six items. First, all seasonal influenza vaccines available in the United States for the 2021-22 season are expected to be quadrivalent. Second, the composition of 2021-22 U.S. influenza vaccines includes updates to the influenza A(H1N1)pdm09 and influenza A(H3N2) components. U.S.-licensed influenza vaccines will contain hemagglutinin derived from an influenza A/Victoria/2570/2019 (H1N1)pdm09-like virus (for egg-based vaccines) or an influenza A/Wisconsin/588/2019 (H1N1)pdm09-like virus (for cell culture-based and recombinant vaccines), an influenza A/Cambodia/e0826360/2020 (H3N2)-like virus, an influenza B/Washington/02/2019 (Victoria lineage)-like virus, and an influenza B/Phuket/3073/2013 (Yamagata lineage)-like virus. Third, the approved age indication for the cell culture-based inactivated influenza vaccine, Flucelvax Quadrivalent (ccIIV4), has been expanded from ages ≥4 years to ages ≥2 years. Fourth, discussion of administration of influenza vaccines with other vaccines includes considerations for coadministration of influenza vaccines and COVID-19 vaccines. Providers should also consult current ACIP COVID-19 vaccine recommendations and CDC guidance concerning coadministration of these vaccines with influenza vaccines. Vaccines that are given at the same time should be administered in separate anatomic sites. Fifth, guidance concerning timing of influenza vaccination now states that vaccination soon after vaccine becomes available can be considered for pregnant women in the third trimester. As previously recommended, children who need 2 doses (children aged 6 months through 8 years who have never received influenza vaccine or who have not previously received a lifetime total of ≥2 doses) should receive their first dose as soon as possible after vaccine becomes available to allow the second dose (which must be administered ≥4 weeks later) to be received by the end of October. For nonpregnant adults, vaccination in July and August should be avoided unless there is concern that later vaccination might not be possible. Sixth, contraindications and precautions to the use of ccIIV4 and RIV4 have been modified, specifically with regard to persons with a history of severe allergic reaction (e.g., anaphylaxis) to an influenza vaccine. A history of a severe allergic reaction to a previous dose of any egg-based IIV, LAIV, or RIV of any valency is a precaution to use of ccIIV4. A history of a severe allergic reaction to a previous dose of any egg-based IIV, ccIIV, or LAIV of any valency is a precaution to use of RIV4. Use of ccIIV4 and RIV4 in such instances should occur in an inpatient or outpatient medical setting under supervision of a provider who can recognize and manage a severe allergic reaction; providers can also consider consulting with an allergist to help identify the vaccine component responsible for the reaction. For ccIIV4, history of a severe allergic reaction (e.g., anaphylaxis) to any ccIIV of any valency or any component of ccIIV4 is a contraindication to future use of ccIIV4. For RIV4, history of a severe allergic reaction (e.g., anaphylaxis) to any RIV of any valency or any component of RIV4 is a contraindication to future use of RIV4. This report focuses on recommendations for the use of vaccines for the prevention and control of seasonal influenza during the 2021-22 influenza season in the United States. A brief summary of the recommendations and a link to the most recent Background Document containing additional information are available at https://www.cdc.gov/vaccines/hcp/acip-recs/vacc-specific/flu.html. These recommendations apply to U.S.-licensed influenza vaccines used according to Food and Drug Administration-licensed indications. Updates and other information are available from CDC's influenza website (https://www.cdc.gov/flu); vaccination and health care providers should check this site periodically for additional information.

Abstract Many‐body (diagrammatic) perturbation theory ( MBPT ), coupled‐pair many‐electron theory ( CPMET ), and configuration interaction ( CI ) are investigated with particular emphasis on the importance of quadruple excitations in correlation theories. These different methods are used to obtain single, double, and quadruple excitation contributions to the correlation energy for a series of molecules including CO 2 , HCN, N 2 , CO, BH 3 , and NH 3 . It is demonstrated that the sum of double and quadruple excitation diagrams through fourth‐order perturbation theory is usually quite close to the CPMET result for these molecules at equilibrium geometries. The superior reliability of the CPMET model as a function of internuclear separation is illustrated by studying the 1 ∑ potential curve of Be 2 . This molecule violates the assumption common to nondegenerate perturbation theory that only a single reference function is important and this causes improper behavior of the potential curve as a function of R . This is resolved once the quadruple excitation terms are fully included by CPMET .

