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Application of Contraction Mappings to the Control of Nonlinear Systems

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Killingsworth, W. R., Jr.↗

On the design of contractions and settling chambers for optimal turbulence manipulations in wind tunnels

The sensitivity of a moderate axisymmetric contraction of turbulence to upstream conditions is parametrically investigated in terms of turbulence intensities and integral length scales. Semi-empirical correlations are derived to characterize the development of turbulence intensities and integral length scales downstream of typical wind-tunnel turbulence manipulators. A new approach is described, permitting wind-tunnel designers to select the characteristic mesh of the turbulence manipulators, a well as the distance from them to the contraction, in order to obtain certain required turbulence characteristics in the test section at the exit of the contraction. The design charts strongly suggest that it may not be possible to achieve small scales and low intensities simultaneously, when using a contraction ratio of nine or larger. The results also confirm that the rapid distortion theory is only valid, with a proper viscous dissipation correction, up to the 'critical point' of a contraction. At that point, the scales of the various components of the velocity are equal and intercomponent transfer from the lateral to the streamwise velocities commences.

Nagib, H. M.↗

The Theory of Propellers III : the Slipstream Contraction with Numerical Values for Two-Blade and Four-Blade Propellers

As the conditions of the ultimate wake are concerned both theoretically and practically, the magnitude of the slipstream contraction has been calculated. It will be noted that the contraction in a representative case is of the order of only 1 percent of the propeller diameter. In consequence, all calculations need involve only first-order effects. Curves and tables are given for the contraction coefficient of two-blade and four-blade propellers for various values of the advance ratio; the contraction coefficient is defined as the contraction in the diameter of the wake helix in terms of the wake diameter at infinity. The contour lines of the wake helix are also shown at four values of the advance ratio in comparison with the contour lines for an infinite number of blades.

Theodorsen, Theodore↗

The advantages of cost plus award fee contracts

A Cost Plus Award Fee contract is the best procurement vehicle for the high-tech, one-of-a-kind, development projects that constitute most of NASA'S projects. The use of this type of contract requires more government and contractor effort than any other forms of contracts. An award fee contract is described as an arrangement whereby the government periodically awards a fee consistent with the cost, schedule and technical performance that is achieved by a contractor during a preset period with preset award fee pools. It's the only contracting method where both the government and contractor goals are closely linked. It also has a built-in mechanism to conveniently alter and emphasize program events in order to current external and internal situations. The award fee process also demands good communication between government and contractor participants.

Keathley, William C.↗

Advanced Transportation System Studies Technical Area 2 (TA-2) Heavy Lift Launch Vehicle Development Contract: Technical Results - Volume 2

The purpose of the Advanced Transportation System Studies (ATSS) Technical Area 2 (TA-2) Heavy Lift Launch Vehicle Development contract was to provide advanced launch vehicle concept definition and analysis to assist NASA in the identification of future launch vehicle requirements. Contracted analysis activities included vehicle sizing and performance analysis, subsystem concept definition, propulsion subsystem definition (foreign and domestic), ground operations and facilities analysis, and life cycle cost estimation. This document is Volume 2 of the final report for the contract. It provides documentation of selected technical results from various TA-2 analysis activities, including a detailed narrative description of the SSTO concept assessment results, a user's guide for the associated SSTO sizing tools, an SSTO turnaround assessment report, an executive summary of the ground operations assessments performed during the first year of the contract, a configuration-independent vehicle health management system requirements report, a copy of all major TA-2 contract presentations, a copy of the FLO launch vehicle final report, and references to Pratt & Whitney's TA-2 sponsored final reports regarding the identification of Russian main propulsion technologies.

Source record↗

Neural Correlates of Birth: Labor Contractions Induce C-Fos Expression In Newborn Rat Brain

At birth, the newborn mammal must make rapid adaptations to the extrauterine environment to survive. We have previously shown that labor contractions augment the appearance of adaptive responses at birth, viz., postpartum breathing and the onset of suckling. Since neuronal activity has been shown to upregulate the activity of immediate early genes (IEGs) in the brain, we analyzed the neural distribution of c-Fos protein expression in newborn rats using immunohistochemistry. Previous studies have reported a burst of c-Fos mRNA expression in mouse and rat brain at birth however relationships to labor and delivery have not been examined. In the present study, we exposed near-term rat fetuses to elements of the vaginal birth process: 1) Simulated labor contractions. 2) Postpartum cooling (22 deg C). 3) Umbilical cord occlusion. and 4) Stroking to mimic postpartum licking by the dam. Cardinally delivered newborns (VG) were compared with those delivered by cesarean section following either prenatal exposure to compressions (C) [simulated labor contractions], or no compressions (NC) [no labor contractions]. Similar patterns of c-fos activation were observed throughout hypothalamic and thalamic nuclei, hippocampus and cerebral cortex in VG and C newborns that were not apparent in NC newborns. Our results indicate that labor contractions play a role in the induction of widespread neural activation in the newborn brain.

