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Here we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features., Comment: Accepted for publication in the Journal of the Acoustical Society of America

In quantitative analysis of seafloor imagery, it is common to model the collection of individual pixel intensities scattered by the seafloor as a random variable with a given statistical distribution. There is a considerable literature on statistical models for seafloor scattering, mostly focused on areas with statistically homogeneous properties (i.e. exhibiting spatial stationarity). For more complex seafloors, the pixel intensity distribution is more appropriately modeled using a mixture of simple distributions. For very complex seafloors, fitting 3 or more mixture components makes physical sense, but the statistical model becomes much more complex in these cases. Therefore, picking the number of components of the mixture model is a decision that must be made, using a priori information, or using a data driven approach. However, this information is time consuming to collect, and depends on the skill and experience of the human. Therefore, a data-driven approach is advantageous to use, and is explored in this work. Criteria for choosing a model always need to balance the trade-off for the best fit for the data on the one hand and the model complexity on the other hand. In this work, we compare several statistical model selection criteria, e.g., the Bayesian information criterion. Examples are given for SAS data collected by an autonomous underwater vehicle in a rocky environment off the coast of Bergen, Norway using data from the HISAS-1032 synthetic aperture sonar system., Comment: Paper presented at the 5th International Conference on Synthetic Aperture Radar and Sonar, Lyric Italy, September 2023

The Kirchhoff integral is a fundamental integral in scattering theory, appearing in both the Kirchhoff approximation, as well as the small slope approximation. In this work, a functional Taylor series approximation to the-eps-converted-to.pdf Kirchhoff integral is presented, under the condition that the roughness covariance function follows either an exponential or Gaussian form--in both the one-dimensional and two-dimensional cases. Previous approximations to the Kirchhoff integral [Gragg et al. J. Acoust. Soc. Am. 2001, Drumheller and Gragg J. Acoust. Soc. Am., 2001] assumed that the outer scale of the roughness was very large compared to the wavelength, whereas the proposed method can treat arbitrary outer scales. Assuming an infinite outer scale implies that the root mean square (rms) roughness is infinite. The proposed method can efficiently treat surfaces with finite outer scale, and therefore finite rms height. This series is shown to converge independently of roughness or acoustic parameters, and converges to within roundoff error with a reasonable number of terms for a wide variety of dimensionless roughness parameters. The series converges quickly when the dimensionless rms height is small, and slowly when it is large., Comment: 9 pages, 5 figures, published in the J. Acoust Soc. Am

Contemporary high-resolution sonar systems use broadband pulses and long arrays to achieve high resolution. It is important to understand effects that high-resolution sonar systems might have on quantitative measures of the scattered field due to the seafloor. A quantity called the broadband scattering cross section is defined, appropriate for high-resolution measurements. The dependence of the broadband scattering cross section, $\sigma_{bb}$ and the scintillation index, $SI$ on resolution was investigated for one-dimensional rough surfaces with power-law spectra and backscattering geometries. Using integral equations and Fourier synthesis, no resolution dependence of $\sigma_{bb}$ was found. The incoherently-averaged frequency-domain scattering cross section has negligible bandwidth dependence. $SI$ increases as resolution increases, grazing angle decreases, and spectral strength increases. This trend is confirmed for center frequencies of 100 kHz and 10 kHz, as well as for power-law spectral exponents of 1.5, 2, and 2.5. The hypothesis that local tilting at the scale of the acoustic resolution is responsible for intensity fluctuations was examined using a representative model for the effect of slopes (inspired by the composite roughness approximation). It was found that slopes are responsible in part for the fluctuations, but other effects, such as multiple scattering and shadowing may also play a role., Comment: 22 pages, 10 figures, preprint version of paper published in the Journal of the Acoustical Society of America, at \url{https://doi.org/10.1121/10.0002974}

