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Rolling, slip and traction measurements on low modulus materials

Traction and wear tests were performed on six low modulus materials (LMM). Three different traction tests were performed to determine the suitability of the material for use as traction rollers. These were the rolling, slip and endurance traction tests. For each material the combination LMM on LMM and LMM on steel were evaluated. Rolling traction test were conducted to determine the load - velocity limits, the rolling traction coefficient of the materials and to establish the type of failures that would result when loading beyond the limit. It was found that in general a simple constant rolling traction coefficient was enough to describe the results of all the test. The slip traction tests revealed that the peak traction coefficients were considerably higher than for lubricated traction contacts. The endurance traction tests were performed to establish the durability of the LMM under conditions of prolonged traction. Wear measurements were performed during and after the test. Energetic wear rates were determined from the wear measurements conducted in the endurance traction tests. These values show that the roller wear is not severe when reasonable levels of traction are transmitted.

Tevaarwerk, J. L.

Advanced Colloids Experiment (ACE) Science Overview

The Advanced Colloids Experiment is being conducted on the International Space Station (ISS) using the Light Microscopy Module (LMM) in the Fluids Integrated Rack (FIR). Work to date will be discussed and future plans and opportunities will be highlighted. The LMM is a microscope facility designed to allow scientists to process, manipulate, and characterize colloidal samples in micro-gravity where the absence of gravitational settling and particle jamming enables scientists to study such things as:a.The role that disordered and ordered-packing of spheres play in the phase diagram and equation of state of hard sphere systems,b.crystal nucleation and growth, growth instabilities, and the glass transition, c.gelation and phase separation of colloid polymer mixtures,d.crystallization of colloidal binary alloys,e.competition between crystallization and phase separation,f.effects of anisotropy and specific interactions on packing, aggregation, frustration and crystallization,g.effects of specific reversible and irreversible interactions mediated in the first case by hybridization of complementary DNA strands attached to separate colloidal particles,h.Lock and key interactions between colloids with dimples and spheres which match the size and shape of the dimples,i.finding the phase diagrams of isotropic and interacting particles,j.new techniques for complex self-assembly including scenarios for self-replication, k.critical Casimir forces,l.biology (real and model systems) in microgravity,m.etc. By adding additional microscopy capabilities to the existing LMM, NASA will increase the tools available for scientists that fly experiments on the ISS enabling scientists to observe directly what is happening at the particle level. Presently, theories are needed to bridge the gap between what is being observed (at a macroscopic level when photographing samples) with what is happening at a particle (or microscopic) level. What is happening at a microscopic level will be directly accessible with the availability of the Light Microscopy Module (LMM) on ISS. To meet these goals, the ACE experiment is being built-up in stages, with the availability of confocal microscopy being the ultimate objective. Supported by NASAs Physical Sciences Research Program, ESAESTEC, and the authors respective governments.

Microgravity Biology Research

The Light Microscopy Module A Facility Overview-History and Science

We will share a brief history and provide a science overview of the many accomplishments of the Light Microscopy Module (LMM), a microscope that has been operating in the microgravity environment of the International Space Station (ISS) since 2010. It will be removed in October 2021. It was initially outfitted for the Constrained Vapor Bubble – Wickless Heat Pipe experiment. It was later reconfigured and upgraded many times to support a broad portfolio of Physical science and Biological experiments including: Complex Fluids, Colloids, Macro-Molecular Biophysics, Protein Crystals, and Plant Biology. The LMM has enabled many significant studies and discoveries and has seen its fair share of pleasant surprises. These include recording order arising out of disorder, e.g., systems of colloids that were glasses on Earth crystallizing to form large defect-free crystals, nematic ordering of elliptical colloids, and colloidal-polymer systems crystallizing. The LMM science teams have also seen how to improve product stabilizers once the effects of sedimentation on Earth were removed; they were able to see which tagged genes express in plants when gravity is removed, telling them which genes are essential for growing plants in space; they’ve tested protein crystal growth models; checked models for creating bijel electrodes that turn batteries into fast-charging supercapacitors; tested many forms of colloidal self-assembly: including those using depletion attraction, magnetic fields, and critical Casimir forces; they’ve observed explosive bubble nucleation in a wickless heat pipe, and much more. This work has been supported by the NASA Biological and Physical Sciences (BPS) Division and the ISS Program Office, Johnson Space Center Code OZ and Code OB, the Center for the Advancement of Science in Space (CASIS) / ISS National Lab, EPSCoR, and ISS international partners from ESA – the Netherlands and Italy, CSA, JAXA and S. Korea, and by Space Act Agreements with Procter and Gamble (P&G).

