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Previous article Next article On the Construction and Comparison of Difference SchemesGilbert StrangGilbert Stranghttps://doi.org/10.1137/0705041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. Barkley Rosser, A Runge-Kutta for all seasons, SIAM Rev., 9 (1967), 417–452 10.1137/1009069 MR0219242 0243.65041 LinkISIGoogle Scholar[2] Robert D. Richtmyer and , K. W. Morton, Difference methods for initial-value problems, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967xiv+405 MR0220455 0155.47502 Google Scholar[3] Peter D. Lax and , Burton Wendroff, Difference schemes for hyperbolic equations with high order of accuracy, Comm. Pure Appl. Math., 17 (1964), 381–398 MR0170484 0233.65050 CrossrefISIGoogle Scholar[4] Samuel Z. Burstein, Numerical methods in multidimensional shocked flows, AIAA J., 2 (1964), 2111–2117 MR0180067 CrossrefGoogle Scholar[5] S. Z. Burstein, Finite-difference calculations for hydrodynamic flows containing discontinuities, J. Comp. Phys., 2 (1967), 198–222 0166.22103 Google Scholar[6] C. Berger, On the numerical range of powers of an operator, to appear Google Scholar[7] W. P. Crowley, Second-order numerical advection, J. Comp. Phys., 1 (1967), 471–484 10.1016/0021-9991(67)90053-8 0149.44403 CrossrefGoogle Scholar[8] Gilbert Strang, Accurate partial difference methods. I. Linear Cauchy problems, Arch. Rational Mech. Anal., 12 (1963), 392–402 MR0146970 0113.32303 CrossrefISIGoogle Scholar[9] A. R. Gourlay and , J. Ll. Morris, A multistep formulation of the optimized Lax-Wendroff method for nonlinear hyperbolic systems in two space variables, Math. Comp., 22 (1968), 715–719 MR0251931 0172.19904 CrossrefISIGoogle Scholar[10] Peter Lax and , Burton Wendroff, Systems of conservation laws, Comm. Pure Appl. Math., 13 (1960), 217–237 MR0120774 0152.44802 CrossrefISIGoogle Scholar[11] R. D. Richtmyer, A survey of difference methods for nonsteady fluid dynamics, Tech. Note, 63-2, National Center for Atmospheric Research, Boulder, Colorado, 1962 Google Scholar[12] Gilbert Strang, Accurate partial difference methods. II. Non-linear problems, Numer. Math., 6 (1964), 37–46 10.1007/BF01386051 MR0166942 0143.38204 CrossrefGoogle Scholar[13] Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962xi+407 MR0135729 0112.34901 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Semiexplicit symplectic integrators for non-separable Hamiltonian systems23 September 2022 | Mathematics of Computation, Vol. 92, No. 339 Cross Ref A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemesJournal of Computational Physics, Vol. 472 Cross Ref Numerical computation for rogue waves in the coupled nonlinear Schrödinger equations with the coherent coupling effect29 April 2022 | International Journal of Computer Mathematics, Vol. 99, No. 12 Cross Ref A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systemsMathematics and Computers in Simulation, Vol. 202 Cross Ref Ultrafast laser matter interactions: modeling approaches, challenges, and prospects27 September 2022 | Modelling and Simulation in Materials Science and Engineering, Vol. 30, No. 8 Cross Ref An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gasesJournal of Computational Physics, Vol. 471 Cross Ref Implications of CO 2 mass transport dynamics for large-scale CCS in basalt formationsInternational Journal of Greenhouse Gas Control, Vol. 121 Cross Ref A charge-preserving compact splitting method for solving the coupled stochastic nonlinear Schrödinger equationsApplied Numerical Mathematics, Vol. 181 Cross Ref Local effects in vortex-flame interactions: Implications for turbulent premixed flame scaling and observablesCombustion and Flame, Vol. 245 Cross Ref Hamiltonian preserving nonlinear opticsPhysica D: Nonlinear Phenomena, Vol. 439 Cross Ref A fully coupled, fully implicit simulation method for unsteady flames using Jacobian approximation and clusteringCombustion and Flame, Vol. 245 Cross Ref Reactive Transport Modeling with a Coupled OpenFOAM®-PHREEQC Platform7 October 2022 | Transport in Porous Media, Vol. 145, No. 2 Cross Ref Multirate Exponential Rosenbrock MethodsVu Thai Luan, Rujeko Chinomona, and Daniel R. 