Millimeter-wave imaging techniques and systems have been developed at the Pacific Northwest National Laboratory (PNNL), Richland, WA, for the detection of concealed weapons and contraband at airports and other secure locations. These techniques were derived from microwave holography techniques that utilize phase and amplitude information recorded over a two-dimensional aperture to reconstruct a focused image of the target. Millimeter-wave imaging is well suited for the detection of concealed weapons or other contraband carried on personnel since millimeter-waves are nonionizing, readily penetrate common clothing material, and are reflected from the human body and any concealed items. In this paper, a wide-bandwidth three-dimensional holographic microwave imaging technique is described. Practical weapon detection systems for airport or other high-throughput applications require high-speed scanning on the order of 3 to 10 s. To achieve this goal, a prototype imaging system utilizing a 27-33 GHz linear sequentially switched array and a high-speed linear scanner has been developed and tested. This system is described in detail along with numerous imaging results.

This paper describes and evaluates a new Model for Simulating Aerosol Interactions and Chemistry (MOSAIC), with a special focus on addressing the long‐standing issues in solving the dynamic partitioning of semivolatile inorganic gases (HNO 3 , HCl, and NH 3 ) to size‐distributed atmospheric aerosol particles. The coupled ordinary differential equations (ODE) for dynamic gas‐particle mass transfer are extremely stiff, and the available numerical techniques are either very expensive or produce oscillatory solutions. These limitations are overcome in MOSAIC with a new dynamic gas‐particle partitioning module, which is coupled to an efficient and accurate thermodynamics module. The algorithm includes a new concept of “dynamic pH,” a novel formulation for mass transfer to mixed‐phase and solid particles, and an adaptive time stepping scheme, which together hold the key to smooth, accurate, and efficient solutions of gas‐particle partitioning over the entire relative humidity range. MOSAIC is found to be in excellent agreement with a benchmark version of the model that uses a rigorous solver for integrating the stiff ODEs. The steady‐state MOSAIC results for monodisperse aerosol test cases are also in excellent agreement with those obtained with the benchmark equilibrium model AIM. Moreover, the CPU times required for fully dynamic solutions by MOSAIC per size bin per 5 min intervals (typical 3‐D model time steps) are similar to those for bulk equilibrium solutions by the computationally efficient but relatively less accurate model ISORROPIA. These results show that MOSAIC is extremely efficient without compromising accuracy, and is therefore highly attractive for use in air quality and regional/global aerosol models.

Abstract. Simulation results of global aerosol models have been assembled in the framework of the AeroCom intercomparison exercise. In this paper, we analyze the life cycles of dust, sea salt, sulfate, black carbon and particulate organic matter as simulated by sixteen global aerosol models. The differences among the results (model diversities) for sources and sinks, burdens, particle sizes, water uptakes, and spatial dispersals have been established. These diversities have large consequences for the calculated radiative forcing and the aerosol concentrations at the surface. Processes and parameters are identified which deserve further research. The AeroCom all-models-average emissions are dominated by the mass of sea salt (SS), followed by dust (DU), sulfate (SO4), particulate organic matter (POM), and finally black carbon (BC). Interactive parameterizations of the emissions and contrasting particles sizes of SS and DU lead generally to higher diversities of these species, and for total aerosol. The lower diversity of the emissions of the fine aerosols, BC, POM, and SO4, is due to the use of similar emission inventories, and does therefore not necessarily indicate a better understanding of their sources. The diversity of SO4-sources is mainly caused by the disagreement on depositional loss of precursor gases and on chemical production. The diversities of the emissions are passed on to the burdens, but the latter are also strongly affected by the model-specific treatments of transport and aerosol processes. The burdens of dry masses decrease from largest to smallest: DU, SS, SO4, POM, and BC. The all-models-average residence time is shortest for SS with about half a day, followed by SO4 and DU with four days, and POM and BC with six and seven days, respectively. The wet deposition rate is controlled by the solubility and increases from DU, BC, POM to SO4 and SS. It is the dominant sink for SO4, BC, and POM, and contributes about one third to the total removal of SS and DU species. For SS and DU we find high diversities for the removal rate coefficients and deposition pathways. Models do neither agree on the split between wet and dry deposition, nor on that between sedimentation and other dry deposition processes. We diagnose an extremely high diversity for the uptake of ambient water vapor that influences the particle size and thus the sink rate coefficients. Furthermore, we find little agreement among the model results for the partitioning of wet removal into scavenging by convective and stratiform rain. Large differences exist for aerosol dispersal both in the vertical and in the horizontal direction. In some models, a minimum of total aerosol concentration is simulated at the surface. Aerosol dispersal is most pronounced for SO4 and BC and lowest for SS. Diversities are higher for meridional than for vertical dispersal, they are similar for the individual species and highest for SS and DU. For these two components we do not find a correlation between vertical and meridional aerosol dispersal. In addition the degree of dispersals of SS and DU is not related to their residence times. SO4, BC, and POM, however, show increased meridional dispersal in models with larger vertical dispersal, and dispersal is larger for longer simulated residence times.