Colloids

The Light Microscopy Module: An On-Orbit Multi-User Microscope Facility

The Light Microscopy Module (LMM) is planned as a remotely controllable on-orbit microscope subrack facility, allowing flexible scheduling and operation of fluids and biology experiments within the Fluids and Combustion Facility (FCF) Fluids Integrated Rack (FIR) on the International Space Station (ISS). The LMM will be the first integrated payload with the FIR to conduct four fluid physics experiments. A description of the LMM diagnostic capabilities, including video microscopy, interferometry, laser tweezers, confocal, and spectrophotometry, will be provided.

Motil, Susan M.

Microgravity Emissions Laboratory Testing of the Light Microscopy Module Control Box Fan

The Microgravity Emissions Laboratory (MEL) was developed at the NASA Glenn Research Center for the characterization, simulation, and verification of the International Space Station (ISS) microgravity environment. This Glenn lab was developed in support of the Fluids and Combustion Facility (FCF). The MEL is a six-degrees-of-freedom inertial measurement system that can characterize the inertial response forces (emissions) of components, subrack payloads, or rack-level payloads down to 10 7g. The inertial force output data generated from the steady-state or transient operations of the test article are used with finite element analysis, statistical energy analysis, and other analysis tools to predict the on-orbit environment at specific science or rack interface locations. Customers of the MEL have used benefits in isolation performance testing in defining available attenuation during the engineering hardware design phase of their experiment s development. The Light Microscopy Module (LMM) Control Box (LCB) fan was tested in the MEL in June and July of 2002. The LMM is planned as a remotely controllable on-orbit microscope subrack facility that will be accommodated in an FCF Fluids Integrated Rack on the ISS. The disturbances measured in the MEL test resulted from operation of the air-circulation fan within the LCB. The objectives of the testing were (1) to identify an isolator to be added to the LCB fan assembly to reduce fan-speed harmonics and (2) to identify the fan-disturbance forcing functions for use in rack-response analysis of the LMM and Fluids Integrated Rack facility. This report describes the MEL, the testing process, and the results from ground-based MEL LCB fan testing.

McNelis, Anne M.

Ultra-Thin, Triple-Bandgap GaInP/GaAs/GaInAs Monolithic Tandem Solar Cells

The performance of state-of-the-art, series-connected, lattice-matched (LM), triple-junction (TJ), III-V tandem solar cells could be improved substantially (10-12%) by replacing the Ge bottom subcell with a subcell having a bandgap of approx.1 eV. For the last several years, research has been conducted by a number of organizations to develop approx.1-eV, LM GaInAsN to provide such a subcell, but, so far, the approach has proven unsuccessful. Thus, the need for a high-performance, monolithically integrable, 1-eV subcell for TJ tandems has remained. In this paper, we present a new TJ tandem cell design that addresses the above-mentioned problem. Our approach involves inverted epitaxial growth to allow the monolithic integration of a lattice-mismatched (LMM) approx.1- eV GaInAs/GaInP double-heterostructure (DH) bottom subcell with LM GaAs (middle) and GaInP (top) upper subcells. A transparent GaInP compositionally graded layer facilitates the integration of the LM and LMM components. Handle-mounted, ultra-thin device fabrication is a natural consequence of the inverted-structure approach, which results in a number of advantages, including robustness, potential low cost, improved thermal management, incorporation of back-surface reflectors, and possible reclamation/reuse of the parent crystalline substrate for further cost reduction. Our initial work has concerned GaInP/GaAs/GaInAs tandem cells grown on GaAs substrates. In this case, the 1- eV GaInAs experiences 2.2% compressive LMM with respect to the substrate. Specially designed GaInP graded layers are used to produce 1-eV subcells with performance parameters nearly equaling those of LM devices with the same bandgap (e.g., LM, 1-eV GaInAsP grown on InP). Previously, we reported preliminary ultra-thin tandem devices (0.237 cm2) with NREL-confirmed efficiencies of 31.3% (global spectrum, one sun) (1), 29.7% (AM0 spectrum, one sun) (2), and 37.9% (low-AOD direct spectrum, 10.1 suns) (3), all at 25 C. Here, we include recent results of testing similar devices under the concentrated AMO spectrum, and also present the first demonstration of a high-efficiency, ultra-thin GaInP/GaAs/GaInAs tandem cell processed on a flexible kapton handle.