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Previous article Next article The Numerical Solution of Parabolic and Elliptic Differential EquationsD. W. Peaceman and H. H. Rachford, Jr.D. W. Peaceman and H. H. Rachford, Jr.https://doi.org/10.1137/0103003PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. H., Bruce, , D. W., Peaceman, , H. H., Rachford and , J. D. Rice, Calculation of unsteady-state gas flow through porous media, Trans. Amer. Inst. Mining and Met. Engrs., 198 (1953), 79– ISIGoogle Scholar[2] H. S. Carslaw and , J. C. Jaeger, Conduction of Heat in Solids, Oxford, at the Clarendon Press, 1947viii+386 MR0022294 Google Scholar[3] Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables and Other Aids to Computation, 4 (1950), 65–75 MR0046149 CrossrefGoogle Scholar[4] George G. O'Brien, , Morton A. Hyman and , Sidney Kaplan, A study of the numerical solution of partial differential equations, J. Math. Physics, 29 (1951), 223–251 MR0040805 0042.13204 CrossrefISIGoogle Scholar[5] Jim Douglas, Jr., On the numerical integration of $\partial\sp 2u/\partial x\sp 2+\partial\sp 2u/\partial y\sp 2=\partial u/\partial t$ by implicit methods, J. Soc. Indust. Appl. Math., 3 (1955), 42–65 10.1137/0103004 MR0071875 0067.35802 LinkISIGoogle Scholar[6] Jim Douglas, Jr. and , T. M. Gallie, Jr., Variable time steps in the solution of the heat flow equation by a difference equation, Proc. Amer. Math. Soc., 6 (1955), 787–793 MR0078754 0066.10502 CrossrefGoogle Scholar[7] J. Douglas, Jr. and , D. W. 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Control and Optimization, Vol. 48, No. 2 | 25 February 2009AbstractPDF (332 KB)Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and ConvergenceSIAM Journal on Optimization, Vol. 19, No. 3 | 31 October 2008AbstractPDF (335 KB)Efficient Preconditioning of Sequences of Nonsymmetric Linear SystemsSIAM Journal on Scientific Computing, Vol. 29, No. 5 | 28 September 2007AbstractPDF (242 KB)Robin–Robin Domain Decomposition Methods for the Stokes–Darcy CouplingSIAM Journal on Numerical Analysis, Vol. 45, No. 3 | 22 May 2007AbstractPDF (251 KB)An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular PolygonsSIAM Journal on Scientific Computing, Vol. 28, No. 3 | 4 August 2006AbstractPDF (241 KB)An Accelerated Splitting-up Method for Parabolic EquationsSIAM Journal on Mathematical Analysis, Vol. 37, No. 4 | 1 August 2006AbstractPDF (267 KB)An ADI-Like Preconditioner for Boltzmann TransportSIAM Journal on Scientific Computing, Vol. 26, No. 3 | 25 July 2006AbstractPDF (206 KB)Solving Degenerate Reaction-Diffusion Equations via Variable Step Peaceman--Rachford SplittingSIAM Journal on Scientific Computing, Vol. 25, No. 4 | 16 May 2012AbstractPDF (8559 KB)Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear SystemsSIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 3 | 31 July 2006AbstractPDF (257 KB)Stabilized Explicit-Implicit Domain Decomposition Methods for the Numerical Solution of Parabolic EquationsSIAM Journal on Scientific Computing, Vol. 24, No. 1 | 25 July 2006AbstractPDF (216 KB)Difference Graphs of Block ADI MethodSIAM Journal on Numerical Analysis, Vol. 38, No. 3 | 26 July 2006AbstractPDF (162 KB)A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov EquationsSIAM Journal on Scientific Computing, Vol. 21, No. 4 | 25 July 2006AbstractPDF (377 KB)Domain Decomposition Operator Splittings for the Solution of Parabolic EquationsSIAM Journal on Scientific Computing, Vol. 19, No. 3 | 25 July 2006AbstractPDF (406 KB)Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space VariablesSIAM Journal on Numerical Analysis, Vol. 35, No. 2 | 25 July 2006AbstractPDF (458 KB)An ADI Method for Hysteretic Reaction-Diffusion SystemsSIAM Journal on Numerical Analysis, Vol. 34, No. 3 | 25 July 2006AbstractPDF (459 KB)Application of ADI Iterative Methods to the Restoration of Noisy ImagesSIAM Journal on Matrix Analysis and Applications, Vol. 17, No. 1 | 17 February 2012AbstractPDF (2458 KB)Coordination in Coarse-Grained DecompositionSIAM Journal on Optimization, Vol. 4, No. 4 | 13 July 2006AbstractPDF (1888 KB)Alternating Direction Preconditioning for Nonsymmetric Systems of Linear EquationsSIAM Journal on Scientific Computing, Vol. 15, No. 2 | 13 July 2006AbstractPDF (1688 KB)Alternating Direction Implicit Iteration for Systems with Complex SpectraSIAM Journal on Numerical Analysis, Vol. 28, No. 3 | 14 July 2006AbstractPDF (1238 KB)Vectorization of the Odd–Even