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Permanent Monitoring of the Reference Point of the 20m Radio Telescope Wettzell

To achieve the goals of the VLBI2010 project and the Global Geodetic Observing System (GGOS), an automated monitoring of the reference points of the various geodetic space techniques, including Very Long Baseline Interferometry (VLBI), is desirable. The resulting permanent monitoring of the local-tie vectors at co-location stations is essential to obtain the sub-millimeter level in the combinations. For this reason a monitoring system was installed at the Geodetic Observatory Wettzell by the Geodetic Institute of the University of Karlsruhe (GIK) to observe the 20m VLBI radio telescope from May to August 2009. A specially developed software from GIK collected data from automated total station measurements, meteorological sensors, and sensors in the telescope monument (e.g., Invar cable data). A real-time visualization directly offered a live view of the measurements during the regular observation operations. Additional scintillometer measurements allowed refraction corrections during the post-processing. This project is one of the first feasibility studies aimed at determining significant deformations of the VLBI antenna due to, for instance, changes in temperature.

Neidhardt, Alexander↗

Morphogenic Regulator-Mediated Transformation of Maize Inbred B73

Maize B73 is a reference genome and has long been a major resource for genetics and molecular biology research. We have developed an efficient B73 transformation protocol by enabling somatic embryogenesis through differential co-expression of maize morphogenic regulators BBM and WUS2. We describe a successful protocol that utilizes Agrobacterium tumefaciens strain AGL1 harboring binary vector PHP78891 that comprises a BBM and WUS2 expression cassette as well as a green fluorescent protein (GFP) reporter cassette. The PHP78891 vector also contains, within the T-DNA region, a CRE/lox recombination system flanking the CRE/BBM/WUS2 co-expression cassette driven by the desiccation inducible RAB17 promoter that allows removal of the BBM/WUS2 cassette. Introduction and co-expression of BBM and WUS2 induced direct somatic embryogenesis (SE) in non-regenerable maize B73 from immature embryo explants. Removal of the CRE/BBM/WUS2 cassette is essential to allow regeneration to fertile plants. The GFP expression cassette outside the lox excision sites is retained in the transgenic plant genome, allowing subsequent phenotypic analysis of calli and regenerated transgenic events. This transformation system enables a selectable marker-free transformation process by taking advantage of BBM/WUS2-induced SE as a developmental selection system.

59 BASIC BIOLOGICAL SCIENCES↗

Neutron irradiation-induced microstructure damage in ultra-high temperature ceramic TiC

Titanium carbide (TiC) is an ultra-high temperature ceramic with potential as a structural material candidate for advanced reactor concepts. However, the irradiation tolerance of TiC is not well understood. Here, we reveal the key irradiation damage microstructure degradation processes in TiC using mixed spectrum neutron irradiations at dose of ~2 displacements per atom (dpa) at temperatures of ~220, 620, and 1115 °C, combined with state-of-art microstructure characterization using transmission electron microscopy (TEM) and high-resolution TEM (HRTEM). The helium injection (~65 atomic parts per million) produced by neutron transmutation also occurred in the sample. TiC was observed to form irradiation-induced interstitial-type dislocation loops and He-stabilized cavities. At 220 and 620 °C, the analysis of the electron diffraction patterns, rel-rod imaging and HRTEM revealed that the dislocation loops were faulted Frank loops with Burgers vector b Frank = 1/3<111> lying on {111} planes. A detailed Burgers vector identification performed by the g.b technique revealed that the dislocation loops forming at 1115 °C were unfaulted, edge-type, with Burgers vectors b = a<100> and a/2<110> with corresponding {100} and {110} habit planes. Using continuum mechanics, we estimated the critical radius at which a faulted dislocation loop transitions to a perfect loop to be 9 nm. Further, no amorphization occurred in TiC under-investigated irradiation conditions while macroscopic swelling under point defect swelling regime was observed. He-stabilized cavities were detected at 1115 °C, but not at lower temperature irradiation. These observations indicate the onset of long-range vacancy migration in TiC occurs between 620 and 1115 °C.