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

Abstract The purpose of this review paper is to present the technical basis for establishing sediment quality criteria using equilibrium partitioning (EqP). Equilibrium partitioning is chosen because it addresses the two principal technical issues that must be resolved: the varying bioavailability of chemicals in sediments and the choice of the appropriate biological effects concentration. The data that are used to examine the question of varying bioavailability across sediments are from toxicity and bioaccumulation experiments utilizing the same chemical and test organism but different sediments. It has been found that if the different sediments in each experiment are compared, there is essentially no relationship between sediment chemical concentrations on a dry weight basis and biological effects. However, if the chemical concentrations in the pore water of the sediment are used (for chemicals that are not highly hydrophobic) or if the sediment chemical concentrations on an organic carbon basis are used, then the biological effects occur at similar concentrations (within a factor of two) for the different sediments. In addition, the effects concentrations are the same as, or they can be predicted from, the effects concentration determined in water- only exposures. The EqP methodology rationalizes these results by assuming that the partitioning of the chemical between sediment organic carbon and pore water is at equilibrium. In each of these phases, the fugacity or activity of the chemical is the same at equilibrium. As a consequence, it is assumed that the organism receives an equivalent exposure from a water-only exposure or from any equilibrated phase, either from pore water via respiration, from sediment carbon via ingestion; or from a mixture of the routes. Thus, the pathway of exposure is not significant. The biological effect is produced by the chemical activity of the single phase or the equilibrated system. Sediment quality criteria for nonionic organic chemicals are based on the chemical concentration in sediment organic carbon. For highly hydrophobic chemicals this is necessary because the pore water concentration is, for those chemicals, no longer a good estimate of the chemical activity. The pore water concentration is the sum of the free chemical concentration, which is bioavailable and represents the chemical activity, and the concentration of chemical complexed to dissolved organic carbon, which, as the data presented below illustrate, is not bioavailable. Using the chemical concentration in sediment organic carbon eliminates this ambiguity. Sediment quality criteria also require that a chemical concentration be chosen that is sufficiently protective of benthic organisms. The final chronic value (FCV) from the U.S. Environmental Protection Agency (EPA) water quality criteria is proposed. An analysis of the data compiled in the water quality criteria documents demonstrates that benthic species, defined as either epibenthic or infaunal species, have a similar sensitivity to water column species. This is the case if the most sensitive species are compared and if all species are compared. The results of benthic colonization experiments also support the use of the FCV. Equilibrium partitioning cannot remove all the variation in the experimentally observed sediment- effects concentration and the concentration predicted from water-only exposures. A variation of approximately a factor of two to three remains. Hence, it is recognized that a quantification of this uncertainty should accompany the sediment quality criteria. The derivation of sediment quality criteria requires the octanol/water partition coefficient of the chemical. It should be measured with modern experimental techniques, which appear to remove the large variation in reported values. The derivation of the final chronic value should also be updated to include the most recent toxicological information.