Hopscotch Scheme and the Alternating Direction Implicit Scheme for the Two-Dimensional Burgers EquationsSIAM Journal on Scientific and Statistical Computing, Vol. 11, No. 2 | 13 July 2006AbstractPDF (1591 KB)The Solution of Two-Point Boundary Value Problems by the Alternating Group Explicit (AGE) MethodSIAM Journal on Scientific and Statistical Computing, Vol. 9, No. 3 | 13 July 2006AbstractPDF (639 KB)Tensor Product Generalized ADI Methods for Separable Elliptic ProblemsSIAM Journal on Numerical Analysis, Vol. 24, No. 1 | 14 July 2006AbstractPDF (1728 KB)Iterated Splitting Method of High Order for Time-Dependent Partial Differential EquationsSIAM Journal on Numerical Analysis, Vol. 21, No. 4 | 17 July 2006AbstractPDF (1855 KB)Multistep Splitting Methods of High Order for Initial Value ProblemsSIAM Journal on Numerical Analysis, Vol. 17, No. 3 | 17 July 2006AbstractPDF (1937 KB)Alternating Direction Implicit Methods for Parabolic Equations with a Mixed DerivativeSIAM Journal on Scientific and Statistical Computing, Vol. 1, No. 1 | 16 May 2012AbstractPDF (2857 KB)Splitting Algorithms for the Sum of Two Nonlinear OperatorsSIAM Journal on Numerical Analysis, Vol. 16, No. 6 | 17 July 2006AbstractPDF (1402 KB)Dynamic ADI Methods for Elliptic EquationsSIAM Journal on Numerical Analysis, Vol. 16, No. 5 | 17 July 2006AbstractPDF (2283 KB)The Alternating Phase Truncation Method for Numerical Solution of a Stefan ProblemSIAM Journal on Numerical Analysis, Vol. 16, No. 4 | 17 July 2006AbstractPDF (2605 KB)The Extrapolation of First Order Methods for Parabolic Partial Differential Equations. ISIAM Journal on Numerical Analysis, Vol. 15, No. 6 | 14 July 2006AbstractPDF (1229 KB)Numerical Solution of a Diffusion Consumption Problem with a Free BoundarySIAM Journal on Numerical Analysis, Vol. 12, No. 4 | 14 July 2006AbstractPDF (2304 KB)A Survey of Modern Numerical AnalysisSIAM Review, Vol. 15, No. 2 | 2 August 2006AbstractPDF (2464 KB)Iterative Solution of Implicit Approximations of Multidimensional Partial Differential EquationsSIAM Journal on Numerical Analysis, Vol. 5, No. 3 | 14 July 2006AbstractPDF (2718 KB)Rounding Errors in Alternating Direction Methods for Parabolic ProblemsSIAM Journal on Numerical Analysis, Vol. 5, No. 2 | 3 August 2006AbstractPDF (1267 KB)A New Computational Procedure for A.D.I. MethodsSIAM Journal on Numerical Analysis, Vol. 4, No. 2 | 14 July 2006AbstractPDF (593 KB)Multistage Alternating Direction MethodsSIAM Journal on Numerical Analysis, Vol. 3, No. 4 | 14 July 2006AbstractPDF (829 KB)Two-Level Difference Schemes for Hyperbolic SystemsSIAM Journal on Numerical Analysis, Vol. 3, No. 3 | 14 July 2006AbstractPDF (882 KB)A New Alternating Direction Method for Parabolic Equations in Three Space VariablesJournal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 4 | 13 July 2006AbstractPDF (641 KB)Nonsymmetric Difference EquationsJournal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 3 | 13 July 2006AbstractPDF (501 KB)Alternating Direction Schemes for the Heat Equation in a General DomainJournal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, Vol. 2, No. 3 | 14 July 2006AbstractPDF (1121 KB)The Solution of Elliptic Difference Equations by Semi-Explicit Iterative TechniquesJournal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, Vol. 2, No. 1 | 3 August 2006AbstractPDF (1718 KB)An Alternating Direction Method for Operator EquationsJournal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 4 | 13 July 2006AbstractPDF (461 KB)The Numerical Solution of the Dirichlet Problem for Laplace’s Equation by Linear ProgrammingJournal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 1 | 13 July 2006AbstractPDF (374 KB)Another Alternating-Direction-Implicit MethodJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 4 | 13 July 2006AbstractPDF (290 KB)Numerical Studies of Transition From Laminar to Turbulent Flow Over a Flat PlateJournal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 4 | 13 July 2006AbstractPDF (2277 KB)On Incomplete Iteration for Implicit Parabolic Difference EquationsJournal of the Society for Industrial and Applied Mathematics, Vol. 9, No. 3 | 10 July 2006AbstractPDF (466 KB)An Alternating-Direction-Implicit Iteration TechniqueJournal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 2 | 10 July 2006AbstractPDF (1508 KB)Simultaneous, Successive and Alternating Direction Iteration SchemesJournal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 1 | 10 July 2006AbstractPDF (1569 KB)A Method of Block IterationJournal of the Society for Industrial and Applied Mathematics, Vol. 4, No. 4 | 10 July 2006AbstractPDF (667 KB)On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit MethodsJim Douglas, Jr.Journal of the Society for Industrial and Applied Mathematics, Vol. 3, No. 1 | 10 July 2006AbstractPDF (1365 KB) Volume 3, Issue 1| 1955Journal of the Society for Industrial and Applied Mathematics1-65 History Submitted:18 October 1954Published online:10 July 2006 InformationCopyright © 1955 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0103003Article page range:pp. 28-41ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

The article “The ecological risk assessment of atrazine in North American surface waters” 1 is one of the few among the 100 most cited articles in Environmental Toxicology and Chemistry to specifically address risk and/or assessment of risk, and it was the first to use probabilistic approaches for a pesticide. As with all science, it was one of many steps in the refinement of procedures for characterizing and assessing risks. Today, we understand that risk must always be expressed as a probability; but, in the general sense, this concept was a late arrival in the area of ecotoxicology. Ecotoxicological risk assessment, as we use it today, traces its scientific origins to risk assessment for the protection of human health, but even that was a relatively recent adoption. Although humans have faced risks since the dawn of society, risk assessment was purely empirical, descriptive, and anecdotal. The concept of risk in mathematical terms became possible only though the adoption of the Hindu-Arabic numbering system by Western society approximately 800 years ago 2. Risk was studied quantitatively only during and after the Renaissance through the work of Chevalier de Méré, Blaise Pascal, Jacob Bernoulli, and Abraham de Moivre, who suggested the structure of the normal distribution. This concept was further refined by Swiss mathematician Carl Fredrick Gauβ and many others, resulting in the process used today. The risk assessment of atrazine 1 typifies the breadth of expertise that is needed to undertake ecotoxicological risk assessment; it was the work of a panel of 12 authors, each contributing equally important and essential components to the process. The final product was brought together in a collegial and nonconfrontational process and the paper prepared for publication by one panel member. This model worked well and has been emulated in many subsequent assessments. The assessment of risks of adverse effects from atrazine in the environment was not completely novel, but it was an important step forward in the development of the concepts of risk in ecotoxicology. The probabilistic characterization of toxicity data was not new. In the arena of human health, this process was suggested for components of food 3, which then led to the use of the threshold of toxicological concern 4 as an important screening tool, an approach now advocated for use in ecotoxicology 5. From the environmental point of view, distributions of toxicity values were used to distinguish between more tolerant or resistant and more susceptible populations of ectoparasites of animals 6, but the notion of using these distributions for setting environmental quality guidelines originated from early work in the Netherlands (N. van Straalen, 1982, personal communication) that was further developed in Europe 7 and the United States 8. These probabilistic methods are now used worldwide for setting guidelines for environmental quality. Though the probabilistic analysis of toxicity was not novel, the ecological risk assessment for atrazine demonstrated how data for toxicity and exposure could be combined into a probabilistic characterization and unified expression of risk. This was a significant advancement over the use of simple quotients based on worst-case values. However, this was also not entirely new, it had been conceptualized in the work of the Aquatic Risk Assessment Dialogue Group 9, a process that was organized in part by the Society of Environmental Toxicology and Chemistry (SETAC) and also involved several authors of the article on the risk assessment for atrazine. The publication of “The ecological risk assessment of atrazine in North American surface waters” was likely the catalyst for a number of joint activities between academia, industry, and regulators, such as the Ecological Committee on Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA) Risk Assessment Methods (ECOFRAM 10) in the United States and the European Framework for Probabilistic Risk Assessment of the Environmental Impacts of Pesticides EUFRAM 11 in the European Union. Both of these have led to the further development of probabilistic assessment of ecotoxicological risks. One such development was the use of the joint probability distribution, first suggested in a computer program developed by the Cadmus Group and refined by ECOFRAM 10 for use in graphically displaying risks and, more recently, using these graphical displays for decision making (see Fig. 4 in 12). Several of the refinements of probabilistic assessment of risk were incorporated in a more comprehensive, larger, and updated evaluation of atrazine that was published as a SETAC book 13, which included significant advances in the modeling of concentrations in surface waters. Probabilistic methods, such as those pioneered in these and subsequent risk assessment authored by others, are likely to become more widely used, particularly for chemicals for which large sets of data are available. A spreadsheet model, the probabilistic risk assessment tool (PRAT) has been developed to aid in the probabilistic assessment of chemicals in the environment 14. Another feature of the risk assessment for atrazine that probably contributed to the number of citations is the large amount of data that it provided about one particular chemical, which is an important herbicide used in production agriculture. The reason for the inclusion of these data in the paper was two-fold: first, the paper was partly a review of the biological and physical properties of atrazine; and second, the authors wished to be as transparent as possible in providing the scientific basis for the conclusions reached in the paper. As has been noted 15, transparency is very important in communicating the results of risk assessments and should be an integral part of the assessment and the decisions that result therefrom. Hopefully, with the ability to include supplemental information in journal articles, such transparency will become the standard for risk assessments in the future. Table S1. (45 KB PDF). Additional Supporting Information may be found in the online version of this article. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

OR MANY YEARS administrators of library collections have sought objective criteria for assembling well-rounded periodical collections in the subject fields represented by their collections. The nearest approach to any criterion which does away with the a priori knowledge of the specialist was first suggested by Gross and Gross in 1927.10 This method consists, essentially, of counting the bibliographic citations at the conclusions of the articles in a basic periodical of the field under consideration, and of arranging the journals cited in order of the frequency of their citation. Thus, in the field of chemistry, the references in the Journal of the American Chemical Society are counted and a list is made of the most frequently cited journals. According to Gross and Gross, the journals which are cited most frequently in the Journal of the American Chemical Society are the most valuable journals for a library to purchase in order to possess a well-rounded collection in chemistry. Since 1927 this method has been used frequently and for many