Wanlass, M. W.

Teal Cycle Ergometer Vibration Isolation and Stabilization System Human-in-the-Loop Ground Evaluation for Long-Duration Spaceflight

Purpose: To counter the deleterious effects of weightlessness on the cardiopulmonary system, astronauts living on the International Space Station exercise on a variety of countermeasure equipment including the Cycle Ergometer Vibration Isolation and Stabilization System (CEVIS). Operational since 2001, the onboard CEVIS will be replaced by a new model, known as Teal CEVIS (TC). As a part of ground evaluation, TC hardware underwent human-in-the-loop (HITL) testing to verify the TC hardware produces workloads that elicit physiologic responses comparable to a laboratory cycle ergometer (LAB). Methods: Seven subjects (5 M/2 F) performed submaximal cycle ergometer testing with indirect calorimetry measures on TC and LAB on separate test days. Testing consisted of graded 30 watt increases in workload until subjects reached 85% of age-predicted max heart rate (HR). Exercise outcomes included rate of oxygen uptake (VO2; liters/min), rate of energy expenditure (REE; kcal/min), and HR (beats/min). Linear mixed models (LMM) were fitted to compare VO2, REE, and HR responses between devices across power outputs with fixed effects for power (P) and device (D) and with random effects for subject. LMM effect coefficients (β), std errors (SE), pseudo-partial R2 of effects (pR2), and model likelihood ratio statistics (χ2, Pr(> chisq); α<.05) are provided. Results: LMM main effects for P and D were observed for VO2 (βp=.0107, SE = .0002, pR2=0.97; βd = -0.075, SE = 0.019, pR2=0.14; χ2(1)= 13.57, p<.001), such that VO2 was higher across stages on TC. Main effects of P and D were observed for REE (βp= .0586, SE = 0.001, pR2= 0.97; βd = -0.33208, SE = 0.099, pR2= 0.056; χ2(1)=10.481, p < .01), such that REE was higher across power outputs on TC. A P x D interaction was observed for HR, along with main effects for P and D (βp x d =-0.048, SE = 0.02, pR2=0.048; βp= 0.42, SE = 0.016, pR2=0.87; χ2(1) = 5.398, p = 0.02), such that higher workloads elicited a greater difference in HR between devices. Conclusions: HITL results show, TC elicits greater physiologic responses across power outputs compared to LAB. However, pR2 for device effects show small differences between devices. Therefore, TC can be expected to provide appropriate physiological stimulus across workloads and be considered a reliable tool to mitigate the effects of weightlessness.

Cycle Ergometer Vibration and Isolation System

Changes in Oculomotor Behavior and PVT Reaction Time During One Night of Sleep Deprivation