Acoustic scattering from layered seafloors exhibits dependence on both the mean geoacoustic layering, as well as the roughness properties of each layer. Several theoretical treatments of this environment exist, including the small roughness perturbation approximation, the Kirchhoff approximation, and three different versions of the small slope approximation. All of these models give different results for the scattering cross section and coherent reflection coefficient, and there is currently no way to distinguish which model is the most correct. In this work, an integral equation for scattering from a layered seafloor with rough interfaces is presented, and compared with small roughness perturbation method, and two of the small slope approximations. It is found that the most recent small slope approximation by Jackson and Olson is the most accurate when the root mean square (rms) roughness is large, and some models are in close agreement with each other when the rms roughness is small., Comment: 11 pages, 10 figures, submitted to the Journal of the Acoustical Society of America

We precisely and rigorously characterise the decay of elastic fields generated by dislocations in crystalline materials, focusing specifically on the role of multilattices. Concretely, we establish that the elastic field generated by a dislocation in a multilattice can be decomposed into a continuum field predicted by a linearised Cauchy-Born elasticity theory, and a discrete and nonlinear core corrector representing the defect core. We demonstrate both analytically and numerically the consequences of this result for cell size effects in numerical simulations.

For the last 4 years, 10 leading education organizations have collaborated on a study series that includes teacher voice in conversations and research about educator effectiveness. Initially conceptualized by teacher leaders from the National Network of State Teachers of the Year (NNSTOY) and with their continued input, the "From Good to Great" study series has asked exemplary teachers to share which professional supports and experiences helped them to increase their effectiveness as educators as they progressed through the various stages of their careers. There are multiple reasons why exemplary teachers' perspectives provide key insights for researchers and policy makers, including: (1) The need for smart investments in teacher development; and (2) The need for teacher voice in policy. This report (the third in the study series) summarizes the findings from a 2016 survey of National Board Certified Teachers (NBCTs) and builds on the results of a similar survey of State and National Teachers of the Year in 2013-2014. Namely: (1) At the preservice stage, once again respondents ranked a high quality clinical practicum as by far the most important experience; (2) This study again confirmed that an effective school principal and mentors (both assigned and informal) rose to the top of the list, with appropriate school placements and common planning time following close behind; (3) National Board Certification and other ongoing formal education (such as graduate coursework) were seen as the most important experiences, followed by self-chosen professional development outside of the school district and collaboration with peers; and (4) At the teacher leader stage, as with the 2013-14 survey, the National Board Certified Teachers (NBCTs) surveyed thought serving as a mentor or coach was most important for helping them continue to improve their practice, even after they had already been established as effective teachers. These findings call attention to the need for applied learning opportunities for early-career teachers, opportunities for collaboration across the career continuum, and teacher leadership. Other themes that emerged from this survey included the importance of a full-year final clinical practicum and teacher choice in ongoing professional development options, including teacher leadership roles.

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset., Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of America

This report is the second in a series from a collaboration of nine leading organizations working to advance teaching and elevate the profession. For years, education leaders have sought to pinpoint how teachers become effective in order to better leverage teachers' impact on student learning and improve student outcomes. Teacher leadership is receiving increased attention as a potential lever for improved instruction, recruitment and retention of effective teachers, and student outcomes. A growing body of research on teacher leadership models and its potential impact on the field suggests that teacher leaders may play a critical role in creating high-functioning schools that can create sustainable improvements in teaching and learning. This report offers insights from teacher leaders themselves on this topic, exploring the specific ways in which teacher leaders can contribute to instructional improvement. This report includes three main sections: (1) the characteristics of teacher leaders; (2) the roles teacher leaders take in improving teacher practice; and (3) the supports and barriers to teacher leadership. The report concludes with specific policy recommendations for supporting teacher leadership in state and local contexts. Contains an appendix. [Originally proposed by the National Network of State Teachers of the Year (NNSTOY) and led by NNSTOY and the Center on Great Teachers and Leaders (GTL Center) at American Institutes for Research, the study involves the following partner organizations, many of which contributed to this second report by assisting in the development of the focus group protocol, analysis of preliminary findings, and review of the report: American Association of Colleges of Teacher Education (AACTE), American Federation of Teachers (AFT), Council for the Accreditation of Educator Preparation (CAEP), Council of Chief State School Officers (CCSSO), GTL Center, National Board for Professional Teaching Standards (NBPTS), National Council on Teacher Quality (NCTQ), National Education Association (NEA), and NNSTOY. For the first report in the series, "From Good to Great: Exemplary Teachers Share Perspectives on Increasing Teacher Effectiveness across the Career Continuum," see ED555657.]

