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Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

Kennedy, Christopher A.↗

A METHOD TO REDUCE BIOBURDEN IN ASTROMATERIALS CURATION FACILITIES WITHOUT INTRODUCING UNWANTED CONTAMINATION

Introduction: NASA curates its Astromaterials collections in cleanrooms that are carefully monitored for particulate, inorganic and trace metal contamination. Current sample collections are not particularly susceptible to organic contamination or biological alteration. However, new collections like those from the OSIRIS-REx and Hayabusa2 missions will have organic contamination requirements and are susceptible to biodegradation. It will be necessary sterilize or at least disinfect curation labs, as well as tools and equipment in a manner that does not introduce additional contamination and does not affect the samples 1. Current curation cleaning procedures utilize isopropyl alcohol which offers some bioburden reduction, but is not effective against spore-forming bacteria or fungal spores 2. We present a modified disinfection method that uses ultrapure hydrogen peroxide to reduce bioburden inside curation labs and glove boxes without introducing contamination or damaging curation equipment. We tested this method in the meteorite processing lab as well as on a glovebox being cleaned for use in processing ANGSA (Apollo Next Generation Sample Analysis) samples and present the results of those tests. We discuss the limitations of this method and describe potential situations in which it will not be applicable. The CDC guidelines for disinfection andsterilization in healthcare facilities discusses over 15different methods for reducing bioburden in hospitalsettings 3. The most common method, steamsterilization, is well suited to sterilizing curationprocessing tools but cannot easily be used to sterilizecleanroom surfaces or large equipment likegloveboxes. Chemical sterilization with bleach(NaOCl) is also a common strategy in healthcare andpharmaceutical settings that presents materialcompatibility issues as well as serious inorganiccontamination concerns for curation facilities.Introducing a new source of Na and Cl into curationlabs is not acceptable. Other chemical methods likeethylene oxide, formaldehyde, iodophors andquaternary ammonium compounds could introduceorganic and inorganic contamination. We chose tofocus on hydrogen peroxide because it is generallycompatible with commonly used curation materialslike stainless steel, aluminum and Teflon and becauseit decomposes to oxygen and water. The CDCguidelines for hydrogen peroxide specify using a 7.5wt% solution at 25 ̊C with a contact time of 30 minutesfor high level disinfection and 6 hours for sterilization.High level disinfection is defined as a technique thatwill kill all microorganisms except large numbers ofbacterial spores 3. Methods: We prepared a solution of 7.5 wt%hydrogen peroxide from a stock solution of ultrapure30 wt% peroxide (JT Baker) and curation gradeultrapure water. This ultrapure water is already used incuration cleaning procedures and thus is not consideredand additional source of contamination. We conducteda materials compatibility test by exposing unanodizedand anodized 6061 T6 Al alloy to the peroxide solutionfor up to six hours and periodically inspecting thesurfaces for visible defects. We used this peroxide todisinfect the floor of the meteorite processing lab andthe interior of a curation glovebox by exposing thesesurfaces to the peroxide solution for 30 min. Thesurfaces were swabbed with a dry macrofoam swabbefore (Puritan Brand 2518051PFRNDFD) and afterperoxide treatment to collect microbes present on thesurfaces. Microbes were extracted by sonication fromthe swab into 15 ml of PBS (phosphate buffered saline)and inoculated onto the following media: TSA (trypticsoy agar) BA (blood agar), R2A (Reasoners 2 agar),Potato Dextrose Agar, Saboraud Dextrose Agar andSaboraud Dextrose Agar with 0.1 mg/ mlchloramphenicol. Four TSA plates and two BA plateswere inoculated with 0.1 ml of PBS each andincubated at 35 and 37 for 48 hours. Two R2A°C°Cplates (0.1 ml of PBS each) were incubated at 25 .°CThe remaining plates were inoculated with 0.2ml ofPBS and incubated at 30 ̊C for seven days. Afterincubation bacterial and fungal isolates were countedand transferred to new plates for identification usingthe VITEK24 automated system or by sequencing aportion of the barcode gene (16S rRNA for bacteria,small subunit gene for fungi) on an ABI 3500 Sangersequencer. Negative controls consisted of swabs thatwere opened in the sampling environment andanalyzed alongside the experimental samples.Results: A 6 hour exposure to hydrogen peroxideresulted in visible pitting on un-anodized 6061 Al, butnot on anodized surfaces. No visible pitting occurredafter a 30 minute exposure. Therefore, we decided tolimit our experimental tests to 30 min. exposures. 17bacterial CFU (colony forming units) representing 4distinct organisms were isolated from the meteorite processing lab floor prior to hydrogen peroxidetreatment. We were unable culture any organisms afterperoxide treatment. In the glovebox we were able toculture three bacterial CFU representing three distinctspecies, including a spore forming bacterium prior todisinfection with peroxide. After the peroxidetreatment we were unable to culture any organisms.Routine monitoring of the meteorite processing lab andthe glovebox did not indicate any increase in unwantedinorganic contamination after these peroxidetreatments. Discussion: A 30 minute treatment with 7.5 wt%peroxide appears to be an effective method forreducing bioburden on typical cleanroom surfaces. Themethod does not introduce unwanted organic orinorganic contamination and is compatible withcommonly used curation materials like stainless steel,Teflon and anodized aluminum alloys. Special careshould be taken with un-anodized aluminum.Prolonged exposure to hydrogen peroxide can causepitting on this material. We recommend using thismethod to disinfect curation labs and equipment whenbiological alteration is a concern. This method iseffective at room temperature and cannot be used todisinfect labs and equipment where the ambienttemperature is < 0 ̊C. Astromaterials samples shouldbe removed from the area where disinfection is tooccur. Hydrogen peroxide is a powerful oxidizingagent and will react with any organic carbon present inthe sample. References: [1.] Mccubbin, F. M. et al.Sp. Sci Rev(2019) doi:10.1007/s11214-019-0615-9. [2.] Mogul, R.et al.Astrobiology 18, ast.2017.1814 (2018). [3.]Rutala, W. A. & Weber, D. J. Guideline for Disinfection and Sterilization in Healthcare Facilities, 2008. [4.] Pincus, D. H. in Encyclopedia of Rapid Microbiological Methods (2005).