A database has been constructed that contains all the crystal structures previously published in the American Mineralogist. The database is called “The American Mineralogist Crystal Structure Database” and is freely accessible from the websites of the Mineralogical Society of America at http://www.minsocam.org/MSA/Crystal_Database.html and the University of Arizona. In addition to the database, a suite of interactive software is provided that can be used to view and manipulate the crystal structures and compute different properties of a crystal such as geometry, diffraction patterns, and procrystal electron densities. The database is set up so that the data can be easily incorporated into other software packages. Included at the website is an evolving set of guides to instruct the user and help with classroom education. parameters; (5) incorporating comments from either the original authors or ourselves when changes are made to the originally published data. Each record in the database consists of a bibliographic reference, cell parameters, symmetry, atomic positions, displacement parameters, and site occupancies. An example of a data set is provided in Figure 1. The first part of each data set contains identifying information, bibliography and notes, while the second part contains the crystallographic parameters. The first line of a data file contains an identifier, such as the name of the mineral or formula of the chemical species. The next line(s) contain the names of the authors, each separated by a comma. This is followed by the journal reference, title of the paper, and additional notes. The crystallographic data begins with a listing of the cell parameters and space group. If the data is given with respect to a non-standard space group origin then an asterisk precedes the space group symbol and the next line contains the translation vector from the standard origin. The 1952 edition of the International Tables for X-ray Crystallography are used to define the standard origin. The rest of the data set is a fixed-formatted listing of the atoms, their positional and displacement parameters, and occupancies. A header is provided that defines rightjustified columns. The name of each atom identifies the occupying elements, with additional identifiers added when appropriate. For instance, “Oco” identifies a particular oxygen atom in the albite structure. Some data sets report a crystallographic site occupied by molecular species rather than elemental, such as OH, water or methane. In most of these cases the atom name is denoted by molecular formula. For example, “CH4” denotes methane, and “Wat” denotes water. The displacement factors are tabulated in one of two formats, U’s or b’s

In the wake of a rash of executive orders and administrative actions aimed at shaping the scale, scope, and focus of the scientific enterprise in the United States during the second Trump Presidency, we have undertaken a survey of members of the American Physical Society, the country's pre-eminent physics professional society to investigate their needs, interests, and priorities, and how their interests may differ from organizational leadership's priorities. This report provides detail on the context for the creation and implementation of the survey, as well as articulating results and some common themes found in responses. Broadly, our informal survey of APS members revealed that a majority of respondents perceive that the Society supports them, cares about their needs as physicists, and is communicating reliably and transparently. However, a sizeable proportion of respondents -- up to 30\% -- harbor concerns about the organization's actions, its prioritization of member needs over corporate interests, or its willingness to listen to members. In addition, a strong majority -- over two-thirds of respondents -- articulated a desire for more concrete and personal support from APS. Wh

Using the Scopus dataset (1996-2007) a grand matrix of aggregated journal-journal citations was constructed. This matrix can be compared in terms of the network structures with the matrix contained in the Journal Citation Reports (JCR) of the Institute of Scientific Information (ISI). Since the Scopus database contains a larger number of journals and covers also the humanities, one would expect richer maps. However, the matrix is in this case sparser than in the case of the ISI data. This is due to (i) the larger number of journals covered by Scopus and (ii) the historical record of citations older than ten years contained in the ISI database. When the data is highly structured, as in the case of large journals, the maps are comparable, although one may have to vary a threshold (because of the differences in densities). In the case of interdisciplinary journals and journals in the social sciences and humanities, the new database does not add a lot to what is possible with the ISI databases.