We formulate the blended force-based quasicontinuum (BQCF) method for multilattices and develop rigorous error estimates in terms of the approximation parameters: atomistic region, blending region and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone--Wales defect in graphene., Comment: Fixed typos and added additional details in section 3.3 and explanations in sections 4.5 and 4.6

We formulate a model for a point defect embedded in a homogeneous multilattice crystal with an empirical interatomic potential interaction. Under a natural, phonon stability assumption we quantify the decay of the long-range elastic fields with increasing distance from the defect. These decay estimates are an essential ingredient in quantifying approximation errors in coarse-grained models and in the construction of optimal numerical methods for approximating crystalline defects.

Measurements of acoustic backscattering from glacially-eroded rock outcrops were made off the coast of Sandefjord, Norway using a high-frequency synthetic aperture sonar (SAS) system. A method by which scattering strength can be estimated from data collected by a SAS system is detailed, as well as a method to estimate an effective calibration parameter for the system. Scattering strength measurements from very smooth areas of the rock outcrops agree with predictions from both the small-slope approximation and perturbation theory, and range between -33 and -26 dB at 20$^\circ$ grazing angle. Scattering strength measurements from very rough areas of the rock outcrops agree with the sine-squared shape of the empirical Lambertian model and fall between -30 and -20 dB at 20$^\circ$ grazing angle. Both perturbation theory and the small-slope approximation are expected to be inaccurate for the very rough area, and overestimate scattering strength by 8 dB or more for all measurements of very rough surfaces. Supporting characterization of the environment was performed in the form of geoacoustic and roughness parameter estimates., Comment: 17 pages, 12 figures, published in the Journal of the Acoustical Society of America, available at http://link.aip.org/link/?JAS/139/1833

For well over a decade, teachers have been recognized as the single most important school-level factor influencing student achievement (Darling-Hammond, 2000; McCaffrey, Lockwood, Koretz, & Hamilton, 2003; Rivkin, Hanushek, & Kain, 2000; Rowan, Correnti & Miller, 2002; Wright, Horn, & Sanders, 1997). Tremendous public resources have been invested across the country in new systems to both assess and address teacher effectiveness. Yet the lion's share of existing research seeking to understand the factors that make teachers effective focuses on quantifiable--yet more surface-level--inputs, such as years on the job, grade point averages, certifications, and degrees. This research leaves many important policy questions unanswered--particularly questions about the specific types of professional experiences and supports necessary to maximize teacher effectiveness. This report helps to fill these gaps through a first-of-its-kind exploratory survey of National and State Teachers of the Year. These teachers are chosen by their states as among the best, and one teacher each year is selected as among the best in the nation (see "Who Are the National and State Teachers of the Year?" on page 3). In this report, we offer insights on the professional experiences and supports that these teachers believe most contributed to their growth and eventual excellence as a teacher. Reflecting back on their careers, from preparation through mastery and even into retirement, the National and State Teachers of the Year surveyed in this study provide education leaders and policymakers with needed information about the formative experiences of great teachers. The findings both surprise us and confirm much of what we knew about how teachers evolve from good to great. The main body of the report takes readers through the four stages that this study used to define the teacher career continuum: Preservice, Novice, Career, and Teacher Leader stages. For each stage, it describes the professional experiences and supports that the National and State Teachers of the Year viewed as increasing teacher effectiveness as they progressed through the stages of their career. The report concludes with considerations for policymakers at the school, district, and state levels as well as for teacher preparation programs. Methodology for the survey is appended. [Proposed by the National Network of State Teachers of the Year (NNSTOY) and led by the Center on Great Teachers and Leaders (GTL Center) at American Institutes for Research, this study involved the following partner organizations, which collaborated extensively on this study, contributing to the development of the survey questions, data analysis, and drafting of the report: American Association of Colleges of Teacher Education, Council for the Accreditation of Educator Preparation, Council of Chief State School Officers, GTL Center, National Council on Teacher Quality, National Education Association, and NNSTOY.]