A. B. Regberg↗

TOWARD A METHOD FOR SCALING HUMAN BODY MODELS IN AN IMU-BASED WORKFLOW

BACKGROUND Scaled biomechanical models can more accurately inform crew health decisions when tailored to the wide range of astronaut sizes. One component to improve scaling of existing models to better represent each unique astronaut’s size is the individual length scaling of limbs. Traditionally, these lengths are determined by motion capture or manual measurement. A new method is herein proposed for length scaling which can be done by measuring linear and angular accelerations at a desired point during isolated motion around a point of rotation, then calculating the distance between the desired point and point of rotation. When an Inertial Measurement Unit (IMU) device is placed at the distal point of a limb, the isolated motion is about that limb’s proximal joint. For example, to measure forearm length, an IMU is placed at the wrist, the point of rotation is at the elbow, and the isolated motion is forearm flexion and extension. These calculated lengths are then used to scale models to each unique astronaut’s size, thereby improving the applicability of the model. This method of scaling limb segments can be used for any limb that has an easily defined proximal joint for the limb to rotate around including hands, arms, legs, feet. Utilizing IMUs for data collection also provides the synergistic ability to record data without a dedicated space in a room with many cameras, therefore reducing the data collection footprint, or record data where optical motion capture is not possible, such as inside a spacesuit. METHODS AND RESULTS To test this method, upper body data collection was performed with 5 Xsens DOT IMUs on a single subject. IMUs consist of an accelerometer, a gyroscope, and a magnetometer which collect linear acceleration, angular velocity, and magnetic fluctuations, respectively. Before any ground-based laboratory collection, the magnetic fluctuations are used to correct the heading of the IMU in space relative to the Earth’s magnetic field. The direct measurement of angular velocity is integrated to calculate angular acceleration. Then the linear acceleration ( a ) and angular acceleration (α) are solved using r = at/α to calculate the radius, which in this case is the distance between the IMU and the point of rotation (i.e., segment length). The IMU must be placed at the most distal point of the limb being measured (i.e., ankle if measuring lower leg length) and the test plan must consist of an isolated motion about that limb’s proximal joint (i.e., knee flexion and extension if measuring lower leg length). The distances (radii) calculated at every time interval were filtered (bandpass filter keeping 5th-90th percentile data) to eliminate outliers and spurious data that occur when the isolated motion was stopped or nearly stopped. The remaining distances were averaged, resulting in the calculated limb length. Scaling factors were then computed by dividing the calculated limb length by the unscaled model’s length. These scale factors are plugged into the Scale Tool in OpenSim [1,2] to apply the scaling to the OpenSim Full Body Rajagopal Model [3,4]. Manual measurements of limb lengths were taken before data collection started and used for comparing against the calculated lengths. The Anthropometric Survey of US Army Personnel (ANSUR II) [5] was also used as a third source of reference for limb length measurements. The following measurements were retrieved from the subject before data collection: 34.5 cm from L1 to C7 (thorax), 25.7 cm from C7 Joint Center (JC) to head vertex (neck and head), 36.3 cm from shoulder JC to elbow JC (humerus), 29.5 cm from elbow JC to wrist JC (forearm), and 16.2 cm from clavicle to acromion (clavicle). Of those five, forearm and humerus lengths were calculated using this proposed method to obtain preliminary results. The forearm length after filtering and averaging was calculated to be 37.6 cm. This is a 28% overestimation from the measured forearm length (29.5 cm). The humerus length after filtering and averaging was calculated to be 47.8 cm. This is a 31% difference from the measured subject length (36.3 cm). Sources of error include imperfect isolated motion (method currently expects that motion should be perfectly circular in a 2D plane, include no rotation of the IMU, and be relatively smooth; a more secure IMU attachment method will help), unrefined filter techniques (removed highest and lowest values with 20% high and low pass filters and no smoothing filters), arbitrary removal of stopped or near stopped data (kept data for only a short range before and after the angular velocity peaking), and a more representative method for removing gravitational acceleration is needed (current method is to zero all accelerations against a baseline taken just before the isolated motion which does not account for the gravitational acceleration changed due to IMU rotation during movement). Addressing these error sources will improve the accuracy of the limb length calculation. Next steps include creating a method for whole-body scaling estimation using individual limb scale factors. Continued pursuit of these techniques is expected to enable acquiring anthropometric information using only IMUs in real-time.