Ronca, A. E.↗

The River Corridor Closure Contract How Washington Closure Hanford is Closing A Unique Department of Energy Project - 12425

Cleanup of the Hanford River Corridor has been one of Hanford Site's top priorities since the early 1990's. This urgency is due to the proximity of hundreds of waste sites to the Columbia River and the groundwater that continues to threaten the Columbia River. In April 2005, the U.S. Department of Energy, Richland Operations Office (DOE-RL) awarded the Hanford River Corridor Closure Contract (RCCC), a cost-plus incentive-fee closure contract with a 2015 end date and first of its kind at Hanford Site, to Washington Closure Hanford (WCH), a limited-liability company owned by URS, Bechtel National, and CH2M HILL. WCH is a single-purpose company whose goal is to safely, compliantly, and efficiently accelerate cleanup in the Hanford River Corridor and reduce or eliminate future obligations to DOE-RL for maintaining long-term stewardship over the site. Accelerated performance of the work-scope while keeping a perspective on contract completion presents challenges that require proactive strategies to support the remaining work-scope through the end of the RCCC. This paper outlines the processes to address the challenges of completing work-scope while planning for contract termination. WCH is responsible for cleanup of the River Corridor 569.8 km{sup 2} (220 mi{sup 2}) of the 1,517.7 km{sup 2} (586 mi{sup 2}) Hanford Site's footprint reduction. At the end of calendar year 2011, WCH's closure implementation is well underway. Fieldwork is complete in three of the largest areas within the RCCC scope (Segments 1, 2, and 3), approximately 44.5% of the River Corridor (Figure 3). Working together, DOE-RL and WCH are in the process of completing the 'paper work' that will document the completion of the work-scope and allow DOE-RL to relieve WCH of contractual responsibilities and transition the completed areas to the Long-Term Stewardship Program, pending final action RODs. Within the next 4 years, WCH will continue to complete cleanup of the River Corridor following the completion goals. As field work-scope is completed, progressive reductions of business processes, physical facilities, and staff will occur. Organizations will collapse and flatten commensurate with workload. WCH employees will move on to new endeavors, proud of their accomplishments and the legacy they are leaving behind as being the first and largest environmental cleanup closure contract at Hanford. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Best Practices for Smart Grid-Interactive Efficient Building Ready Performance Contracts

Grid-interactive efficient building (GEB) measures reduce costs and optimize energy use for additional grid services by coordinating building energy loads and providing continuous demand management. Incorporating GEB energy conservation measures (ECMs) in performance contracts is reliant upon multiple factors. These factors include site selection with utility tariffs and incentives favorable to GEB, the identification of GEB as a priority in the initial stages of the contracting process, integration of GEB within comprehensive performance contracts with multiple other ECMs, and careful consideration of GEB measurement and verification (M&V) for energy savings performance contracts (ESPCs) and performance assurance for utility energy service contracts (UESCs).

building energy loads↗

Optimal carbon capture and storage contracts using historical CO 2 emissions levels

In an effort to reduce carbon dioxide (CO 2 ) emissions to the atmosphere, carbon capture and storage (CCS) technology has been developed to collect CO 2 from emissions generators and store it underground. Recent proposed legislation would limit the volume of emissions generated from power sources, effectively requiring some sources to participate in CCS. Both emissions sources and storage operators require incentives to enter into contracts to capture excess emissions at the source, and transport and store the CO 2 underground. As the level of emissions from power plants is stochastic and carryover into future time periods is expensive, we develop a newsvendor model to determine the optimal price and volume of these contracts to maximize the expected profit of the storage operator and encourage the participation of multiple emissions sources. Because the storage operator has a limit on the amount of CO 2 that can be injected each month, this limit affects the allocation of the optimal contract amounts between the emitters. Furthermore, the distribution of emissions and relative costs of transportation also influence the optimal policy. In addition to analytical solutions, we present data-driven methods for using correlated emissions data to determine the optimal price and volume of these contracts.