INTRODUCTION: The Psychomotor Vigilance Test (PVT) is a widely used objective measure of sustained attention, alertness, and fatigue. Previous studies consistently show that prolonged wakefulness and disrupted sleep patterns lead to increased lapses of attention and slower reaction times. These findings have critical implications for various professions, including healthcare, aviation, transportation safety, and spaceflight. In this study, we employed linear mixed models (LMM) to investigate hourly-measured 5-minute PVT reaction times during one night of total sleep deprivation. Our goal was to characterize the contribution of homeostatic sleep pressure (time awake) and circadian phase (salivary melatonin levels) on the dynamics of PVT reaction time. MATERIALS & METHODS: Data from twelve human participants were used in the analysis. Participants were healthy non-smokers, aged 18 and 40, with normal sleep habits defined as Pittsburg Sleep Quality Index scores < 5, and Morningness – Eveningness Questionnaire scores > 42 and < 58, respectively. Participants followed a constant-routine protocol and arrived at the NASA sleep laboratory approximately 1 to 2 hours after their habitual waking time. Tympanic temperature was measured every 30 min to provide a real-time estimate of circadian phase. Participants were required to stay awake throughout the laboratory experiment, which continued until their tympanic temperature had returned to baseline levels. This approach ensured that we could capture each participant's circadian trough and recovery, typically occurring between 24 and 26 hours after waking. The PVT and saliva melatonin were measured every hour, starting approximately from 3 hours after awakening. More information about the measurement protocol can be found in the publication by Stone et al. We used PVT reaction times between 100 and 10000 ms to calculate Reciprocal Reaction Times (RRTs). LMM models were employed to assess the contribution of time awake and saliva melatonin levels on changes in RRTs. Two models were created: the first model treated time awake as a fixed effect and the second model considered both the salivary melatonin level and time awake as fixed effects. Participants were included as a random effect in both models. We compared the models using an Analysis of Variance (ANOVA). The models were computed using the 'lmer' function from the 'lme4' package in R, and LMM p-values were determined using Satterthwaite's method. RESULTS: We found that time awake had a statistically significant effect on PVT RRTs during one night of sleep deprivation [χ2 = 2132.4, df = 1, p < 0.001]. In addition, the model including both saliva melatonin levels and time awake was statistically significantly better than one that uses just time awake [χ2 = 17.4, df = 1, p < 0.001]. DISCUSSION & CONCLUSION: As expected, these preliminary results suggest that the time awake and circadian phase each contribute to performance reductions as measured by the PVT. Future analyses will explore the contributions of other factors to the model.

sleep deprivation

An extension of A-stability to alternating direction implicit methods

An alternating direction implicit (ADI) scheme was constructed by the method of approximate factorization. An A-stable linear multistep method (LMM) was used to integrate a model two-dimensional hyperbolic-parabolic partial differential equation. Sufficient conditions for the A-stability of the LMM were determined by applying the theory of positive real functions to reduce the stability analysis of the partial differential equations to a simple algebraic test. A linear test equation for partial differential equations is defined and then used to analyze the stability of approximate factorization schemes. An ADI method for the three-dimensional heat equation is also presented.

Warming, R. F.

Physics of Hard Sphere Experiment: Scattering, Rheology and Microscopy Study of Colloidal Particles

The Physics of Hard Sphere Experiment has two incarnations: the first as a scattering and rheology experiment on STS-83 and STS-94 and the second as a microscopy experiment to be performed in the future on LMM on the space station. Here we describe some of the quantitative and qualitative results from previous flights on the dynamics of crystallization in microgravity and especially the observed interaction of growing crystallites in the coexistance regime. To clarify rheological measurements we also present ground based experiments on the low shear rate viscosity and diffusion coefficient of several hard sphere experiments at high volume fraction. We also show how these experiments will be performed with confocal microscopy and laser tweezers in our lab and as preparation for the phAse II experiments on LMM. One of the main aims of the microscopy study will be the control of colloidal samples using an array of applied fields with an eye toward colloidal architectures. Temperature gradients, electric field gradients, laser tweezers and a variety of switchable imposed surface patterns are used toward this control.