E. K. Marecki↗

Treatment of Nonuniform Temperature Distribution by Subgroup Method

The subgroup method divides an energy group into several subgroups according to the magnitude of the cross section. The subgroup fixed source equation is formulated on the energy range of a subgroup, the ratio of which to the energy range of an energy group is defined as subgroup probability. Typically the physical probability table or the mathematical probability table is applied. However, both of the tables are not guaranteed to share the same set of subgroup probabilities for a resonant nuclide at different temperatures. This means that the subgroup fixed source equation cannot be formulated and the subgroup method will not work when the temperature distribution is nonuniform. To overcome this defect, the subgroup method based on partial cross section fit scheme (PXSFS) and the simplified partial cross section fit scheme (SPXSFS) are proposed. These methods fit the cross sections at different temperatures as partial cross sections to share a same set of subgroup probabilities. The new methods is compared to the conventional subgroup method (CSM) based on physical probability table and the preexisting methods: the correlation model (CM), the subgroup level adjustment scheme (SLAS) and the number density adjustment scheme (NDAS). The numerical results show that the new methods can better predict the spatial dependent reaction rate than preexisting methods. Within these two methods, the simplified scheme consumes less time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Fast iterative refinement method for mixed systems of integral and fractional integro-differential equations

The authors’ new method of iterative refinement has been successfully applied to the linear fractional Fredholm integro-differential equation. In this work, we adapt our method to obtain approximate analytical solutions for linear Volterra equations of both the first and the second kind of fractional type. A detailed convergence analysis is presented for each kind. The authors also apply their method to the challenging first kind linear Fredholm integral equation. Three different cases are considered to test the efficacy of our method. These include mixed systems of various forms of linear integral and fractional integro-differential equations. We compare our method with six well-established methods: Picard’s successive approximations, an accelerated form of the latter, the Adomian decomposition, the variational iteration, the homotopy perturbation and the homotopy analysis. The results show the versatility of the new method in solving a wide variety of equations, its high convergence speed and accuracy and its capability of directly dealing with equations of the first kind. We also prove that Picard’s method for linear equations is a special case of our method.