We examine the Petviashvilli method for solving the equation $ \phi - \Delta \phi = |\phi|^{p-1} \phi$ on a bounded domain $\Omega \subset \mathbb{R}^d$ with Dirichlet boundary conditions. We prove a local convergence result, using spectral analysis, akin to the result for the problem on $\mathbb{R}$ by Pelinovsky & Stepanyants, 2004. We also prove a global convergence result by generating a suite of nonlinear inequalities for the iteration sequence, and we show that the sequence has a natural energy that decreases along the sequence., Comment: 24 pages, 7 figures, shortened for publication with some corrections. See v1 for more detailed proofs of the local convergence

We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Near the defect core the method employs a potential-based atomistic model, which enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.

Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in arXiv:1304.4976 for linear, one-dimensional problems to multi-dimensional settings and arbitrary interatomic potentials. We conjecture optimal error estimates for the multidimensional AtC, outline an implementation procedure, and provide numerical results to corroborate the conjecture for a 1D Lennard-Jones system with next-nearest neighbor interactions., Comment: 12 pages, 3 figures

We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the interfaces between the atomistic and continuum subdomains. The optimization objective is to minimize the error between the atomistic and continuum solutions on the overlap between the two subdomains, while the atomistic and continuum force balance equations provide the constraints. Splitting of the atomistic and continuum problems instead of blending them and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. We present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body next-nearest neighbor interactions., Comment: 19 pages, 2 figures

The Solid Rocket Booster (SRB) element integrates all the subsystems needed for ascent flight, entry, and recovery of the combined Booster and Motor system. These include the structures, avionics, thrust vector control, pyrotechnic, range safety, deceleration, thermal protection, and retrieval systems. This represents the only human-rated, recoverable and refurbishable solid rocket ever developed and flown. Challenges included subsystem integration, thermal environments and severe loads (including water impact), sometimes resulting in hardware attrition. Several of the subsystems evolved during the program through design changes. These included the thermal protection system, range safety system, parachute/recovery system, and others. Because the system was recovered, the SRB was ideal for data and imagery acquisition, which proved essential for understanding loads, environments and system response. The three main parachutes that lower the SRBs to the ocean are the largest parachutes ever designed, and the SRBs are the largest structures ever to be lowered by parachutes. SRB recovery from the ocean was a unique process and represented a significant operational challenge; requiring personnel, facilities, transportation, and ground support equipment. The SRB element achieved reliability via extensive system testing and checkout, redundancy management, and a thorough postflight assessment process. However, the in-flight data and postflight assessment process revealed the hardware was affected much more strongly than originally anticipated. Assembly and integration of the booster subsystems required acceptance testing of reused hardware components for each build. Extensive testing was done to assure hardware functionality at each level of stage integration. Because the booster element is recoverable, subsystems were available for inspection and testing postflight, unique to the Shuttle launch vehicle. Problems were noted and corrective actions were implemented as needed. The postflight assessment process was quite detailed and a significant portion of flight operations. The SRBs provided fully redundant critical systems including thrust vector control, mission critical pyrotechnics, avionics, and parachute recovery system. The design intent was to lift off with full redundancy. On occasion, the redundancy management scheme was needed during flight operations. This paper describes some of the design challenges and technical issues, how the design evolved with time, and key areas where hardware reusability contributed to improved system level understanding.