Simulating rare events using a Weighted Ensemble-based string method

We introduce an extension to the Weighted Ensemble (WE) path sampling method to restrict sampling to a one dimensional path through a high dimensional phase space. Our method, which is based on the finite-temperature string method, permits efficient sampling of both equilibrium and non-equilibrium systems. Sampling obtained from the WE method guides the adaptive refinement of a Voronoi tessellation of order parameter space, whose generating points, upon convergence, coincide with the principle reaction pathway. We demonstrate the application of this method to several simple, two-dimensional models of driven Brownian motion and to the conformational change of the nitrogen regulatory protein C receiver domain using an elastic network model. The simplicity of the two-dimensional models allows us to directly compare the efficiency of the WE method to conventional brute force simulations and other path sampling algorithms, while the example of protein conformational change demonstrates how the method can be used to efficiently study transitions in the space of many collective variables

Inclusion of explicit thermal requirements in optimum structural design

A finite-element based procedure is described for obtaining minimum mass designs of structures subjected to combined thermal and mechanical loading and both strength and thermal constraints. The procedure is based on a mathematical programming method using the Sequence of Unconstrained Minimizations Technique (SUMT) in which design requirements are incorporated by an exterior penalty function. The procedure is limited to steady-state temperatures which are controlled by structural sizing only. The optimization procedure is demonstrated by the design of a structural wing box with both mechanical loading and external heating, subject to design constraints on stress, minimum gage, and temperature. The final design for these conditions is compared with a corresponding design in which temperature constraints are omitted

Integrated Thermal-structural-electromagnetic Design Optimization of Large Space Antenna Reflectors

The requirements for low mass and high electromagnetic (EM) performance in large, flexible space antenna structures is motivating the development of a systematic procedure for antenna design. In contrast to previous work which concentrated on reducing rms distortions of the reflector surface, thereby indirectly increasing antenna performance, the current work involves a direct approach to increasing electromagnetic performance using mathematical optimization. The thermal, structural, and EM analyses are fully integrated in the context of an optimization procedure, and consequently, the interaction of the various responses is accounted for directly and automatically. Preliminary results are presented for sizing cross-sectional areas of a tetrahedral truss reflector. The results indicate potential for this integrated procedure from the standpoint of mass reduction, performance increase, and efficiency of the design process

Addressing barriers to learning: In the classroom and schoolwide.

IntroductionPublic education is at a crossroads. Moving in new directions is imperative. Just tweaking and tinkering with old ideas is a recipe for disaster.Continuing challenges confronting public education highlight why moving school improvement policy and practice in new directions is imperative. With a view to enhancing graduation rates and successful transitions to post-secondary opportunities and well-being, pressing challenges include:Increasing equity of opportunity for every student to succeed, narrowing the achievement gap, and countering the school to prison pipeline Reducing unnecessary referrals for special assistance and special education; Improving school climate and retaining good teachers Reducing the number of low performing schools.As education leaders well know, meeting these challenges requires making sustainable progress inimproving supports for specific subgroups (e.g., English Learners, immigrant newcomers, lagging minorities, homeless students, students with disabilities) increasing the number of disconnected students who re-engage in classroom learning and thus improving attendance, reducing disruptive behaviors (e.g., including bullying and sexual harassment), and decreasing suspensions and dropouts increasing family and community engagement with schools responding effectively when schools experience crises events and preventing crises whenever possible.In some schools, continuous progress related to these concerns is being made. For many districts, however, sustainable progress remains elusive – and will continue to be so as long as the focus of school improvement policy and practice is mainly on improving instruction. Efforts to expand the use of instructional technology, develop new curriculum standards, make teachers more accountable, and improve teacher preparation and licensing all have merit; but they are insufficient for addressing the many everyday barriers to learning and teaching that interfere with effective student engagement in classroom instruction.Most policy makers and administrators know that good instruction delivered by highly qualified teachers cannot ensure that all students have an equal opportunity to succeed at school.Even the best teacher can’t do the job alone. Teachers need student and learning supports in the classroom and schoolwide in order to personalize instruction and provide special assistance when students manifest learning, behavior, and emotional problems. Unfortunately, school improvement plans continue to give short shrift to these critical matters.We recognize, as did a Carnegie Task Force on Education, that school systems are not responsible for meeting every need of their students. But as the task force stressed: when the need directly affects learning, the school must meet the challenge.The most pressing challenge is to enhance equity of opportunity by fundamentally improving how schools address barriers to learning and teaching. The future of public education depends on moving in new directions to accomplish this.Now is the time to fundamentally transform how schools address factors that keep too many students from doing well at school. And while transformation is never easy, pioneering work across the country is showing the way. Trailblazers are redeploying existing funds allocated for addressing barriers to learning and weaving these together with the invaluable resources that can be garnered by collaboration with other agencies and with community stakeholders, family members, and students themselves.The first step in moving forward is to escape old ideas. The second step is to incorporate a new vision in school improvement planning for addressing barriers to learning and teaching and re-engaging disconnected students. Our analyses envision a plan that designs and develops a unified, comprehensive, and equitable system of student and learning supports. The third step is to develop a strategic plan for systemic change, scale-up, and sustainability.This book highlights each of these matters. We invite you to join us in the quest to enhance equity of opportunity for all students to succeed at school and beyond. And we look forward to hearing from you about moving schools forward to make the rhetoric of the Every Student Succeeds Act a reality

Vortex Studies Relating to Boundary Layer Turbulence and Noise

The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Further, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques

Integrated structure electromagnetic optimization of large space antenna reflectors

The requirements for extremely precise and powerful large space antenna reflectors have motivated the development of a procedure for shape control of the reflector surface. A mathematical optimization procedure has been developed which improves antenna performance while minimizing necessary shape correction effort. In contrast to previous work which proposed controlling the rms distortion error of the surface thereby indirectly improving antenna performance, the current work includes electromagnetic (EM) performance calculations as an integral of the control procedure. The application of the procedure to a radiometer design with a tetrahedral truss backup structure demonstrates the potential for significant improvement. The results indicate the benefit of including EM performance calculations in procedures for shape control of large space antenna reflectors

Recent advances in multidisciplinary optimization of rotorcraft

A joint activity involving NASA and Army researchers at NASA LaRC to develop optimization procedures to improve the rotor blade design process by integrating appropriate disciplines and accounting for all of the important interactions among the disciplines is described. The disciplines involved include rotor aerodynamics, rotor dynamics, rotor structures, airframe dynamics, and acoustics. The work is focused on combining these five key disciplines in an optimization procedure capable of designing a rotor system to satisfy multidisciplinary design requirements. Fundamental to the plan is a three-phased approach. In phase 1, the disciplines of blade dynamics, blade aerodynamics, and blade structure are closely coupled while acoustics and airframe dynamics are decoupled and are accounted for as effective constraints on the design for the first three disciplines. In phase 2, acoustics is integrated with the first three disciplines. Finally, in phase 3, airframe dynamics is integrated with the other four disciplines. Representative results from work performed to date are described. These include optimal placement of tuning masses for reduction of blade vibratory shear forces, integrated aerodynamic/dynamic optimization, and integrated aerodynamic/dynamic/structural optimization. Examples of validating procedures are described

Structural sensitivity analysis: Methods, applications, and needs

Some innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. These techniques include a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Finally, some of the critical needs in the structural sensitivity area are indicated along with Langley plans for dealing with some of these needs