97 MATHEMATICS AND COMPUTING↗

Impact of hydrogen SAE J2601 fueling methods on fueling time of light-duty fuel cell electric vehicles

Hydrogen fuel cell electric vehicles (HFCEVs) are zero-emission vehicles (ZEVs) that can provide drivers a similar experience to conventional internal combustion engine vehicles (ICEVs), in terms of fueling time and performance (i.e. power and driving range). The Society of Automotive Engineers (SAE) developed fueling protocol J2601 for light-duty HFCEVs to ensure safe vehicle fills while maximizing fueling performance. This study employs a physical model that simulates and compares the fueling performance of two fueling methods, known as the “lookup table” method and the “MC formula” method, within the SAE J2601 protocol. Both the fueling methods provide fast fueling of HFCEVs within minutes, but the MC formula method takes advantage of active measurement of precooling temperature to dynamically control the fueling process, and thereby provides faster vehicle fills. Here, the MC formula method greatly reduces fueling time compared to the lookup table method at higher ambient temperatures, as well as when the precooling temperature falls on the colder side of the expected temperature window for all station types. Although the SAE J2601 lookup table method is the currently implemented standard for refueling hydrogen fuel cell vehicles, the MC formula method provides significant fueling time advantages in certain conditions; these warrant its implementation in future hydrogen refueling stations for better customer satisfaction with fueling experience of HFCEVs.

13 HYDRO ENERGY↗

A verification study of fatigue-based methods in API RP 1183 for estimating fatigue life of pipeline dents

Pipeline dents are mechanical damage caused by a third party in buried pipelines during construction or maintenance repair. Dents are recognized as a leading cause of pipeline failures for both liquid and gas transmission lines, and their assessment and management are critical to pipeline integrity. To meet the industry need, American Institute of Petroleum (API) in 2020 published a recommended practice (RP) 1183 – Assessment and Management of Pipeline Dents. This API code provides the pipeline industry “standard methods” for evaluating severity and fatigue life of pipeline dents with a single peak. This paper performed an initial verification study of fatigue-based methods prescribed in API RP 1183 for estimating fatigue life of pipeline dents. A brief review was first given to the dent fatigue-based methods, including three dent screening methods for estimating dent fatigue life in Sections 7.4.1, 7.4.2, and 7.4.3 of API 1183 and one dent assessment method for predicting fatigue life in Section 8.3.4. In order to verify these fatigue life prediction methods, a set of “standard examples” of dents provided in Annexes A.1 to A.5 of API RP 1183 were utilized in this study to calculate fatigue life, to determine restraint condition, and to evaluate both screening and assessment methods for single-peak dents. Through detailed calculations and comparisons, this study confirmed some specifications of API RP 1183, but also found some self-inconsistences and errors existing in this new API code. Furthermore, this includes the self-inconsistences between three screening methods and the self-inconsistence between the screening and assessment methods. On this basis, recommendations were made on how the operators should use API RP 1183, and what actions API should take to improve this code.

42 ENGINEERING↗

An Immersed Boundary method with divergence-free velocity interpolation and force spreading

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least $\mathscr{C}$ 1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. Finally, the method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.

97 MATHEMATICS AND COMPUTING↗

Influence of sampling frequency and estimation method on phosphorus load uncertainty in the Western Lake Erie Basin, Ohio, USA

Accurate estimates of nutrient loads are necessary to identify critical source areas and quantify the impact of management practices on pollutant export. Previous studies have investigated nutrient load estimate uncertainty, but they often focus on nutrient loads estimated using an interpolation method for large-scale watersheds with short-term datasets. The study objective was to quantify uncertainty in soluble reactive phosphorus (SRP), total phosphorus (TP), and suspended solids (SS) load estimates from two small (<10 3 km 2 ) agricultural watersheds in the western Lake Erie Basin resulting from different sampling frequencies. Each watershed had high temporal resolution datasets of discharge (15 min) and nutrient concentration (1 to 3 samples per day) collected over a 30-year period (1990–2020). Firstly, SRP, TP, and SS loads were calculated using the high temporal resolution datasets, which was assumed as “true loads”. Secondly, the high temporal concentration data were decomposed to semiweekly, weekly, biweekly, and monthly sampling and annual loads were estimated using four common load estimation methods to assess the effect of sampling frequency and load estimation method on load estimate error. Across the four different methods, the composite method had the lowest relative root mean square and absolute bias, but the rectangular interpolation method was the most precise. Furthermore, even with semiweekly sampling, the composite method resulted in an unacceptable level of precision (average imprecision = 39 %), while the interpolation method resulted in an unacceptable bias (average absolute bias = 16 %). Because neither method could provide acceptable accuracy and precision at the lowest decrease in sampling (e.t. semiweekly sampling), continued daily sampling is recommended in these watersheds.