Z D Cheng

R and D work on the constrained vapor bubble system for a microgravity experiment

We are working with Project Scientists R. Balasubramanian and Sang Young Son, and a NASA Projects Team headed by Sue Motil at the Glenn Research Center on the design and development of an experimental system for use on the International Space Station during the year 2006. John Eustace is the coordinator for the flight experiment at Zin-Tech (previously Northrop-Grumman) for the design and development of the Constrained Vapor Bubble Heat Exchanger, CVBHX, cell which will fit into the Light Microscope Module, LMM. Good progress is being made. The CDR for the LMM being developed was held on December 10-1 1,2003. Experimental results obtained under microgravity conditions will be compared with those obtained at Rensselaer. Basic and applied research at Rensselaer continues on the experimental and theoretical details associated with passive phase change heat transfer processes controlled by interfacial forces in the CVBHX. The extensive results of our current research are presented in the 23 external publications listed below. Twenty-two external presentations have been given. Briefly, evaporation/condensation data from both vertical and horizontal CVBHX systems were obtained and analyzed for both polar (wetting) and apolar (partially wetting) fluids. The vertical system is axi-symmetric, but strongly effected by gravity. Whereas, the horizontal system is asymmetric, but weakly effected by gravity. Therefore, there will be significant differences in the operation of the cell in the earth s environment versus the operation under microgravity conditions. Due to its relative large size, the system s performance should be optimum under micro-gravity conditions, where the CVBHX should be a very effective passive heat exchanger. The CVBHX was found to be an ideal experimental setup in which to study the effects of interfacial phenomena on both the evaporation and drop-wise condensation processes. The optical technique (Image Analyzing Interferometry, IAI), which is based on the measurement and analysis of the reflectivity pattern of a thin film, was significantly improved. The accuracy of the IAI system is of critical importance to the success of the mission because it is used to measure the details of the pressure field in the liquid by measuring the film thickness profile. The accuracy was found to be excellent and various publications/presentations documenting these new results were written. Significant new results were also obtained for the effect of the oscillating contact line region on evaporation. Three doctoral students graduated under this grant. All three work in US industry, two for Intel. Another doctoral student is in his third year of study and will finish under an extension of the NASA grant: # NNC05GA27G.

Wayner, P. C., Jr.

Light Microscopy Module: On-Orbit Microscope Planned for the Fluids Integrated Rack on the International Space Station

The Light Microscopy Module (LMM) is planned as a remotely controllable, automated, on-orbit facility, allowing flexible scheduling and control of physical science and biological science experiments within the Fluids Integrated Rack (FIR) on the International Space Station. Initially four fluid physics experiments in the FIR will use the LMM the Constrained Vapor Bubble, the Physics of Hard Spheres Experiment-2, Physics of Colloids in Space-2, and Low Volume Fraction Entropically Driven Colloidal Assembly. The first experiment will investigate heat conductance in microgravity as a function of liquid volume and heat flow rate to determine, in detail, the transport process characteristics in a curved liquid film. The other three experiments will investigate various complementary aspects of the nucleation, growth, structure, and properties of colloidal crystals in microgravity and the effects of micromanipulation upon their properties.

Motil, Susan M.

High Temperature Protonic Conductors

High Temperature Protonic Conductors (HTPC) with the perovskite structure are envisioned for electrochemical membrane applications such as H2 separation, H2 sensors and fuel cells. Successive membrane commercialization is dependent upon addressing issues with H2 permeation rate and environmental stability with CO2 and H2O. HTPC membranes are conventionally fabricated by solid-state sintering. Grain boundaries and the presence of intergranular second phases reduce the proton mobility by orders of magnitude than the bulk crystalline grain. To enhanced protonic mobility, alternative processing routes were evaluated. A laser melt modulation (LMM) process was utilized to fabricate bulk samples, while pulsed laser deposition (PLD) was utilized to fabricate thin film membranes . Sr3Ca(1+x)Nb(2-x)O9 and SrCe(1-x)Y(x)O3 bulk samples were fabricated by LMM. Thin film BaCe(0.85)Y(0.15)O3 membranes were fabricated by PLD on porous substrates. Electron microscopy with chemical mapping was done to characterize the resultant microstructures. High temperature protonic conduction was measured by impedance spectroscopy in wet air or H2 environments. The results demonstrate the advantage of thin film membranes to thick membranes but also reveal the negative impact of defects or nanoscale domains on protonic conductivity.