This paper is a review of the developments in the field of catalytic hydroprocessing of biomass-derived liquefaction conversion products (bio-oil) over the past 25 years. Work has been underway, primarily in the U.S. and Europe, in catalytic hydrotreating and hydrocracking of bio-oil in both batch-fed and continuous-flow bench-scale reactor systems. A range of heterogeneous catalyst materials have been tested, including conventional sulfided catalysts developed for petroleum hydroprocessing and precious metal catalysts. The important processing differences have been identified, which required adjustments to conventional hydroprocessing as applied to petroleum feedstocks. This application of hydroprocessing is seen as an extension of petroleum processing and system requirements are not far outside the range of conventional hydroprocessing. The technology is still under development but can play a significant role in supplementing increasingly expensive petroleum.

Abstract Rechargeable lithium‐metal batteries (LMBs) are regarded as the “holy grail” of energy‐storage systems, but the electrolytes that are highly stable with both a lithium‐metal anode and high‐voltage cathodes still remain a great challenge. Here a novel “localized high‐concentration electrolyte” (HCE; 1.2 m lithium bis(fluorosulfonyl)imide in a mixture of dimethyl carbonate/bis(2,2,2‐trifluoroethyl) ether (1:2 by mol)) is reported that enables dendrite‐free cycling of lithium‐metal anodes with high Coulombic efficiency (99.5%) and excellent capacity retention (>80% after 700 cycles) of Li||LiNi 1/3 Mn 1/3 Co 1/3 O 2 batteries. Unlike the HCEs reported before, the electrolyte reported in this work exhibits low concentration, low cost, low viscosity, improved conductivity, and good wettability that make LMBs closer to practical applications. The fundamental concept of “localized HCEs” developed in this work can also be applied to other battery systems, sensors, supercapacitors, and other electrochemical systems.

= 176). OA was diagnosed based on the presence of eburnation (polish from bone-on-bone contact). Overall, knee OA prevalence was found to be 16% among the postindustrial sample but only 6% and 8% among the early industrial and prehistoric samples, respectively. After controlling for age, BMI, and other variables, knee OA prevalence was 2.1-fold higher (95% confidence interval, 1.5-3.1) in the postindustrial sample than in the early industrial sample. Our results indicate that increases in longevity and BMI are insufficient to explain the approximate doubling of knee OA prevalence that has occurred in the United States since the mid-20th century. Knee OA is thus more preventable than is commonly assumed, but prevention will require research on additional independent risk factors that either arose or have become amplified in the postindustrial era.

Little is known about the factors affecting the relative influences of stochastic and deterministic processes that govern the assembly of microbial communities in successional soils. Here, we conducted a meta-analysis of bacterial communities using six different successional soil datasets distributed across different regions. Different relationships between pH and successional age across these datasets allowed us to separate the influences of successional age (i.e., time) from soil pH. We found that extreme acidic or alkaline pH conditions lead to assembly of phylogenetically more clustered bacterial communities through deterministic processes, whereas pH conditions close to neutral lead to phylogenetically less clustered bacterial communities with more stochasticity. We suggest that the influence of pH, rather than successional age, is the main driving force in producing trends in phylogenetic assembly of bacteria, and that pH also influences the relative balance of stochastic and deterministic processes along successional soils. Given that pH had a much stronger association with community assembly than did successional age, we evaluated whether the inferred influence of pH was maintained when studying globally distributed samples collected without regard for successional age. This dataset confirmed the strong influence of pH, suggesting that the influence of soil pH on community assembly processes occurs globally. Extreme pH conditions likely exert more stringent limits on survival and fitness, imposing strong selective pressures through ecological and evolutionary time. Taken together, these findings suggest that the degree to which stochastic vs. deterministic processes shape soil bacterial community assembly is a consequence of soil pH rather than successional age.

A procedure is described for developing an interconnection matrix that specifies a cascade connection of two known digraphs to form a digraph. The solution of this form of the interconnection problem can be applied to complete the process of description of a binary relation initiated by the process of partitioning on elements described in a companion paper [3]. It is assumed that the contextual relation being modeled is transitive. Based on this assumption, it is shown that the possibilities of interconnection can be completely prescribed in a characteristic logic equation. This equation can be used as the complete basis for development of an interconnection matrix. An example of its use is given. Much of the burden of structural modeling is assigned to the computer, leaving to the developer the tasks requiring substantive knowledge of the system being modeled.