54 ENVIRONMENTAL SCIENCES↗

An improved method for quantitatively measuring antifouling coating performance using a mussel single thread tensile adhesion test

Surface biofouling reduces the efficiency and lifespan of equipment across many industries. The development of high-performance antifouling surfaces, such as foul release coatings, benefits from test methods that can quickly identify superior antifouling surfaces in the laboratory during material development. Existing test methods poorly discriminate between different foul release coatings. Here is presented a method to assess the ability of surfaces to resist mussel adhesion using a quantitative, controlled single thread adhesion test (STAT) method, allowing for meaningful comparisons between low adhesion foul release surfaces. This method provides greater accuracy and finer resolution than push-based mussel shear adhesion methods without the difficulties associated with mussel size, thread attachment angle, or harming the mussels. The single thread tensile method is demonstrated on a variety of standard and high-performance coatings, and it is shown that the method detects differentiation between commercial foul release coatings that could not be resolved using other methods.

42 ENGINEERING↗

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗

Preliminary Study on the Suitability of a Second-Order Reconstructed Discontinuous Galerkin Method for RELAP-7 Thermal-Hydraulic Modeling

This document presents a preliminary study on the suitability of a second-order reconstructed discontinuous Galerkin (rDG) method for RELAP-7 thermal-hydraulic modeling. The document begins with a brief description of the governing equations for compressible, two-phase vapor and liquid flow, with a presentation of the seven-equation formulation details. A comparative study between the second-order rDG method and the RELAP-7's finite element method (FEM) with a entropy viscosity method (EVM) based numerical stabilization scheme (namely FEM-EVM) over a series of benchmark test problems is demonstrated. The intent for this suite of test problems is to provide baseline comparison data that demonstrate the performance of 1) the rDG solution and 2) the RELAP-7's FEM-EVM solution (with RELAP-7 code version dated August 15, 2017), on problems from single- to specific, limited two-phase flows. For all the test problems in this document, the rDG solutions were obtained with a second-order, two-step, explicit strong stability preserving Runge-Kutta time integration method. The computational results clearly indicate that the performance of the rDG method is superior to that of the RELAP-7's FEM-EVM method in all the test problems presented. Therefore, as far as the test problems in this document are considered, the second-order rDG method is recommended as an improved solution method option for RELAP-7.

97 MATHEMATICS AND COMPUTING↗

A Review of Existing Test Methods for Occupancy Sensors

One of the key new features of connected lighting systems (CLS) is their ability to collect data from various types of integral sensors and share that data with other lighting or building systems. Occupancy and vacancy sensors have been widely adopted as an energy-saving strategy in buildings, yet published test methods for reproducibly characterizing their performance remain few and limited in their sophistication. As a result, it has been difficult to predict the performance of such sensors in a specific application, and in practice, they frequently do not meet energy-savings expectations. Occupants at times remove or otherwise bypass occupancy sensors that hinder their work or otherwise do not perform as expected, thereby compromising the sensors’ potential to reduce energy consumption. Poor performance can result from multiple causes – ranging from fundamental limitations of the sensor technology, to misconfiguration, to poor placement in the room or space. Innovative occupancy sensors, some of them combining multiple sensing technologies (i.e., multimodal), have come on the market over the years, with claims of improved performance compared to their predecessors. However, in practice, their performance has neither differed enough from the performance of previous products to necessitate a test method that facilitated comparison between them, nor has it led to high deployment or high user satisfaction in human-occupied spaces with persistent presence. While the performance of both common and novel occupancy sensors has been the subject of many published research articles, the test methods that have been employed for them typically have been loosely described and have incorporated custom equipment or techniques that render them difficult to reproduce, or have been limited in their ability to fairly characterize devices that utilize varying sensor technology. The lack of a fully described, technology-agnostic test method that yields reproducible results across different implementations has been a barrier to the commercial success of new occupancy-sensor products, as users and specifiers who have been disappointed with previous products are often unwilling to take a chance with new ones. Motivated by a desire to fairly characterize new technologies that continue to enter the market and claim not only improved occupancy detection but, in some cases, additional capabilities (e.g., the ability to measure traffic or discern between different object types), this report presents the results of a literature review of recently published fully described test methods for characterizing occupancy-sensor performance, as well as research articles containing ad-hoc test methods. The review also identifies and consolidates test conditions for characterizing sensor performance in indoor spaces and identifies apparent test method gaps that need to be filled in order to evaluate emerging technologies and products. The identified test-method conditions are intended to enable the development of a future technology-agnostic test method that facilitates occupancy-sensor performance characterization more-accurately representing performance in buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Comparison of Two Load Prediction Methods for Strain-Gage Balances