Dynys, Fred

Light Microsopy Module, International Space Station Premier Automated Microscope

The Light Microscopy Module (LMM) was launched to the International Space Station (ISS) in 2009 and began science operations in 2010. It continues to support Physical and Biological scientific research on ISS. During 2015, if all goes as planned, five experiments will be completed: [1] Advanced Colloids Experiments with a manual sample base -3 (ACE-M-3), [2] the Advanced Colloids Experiment with a Heated Base -1 (ACE-H-1), [3] (ACE-H-2), [4] the Advanced Plant Experiment -03 (APEX-03), and [5] the Microchannel Diffusion Experiment (MDE). Preliminary results, along with an overview of present and future LMM capabilities will be presented; this includes details on the planned data imaging processing and storage system, along with the confocal upgrade to the core microscope. [1] New York University: Paul Chaikin, Andrew Hollingsworth, and Stefano Sacanna, [2] University of Pennsylvania: Arjun Yodh and Matthew Gratale, [3] a consortium of universities from the State of Kentucky working through the Experimental Program to Stimulate Competitive Research (EPSCoR): Stuart Williams, Gerold Willing, Hemali Rathnayake, et al., [4] from the University of Florida and CASIS: Anna-Lisa Paul and Rob Ferl, and [5] from the Methodist Hospital Research Institute from CASIS: Alessandro Grattoni and Giancarlo Canavese.

Microscopy

Light Microscopy Module: International Space Station Premier Automated Microscope

The Light Microscopy Module (LMM) was launched to the International Space Station (ISS) in 2009 and began hardware operations in 2010. It continues to support Physical and Biological scientific research on ISS. During 2016, if all goes as planned, three experiments will be completed: [1] Advanced Colloids Experiments with Heated base-2 (ACE-H2) and [2] Advanced Colloids Experiments with Temperature control (ACE-T1). Preliminary results, along with an overview of present and future LMM capabilities will be presented; this includes details on the planned data imaging processing and storage system, along with the confocal upgrade to the core microscope. [1] a consortium of universities from the State of Kentucky working through the Experimental Program to Stimulate Competitive Research (EPSCoR): Stuart Williams, Gerold Willing, Hemali Rathnayake, et al. and [2] from Chungnam National University, Daejeon, S. Korea: Chang-Soo Lee, et al.

Microgravity Biology Research

Interaction of atomic oxygen with thin film and bulk copper: An XPS, AES, XRD, and profilometer study

The University of Alabama in Huntsville (UAH) experiment A-0114 was designed primarily to study degradation of material surfaces due to low earth orbital (LEO) atmospheric oxygen. The experiment contained 128 one inch circular samples: metals, polymers, carbons, and semiconductors. Among metal samples, copper has shown some interesting new results. Two types of copper samples, a film sputter coated on fused silica and a bulk piece of OFHC copper, were characterized employing a variety of techniques such as X-ray and Auger electron spectroscopies, X-ray diffraction, and high resolution profilometry. Cu 2p core level spectra were used to characterize the presence of Cu2O and CuO in addition to Cu Auger LMM lines. These results are supported by our recent X-ray diffraction studies which clearly establish the presence of Cu oxides which we were unable to prove in our earlier work. Profilometry showed an increase in thickness of the film sample where exposed to 106.7 +/- 0.5 nm from an initial thickness of 74.2 +/- 1.1 nm. Further studies with SEM and ellipsometry are underway.

Raikar, Genesh N.

Global Asymptotic Behavior of Iterative Implicit Schemes

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

Yee, H. C.

Charge Sharing and Charge Loss in a Cadmium-Zinc-Telluride Fine-Pixel Detector Array

Because of its high atomic number, room temperature operation, low noise, and high spatial resolution a Cadmium-Zinc-Telluride (CZT) multi-pixel detector is ideal for hard x-ray astrophysical observation. As part of on-going research at MSFC (Marshall Space Flight Center) to develop multi-pixel CdZnTe detectors for this purpose, we have measured charge sharing and charge loss for a 4x4 (750micron pitch), lmm thick pixel array and modeled these results using a Monte-Carlo simulation. This model was then used to predict the amount of charge sharing for a much finer pixel array (with a 300micron pitch). Future work will enable us to compare the simulated results for the finer array to measured values.

Gaskin, J. A.