36 MATERIALS SCIENCE↗

A microbenchmark characterization of the Emu chick

The Emu Chick is a prototype system designed around the concept of migratory memory-side processing. Rather than transferring large amounts of data across power-hungry, high-latency interconnects, the Emu Chick moves lightweight thread contexts to near-memory cores before the beginning of each memory read. The current prototype hardware uses FPGAs to implement cache-less “Gossamer” cores for computational work and rely on a typical stationary core (PowerPC) to run basic operating system functions and migrate threads between nodes. In this multi-node characterization of the Emu Chick, we extend an earlier single-node investigation of the the memory bandwidth characteristics of the system through benchmarks like STREAM, pointer chasing, and sparse matrix-vector multiplication. Here, we compare the Emu Chick hardware to architectural simulation and an Intel Xeon-based platform. Our results demonstrate that for many basic operations the Emu Chick can use available memory bandwidth more efficiently than a more traditional, cache-based architecture although bandwidth usage suffers for computationally intensive workloads like SpMV. Moreover, the Emu Chick provides stable, predictable performance with up to 65% of the peak bandwidth utilization on a random-access pointer chasing benchmark with weak locality.

97 MATHEMATICS AND COMPUTING↗

Motion coherence affects human perception and pursuit similarly

Pursuit and perception both require accurate information about the motion of objects. Recovering the motion of objects by integrating the motion of their components is a difficult visual task. Successful integration produces coherent global object motion, while a failure to integrate leaves the incoherent local motions of the components unlinked. We compared the ability of perception and pursuit to perform motion integration by measuring direction judgments and the concomitant eye-movement responses to line-figure parallelograms moving behind stationary rectangular apertures. The apertures were constructed such that only the line segments corresponding to the parallelogram's sides were visible; thus, recovering global motion required the integration of the local segment motion. We investigated several potential motion-integration rules by using stimuli with different object, vector-average, and line-segment terminator-motion directions. We used an oculometric decision rule to directly compare direction discrimination for pursuit and perception. For visible apertures, the percept was a coherent object, and both the pursuit and perceptual performance were close to the object-motion prediction. For invisible apertures, the percept was incoherently moving segments, and both the pursuit and perceptual performance were close to the terminator-motion prediction. Furthermore, both psychometric and oculometric direction thresholds were much higher for invisible apertures than for visible apertures. We constructed a model in which both perception and pursuit are driven by a shared motion-processing stage, with perception having an additional input from an independent static-processing stage. Model simulations were consistent with our perceptual and oculomotor data. Based on these results, we propose the use of pursuit as an objective and continuous measure of perceptual coherence. Our results support the view that pursuit and perception share a common motion-integration stage, perhaps within areas MT or MST.

NASA Center ARC↗

Machine-learning-enabled on-the-fly analysis of RHEED patterns during thin film deposition by molecular beam epitaxy

Thin film deposition is a fundamental technology for the discovery, optimization, and manufacturing of functional materials. Deposition by molecular beam epitaxy (MBE) typically employs reflection high-energy electron diffraction (RHEED) as a real-time in situ probe of the growing film. However, the state-of-the-art for RHEED analysis during deposition requires human observation. Here, we present an approach using machine learning (ML) methods to monitor, analyze, and interpret RHEED images on-the-fly during thin film deposition. In the analysis workflow, RHEED pattern images are collected at one frame per second and featurized using a pretrained deep convolutional neural network. The feature vectors are then statistically analyzed to identify changepoints; these changepoints can be related to changes in the deposition mode from initial film nucleation to a transition regime, smooth film deposition, and in some cases, an additional transition to a rough, islanded deposition regime. The feature vectors are additionally analyzed via graph analysis and community classification. The graph is quantified as a stabilization plot, and we show that inflection points in the stabilization plot correspond to changes in the growth regime. The full RHEED analysis workflow is termed RHAAPsody and includes data transfer and output to a visual dashboard. We demonstrate the functionality of RHAAPsody by analyzing the precaptured RHEED images from epitaxial depositions of anatase TiO2 on SrTiO3(001) and show that the analysis workflow can be executed in less than 1 s. Our approach shows promise as one component of ML-enabled real-time feedback control of the MBE deposition process.