42 ENGINEERING↗

Enhancing Performance Contracts with Monitoring-Based Commissioning (MBCx)

Integrating monitoring-based commissioning (MBCx) software tools into performance contracts is a timely topic given recent developments in MBCx software offerings and the growing number of MBCx deployments nationwide. Many commercial building owners have started to install MBCx software tools that tie in advanced metering infrastructure, building automation systems, and local weather data to enable ongoing commissioning and identify energy conservation measures. To support federal and commercial building owners in understanding, procuring, and implementing MBCx software tools, this report provides an overview of their capabilities, the MBCx process, and how MBCx can be integrated into - and benefit - each phase of a performance contract. This report is intended to spur increased use of MBCx in performance contracts, whether an agency has previously installed or is considering adding MBCx at the time of their project. Additionally, case studies illustrate successful experiences using MBCx within performance contracts at a university campus and across a large number of buildings managed by the General Services Administration.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

ESPC ESA Training Series: Site-Specific/Stand-Alone Contract Vehicle

This webinar provides instructions and resources for financing distributed energy projects (e.g., on–site renewable energy, storage, and combined heat and power) using an energy savings performance contract (ESPC) energy sales agreement (ESA) through the site–specific/stand–alone contract vehicle. The site–specific/stand–alone contract vehicle is a procurement process using a request for proposal (RFP). Topics covered during the webinar include forming a strong project team, validating the feasibility of the distributed energy project at a site, acquisition planning, RFP development, procurement, proposal evaluation and contract award, and the construction and performance period. This webinar also provides an overview of the resources available in the ESPC ESA Toolkit, such as checklists and templates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimizing Tensor Contraction Expressions for Hybrid CPU-GPU Execution

Tensor contractions are generalized multidimensional matrix multiplication operations that widely occur in quantum chemistry. Efficient execution of tensor contractions on Graphics Processing Units (GPUs) requires several challenges to be addressed, including index permutation and small dimension-sizes reducing thread block utilization. Moreover, to apply the same optimizations to various expressions, we need a code generation tool. In this paper, we present our approach to automatically generate CUDA code to execute tensor contractions on GPUs, including management of data movement between CPU and GPU. To evaluate our tool, GPU-enabled code is generated for the most expensive contractions in CCSD(T), a key coupled cluster method, and incorporated into NWChem, a popular computational chemistry suite. For this method, we demonstrate speedup over a factor of 8.4 using one GPU (instead of one core per node) and over 2.6 when utilizing the entire system using hybrid CPU+GPU solution with 2 GPUs and 5 cores (instead of 7 cores per node). Finally, we analyze the implementation behavior on future GPU systems.

CUDA↗

The purinergic component of human bladder smooth muscle cells’ proliferation and contraction under physiological stretch

Highlights: •Stretch induces proliferation and contraction. •Optimum applied stretch in vitro is 5% and 10% equibiaxial stretching respectively. •Expression of P2X1 and P2X2 is upregulated after application of stretch. •P2X2 is possibly more susceptible to stretch related changes. •Purinoceptors functioning may explain conditions with atropine resistance. -- Abstract: Objective: To investigate whether cyclic stretch induces proliferation and contraction of human smooth muscle cells (HBSMCs), mediated by P2X purinoceptor 1 and 2 and the signal transduction mechanisms of this process. Methods: HBSMCs were seeded on silicone membrane and stretched under varying parameters; (equibiaxial elongation: 2.5%, 5%, 10%, 15%, 20%, 25%), (Frequency: 0.05 Hz, 0.1 Hz, 0.2 Hz, 0.5 Hz, 1 Hz). 5-Bromo-2-deoxyuridine assay was employed for proliferative studies. Contractility of the cells was determined using collagen gel contraction assay. After optimal physiological stretch was established; P2X1 and P2X2 were analyzed by real time polymerase chain reaction and Western Blot. Specificity of purinoceptors was maintained by employing specific inhibitors; (NF023 for P2X1, and A317491for P2X2), in some experiments. Results: Optimum proliferation and contractility were observed at 5% and 10% equibiaxial stretching respectively, applied at a frequency of 0.1 Hz; At 5% stretch, proliferation increased from 0.837 ± 0.026 (control) to 1.462 ± 0.023%, p < 0.05. Mean contraction at 10% stretching increased from 31.7 ± 2.3%, (control) to 78.28 ±1.45%, p < 0.05. Expression of P2X1 and P2X2 was upregulated after application of stretch. Inhibition had effects on proliferation (1.232 ± 0.051, p < 0.05 NF023) and (1.302 ± 0.021, p < 0.05 A314791) while contractility was markedly reduced (68.24 ± 2.31, p < 0.05 NF023) and (73.2 ± 2.87, p < 0.05 A314791). These findings shows that mechanical stretch can promote magnitude-dependent proliferative and contractile modulation of HBSMCs in vitro, and P2X1 and 2 are at least partially responsible in this process.