The journal structure in the China Scientific and Technical Papers and Citations Database (CSTPCD) is analysed from three perspectives: the database level, the specialty level and the institutional level (i.e., university journals versus journals issued by the Chinese Academy of Sciences). The results are compared with those for (Chinese) journals included in the Science Citation Index. The frequency of journal-journal citation relations in the CSTPCD is an order of magnitude lower than in the SCI. Chinese journals, especially high-quality journals, prefer to cite international journals rather than domestic ones. However, Chinese journals do not get an equivalent reception from their international counterparts. The international visibility of Chinese journals is low, but varies among fields of science. Journals of the Chinese Academy of Sciences (CAS) have a better reception in the international scientific community than university journals.

In this work, we study the correlation between interdisciplinarity of papers within physical sciences and their citations by using meta data of articles published in American Physical Society's Physical Review journals between 1985 to 2012. We use the Weitzman diversity index to measure the diversity of papers and authors, exploiting the hierarchical structure of PACS (Physics and Astronomy Classification Scheme) codes. We find that the fraction of authors with high diversity is increasing with time, where as the fraction of least diversity are decreasing, and moderate diversity authors have higher tendency to switch over to other diversity groups. The diversity index of papers is correlated with the citations they received in a given time period from their publication year. Papers with lower and higher end of diversity index receive lesser citations than the moderate diversity papers.

Using "Analyze Results" at the Web of Science, one can directly generate overlays onto global journal maps of science. The maps are based on the 10,000+ journals contained in the Journal Citation Reports (JCR) of the Science and Social Science Citation Indices (2011). The disciplinary diversity of the retrieval is measured in terms of Rao-Stirling's "quadratic entropy." Since this indicator of interdisciplinarity is normalized between zero and one, the interdisciplinarity can be compared among document sets and across years, cited or citing. The colors used for the overlays are based on Blondel et al.'s (2008) community-finding algorithms operating on the relations journals included in JCRs. The results can be exported from VOSViewer with different options such as proportional labels, heat maps, or cluster density maps. The maps can also be web-started and/or animated (e.g., using PowerPoint). The "citing" dimension of the aggregated journal-journal citation matrix was found to provide a more comprehensive description than the matrix based on the cited archive. The relations between local and global maps and their different functions in studying the sciences in terms of journal lit

We compare the network of aggregated journal-journal citation relations provided by the Journal Citation Reports (JCR) 2012 of the Science and Social Science Citation Indexes (SCI and SSCI) with similar data based on Scopus 2012. First, global maps were developed for the two sets separately; sets of documents can then be compared using overlays to both maps. Using fuzzy-string matching and ISSN numbers, we were able to match 10,524 journal names between the two sets; that is, 96.4% of the 10,936 journals contained in JCR or 51.2% of the 20,554 journals covered by Scopus. Network analysis was then pursued on the set of journals shared between the two databases and the two sets of unique journals. Citations among the shared journals are more comprehensively covered in JCR than Scopus, so the network in JCR is denser and more connected than in Scopus. The ranking of shared journals in terms of indegree (that is, numbers of citing journals) or total citations is similar in both databases overall (Spearman's \r{ho} > 0.97), but some individual journals rank very differently. Journals that are unique to Scopus seem to be less important--they are citing shared journals rather than bein

This paper, the second in a series of two, provides a set of recommendations that the American Astronomical Society (AAS) can take to create a more diverse and inclusive professional society for astronomers, with a focus on women astronomers. As noted in Paper I, now is the time for the AAS to take decisive action to transform astronomy into a diverse and inclusive profession. By combining the results of our 2019 survey, which is described in Paper I, peer-reviewed academic literature, and findings from many of the white papers submitted to Astro2020, the CSWA has developed 26 specific actions the AAS can take to help end harassment and bullying in astronomy; advance career development for astronomers who are women, members of other underrepresented groups, and intersections of these populations; and improve the climate and culture of AAS meetings. Actions to reduce rates of harassment and bullying include improvements to the AAS's anti-harassment policies and procedures and the development of astronomy-specific anti-harassment training resources. Actions to advance career development include creating a compensation database, improving how jobs are posted in the AAS Job Register, a