Data from a five-component semi-span balance is used to perform a systematic comparison of the load prediction accuracy of two load prediction methods. Both methods independently obtain the load prediction equations from multivariate least squares fits of balance calibration data. The first method is called the Non-Iterative Method. This approach directly uses regression models of the individual load components of a balance for the load prediction. The second method is called the Iterative Method. This alternate approach uses a load iteration equation for the load prediction that is constructed from the regression coefficients of the gage outputs of the balance. Basic characteristics of the two methods are reviewed. Afterwards, both methods are applied to calibration, check load, and wind tunnel test data of a five-component semi-span balance. Selected analysis results are compared. These comparisons confirm that the accuracy of the two methods is the same for all practical purposes.

strain-gage balance↗

Impact of specimen preparation method on photovoltaic backsheet degradation during accelerated aging test

In this study, we highlight some important factors in the specimen preparation methods for evaluating photovoltaic backsheet properties after accelerated aging. Two different sequences are considered: Method (I) cut-then-age: cut into 1-cm wide strips and then expose to stress, and Method (II) age-then-cut: expose a larger sheet to stress and then cut into 1-cm widths for mechanical property measurements. We also compare the effect of three cutting methods, (a) tensile specimen punch, (b) paper cutter, and (c) fresh razor blade. Several commercial backsheets were evaluated, with stress exposures including (a) pressure cooker test (PCT), (b) dry ultraviolet (UV) radiation exposure, and (c) UV combined damp heat tests. Fourier transform infrared spectrometer (FTIR) and intrinsic viscosity (IV) were used to analyze the materials on unstressed materials and samples exposed to PCT. The results show that both the cutting method and the time of cutting have an impact on the backsheet mechanical properties. Additionally, under UV exposure, Method II, age-then-cut, generally resulted in a higher average value, with more variation than Method I; however, if the side strips from Method II were excluded, the variation dropped to the same level. This is because the specimens at the sides of the sheet get additional damage from UV light from the exposed sides of the sample. In contrast to UV exposure, PCT specimens prepared by Method II result in lower average values and higher variability. This is attributed to embrittlement through the bulk of the sample where the cutting of embrittled specimens appears to result in more edge defects which can then initiate a break at smaller strains. The data suggest that for UV exposures, the specimens should be cut after aging and the exposed side specimens discarded, and that for PCT exposures, the specimens should be cut before the exposure.

14 SOLAR ENERGY↗

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

58 GEOSCIENCES↗

Parallelized hybrid optimization methods for nonsmooth problems using NOMAD and linesearch

Two parallelized hybrid methods are presented for single-function optimization problems with side constraints. The optimization problems are difficult not only due to possible existence of local minima and nonsmoothness of functions, but also due to the fact that objective function and constraint values for a solution vector can only be obtained by querying a black box whose execution requires considerable computational effort. Examples are optimization problems in Engineering where objective function and constraint values are computed via complex simulation programs, and where local minima exist and smoothness of functions is not assured. The hybrid methods consist of the well-known method NOMAD and two new methods called DENCON and DENPAR that are based on the linesearch scheme CS-DFN. The hybrid methods compute for each query a set of solution vectors that are evaluated in parallel. The hybrid methods have been tested on a set of difficult optimization problems produced by a certain seeding scheme for multiobjective optimization. We compare computational results with solution by NOMAD, DENCON, and DENPAR as stand-alone methods. It turns out that among the stand-alone methods, NOMAD is significantly better than DENCON and DENPAR. However, the hybrid methods are definitely better than NOMAD.

97 MATHEMATICS AND COMPUTING↗

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction–diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction–diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth. - Highlights: • A hybrid method for stochastic multi-scale models of cells populations that extends existing hybrid methods for reaction–diffusion system. • Our analysis unveils non-trivial macroscopic effects triggered by noise at the level of structuring variables. • Our hybrid method hugely speeds up age-structured SSA simulations while preserving stochastic effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