60 APPLIED LIFE SCIENCES↗

Construction of 3D MHD pressure drop correlation and flow characterization in the contraction region of a fusion blanket manifold

Inlet and outlet manifolds are typical components of liquid metal (LM) blanket designs of a fusion power reactor to be used to distribute the LM flow into breeding channels and collect it at the exit of the blanket. High pressure loss in the magnetohydrodynamic (MHD) flows featuring abrupt geometrical changes is one of the main feasibility issues of such designs. Recently, optimization studies were conducted to construct 3D MHD pressure drop correlations for a LM flow in an electrically insulating manifold with gradual expansion. Here, the 3D computational approach developed in that study is applied to the outlet manifold featuring gradual contraction. A systematic analysis was performed with a total number of 135 flow cases computed with COMSOL Multiphysics for Hartmann numbers 1000 < Ha < 10,000, Reynolds numbers 100 < Re < 12,000, and contraction angles 45° < θ < 75° for a fixed contraction ratio of 4. The effects of Ha, Re and θ on the flow recirculation, development length and the total pressure drop were carefully examined. A linear regression analysis was used to determine the power rule of pressure drop coefficient k related to Ha and Re, demonstrating a good match with the Ludford layer theory. Eventually, a correlation for the 3D MHD pressure drop coefficient was constructed as a function of Ha, Re and θ. Further, the results were compared against the inlet manifold. It was found that the flow in the inlet manifold exhibits larger recirculation zones. In the investigated range of Ha, Re and θ, the pressure drop coefficient k of the LM MHD flow in the gradual contraction is only slightly lower (< 8 %) than that in the gradual expansion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamic contraction of the positive column of a self-sustained glow discharge in air flow

We study the dynamic contraction of a self-sustained glow discharge in air in a rectangular duct with convective cooling. A two dimensional numerical model of the plasma contraction was developed in a cylindrical frame. The process is described by a set of time-dependent continuity equations for the electrons, positive and negative ions; gas and vibrational temperature; and equations which account for the convective heat and plasma losses by the transverse flux. Transition from the uniform to contracted state was analyzed. It was shown that such transition experiences a hysteresis, and that the critical current of the transition increases when the gas density drops. Possible coexistence of the contracted and uniform state of the plasma in the discharge, where the current flows along the density gradient of the background gas, is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Performance Assurance Planning Guide for Utility Energy Service Contracts: 2025 Edition

Administered by the U.S. Department of Energy's (DOE) Federal Energy Management Program (FEMP), the Utility Program has fostered collaboration among federal agencies and their serving utilities for more than 25 years. The Utility Program supports agencies using Utility Energy Service Contracts (UESCs), a well-developed, effective contracting vehicle that enable the latest approaches to cost-effective energy management at federal sites. Federal agencies have successfully used UESCs to award over 2,000 energy and water efficiency and renewable energy projects, investing approximately $\$$2.8 billion in furthering the Federal Government's efforts to reduce energy intensity. Authorized by 42 U.S. Code section 8256 (10 U.S. Code section 2913 for the Department of Defense), a UESC is a limited-source acquisition between a federal agency and an eligible serving utility for energy management services that generate savings from the implementation of energy- and water -conservation measures (collectively referred to as ECMs), with 42 U.S. Code section 8287 (Defense Federal Acquisition Regulation Supplement, Part 241), providing the term of a UESC, which may extend up to 25 years. Through a UESC, the utility partner assesses designs, and implements the desired ECMs - which can range from lighting retrofits and renewable energy systems, to combined heat and power plants or other technologies and strategies, and may provide financing for the project. The agency may use any combination of appropriations and third-party financing to pay for the project, providing useful flexibility. There is no limit to the project size, big or small, that can be implemented using a UESC. To assist agencies implementing a UESC, FEMP has developed a Utility Energy Service Contract Guide and this companion guidance document to help agencies and their utility partners better understand the best practices for to ensure UESCs continue to perform and generate savings throughout their performance period. These best practices utilize a combination of effective project management, communication, documentation, and a detailed Performance Assurance Plan. This plan is a project specific set of actionable protocols that define important tasks and responsibilities throughout the contract term and reflects the site conditions, complexities, agency capabilities, and operating and maintaining planned ECMs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Differences in muscle contraction onset as determined by ultrasound and electromyography

ABSTRACT Introduction We characterize the agreement between the timing of muscle contraction onset detected by surface electromyography (sEMG), fine wire EMG (fwEMG), and motion‐mode (M‐mode) ultrasound for improved interpretations of clinical outcomes. Methods Eighteen healthy adults participated. Differences in contraction onset were compared between sEMG, fwEMG, and M‐mode ultrasound collected during concentric contractions of the vastus lateralis and biceps brachii. Results The mean difference of 13.1 ms (‐33.3–59.9) between sEMG and fwEMG was non‐significant (intraclass correlation [ICC] = 0.60). Ultrasound was significantly different from surface and fine wire EMG (ICC = 0.65 and ICC = 0.40, respectively), occurring 98.6 ms (72.3–124.9) and 111.7 (60.3–163.0) before sEMG and fwEMG, respectively. Nonparametric interquartile ranges were also wide. Conclusions Due to high variability, comparisons between EMG methods should be interpreted with caution. Ultrasound detected onset before either EMG method, which may indicate motion from adjacent muscles during voluntary contractions. Muscle Nerve 59:494–500, 2019

Tweedell, Andrew J.↗