36 MATERIALS SCIENCE↗

Physics-informed neural networks for identification of material properties using standing waves

A metallic structure in its initial stage of failure involves plastic deformation or environmental degradation that changes the elastic modulus and density. This work presents the detection of change in wave velocity (a function of elastic modulus and density) as a system identification problem. A physics-informed neural network (PINN) is proposed to solve the system identification problem. The PINN takes the spatial coordinates of scanning locations and time as inputs and provides the displacement and wave velocity as outputs. The governing partial differential equation of standing waves in a rod is incorporated into the neural network as physics in the form of a loss function. The wave velocity vector is randomly initiated. During the training of the network, physics is used to determine and update the wave velocity target vector from the network’s displacement predictions. The measured data, comprising sparse displacement response on the rod structure, are used to train the PINN. The wave velocity at the sparse locations on the rod is learned from the predicted displacements during the training. Using the predictions of the trained network, the response of free vibration or material property variation can be reconstructed at unscanned locations on the structure to obtain high-resolution maps for full-field imaging to detect and localize the changes caused by plastic deformation. The PINN’s sparse scanning and simultaneous prediction capability during training can lead to high scanning and data-processing speeds. This capability yields a nondestructive evaluation system that can predict the presence of degraded material locations as the structural vibrations are scanned and processed in real time.

Rathod, Vivek↗

Incorporation of star measurements for the determination of orbit and attitude parameters of a geosynchronous satellite: An iterative application of linear regression

Currently on NOAA/NESS's VIRGS system at the World Weather Building star images are being ingested on a daily basis. The image coordinates of the star locations are measured and stored. Subsequently, the information is used to determine the attitude, the misalignment angles between the spin axis and the principal axis of the satellite, and the precession rate and direction. This is done for both the 'East' and 'West' operational geosynchronous satellites. This orientation information is then combined with image measurements of earth based landmarks to determine the orbit of each satellite. The method for determining the orbit is simple. For each landmark measurement one determines a nominal position vector for the satellite by extending a ray from the landmark's position towards the satellite and intersecting the ray with a sphere with center coinciding with the Earth's center and with radius equal to the nominal height for a geosynchronous satellite. The apparent motion of the satellite around the Earth's center is then approximated with a Keplerian model. In turn the variations of the satellite's height, as a function of time found by using this model, are used to redetermine the successive satellite positions by again using the Earth based landmark measurements and intersecting rays from these landmarks with the newly determined spheres. This process is performed iteratively until convergence is achieved. Only three iterations are required.

Phillips, D.↗

Evidence for submergencew of magnetic flux in a growing active region

In NOAA Active Region 2372 (April 1980), 4 x 10 to the 20th power maxwell of magnetic flux concentrated within a 30" circular area disappeared overnight. Vector magnetograms show that all components of the magnetic field weakened together. If the field had weakened through diffusion or fluid flow, 80% of the original flux would still have been detected by the magnetograph within a suitably enlarged area. In fact there was at least a threefold decrease in detected flux. Evidently, magnetic field was removed from the photosphere. Since the disappearing flux was located in a region of low magnetic shear and low activity, it is unlikely that the field dissipated through reconnection. The most likely possibility is that flux submerged. Observations suggest that even in the growth phase of active regions, submergence is a strong process comparable in magnitude to emergence.

Rabin, D. M.↗

SAR image data compression for an on-line archive system

This paper summarizes the investigation of SAR image data compression for an on-line archive data distribution system. This system is planned for the ground processing system of Alaska SAR Facility (ASF) and Shuttle Imaging Radar (SIR-C). The objective of the SAR image data compression is to enable the data archive system to provide the remote users a large data base with good image quality, short response time, low transfer cost, and minimal decoding complexity. The requirements and limitations of the on-line archive data distribution system are presented. The effects of SAR image data characteristics on data compression are addressed. The users' survey results suggest that compression ratios between 10:1 and 20:1 appear suitable. Based on the algorithm evaluation results, the two-level tree-searched vector quantization technique has been recommended as the SAR image data compression algorithm for the on-line archive data distribution system.

Chang, C. Y.↗

Parallelization of the Physical-Space Statistical Analysis System (PSAS)

Atmospheric data assimilation is a method of combining observations with model forecasts to produce a more accurate description of the atmosphere than the observations or forecast alone can provide. Data assimilation plays an increasingly important role in the study of climate and atmospheric chemistry. The NASA Data Assimilation Office (DAO) has developed the Goddard Earth Observing System Data Assimilation System (GEOS DAS) to create assimilated datasets. The core computational components of the GEOS DAS include the GEOS General Circulation Model (GCM) and the Physical-space Statistical Analysis System (PSAS). The need for timely validation of scientific enhancements to the data assimilation system poses computational demands that are best met by distributed parallel software. PSAS is implemented in Fortran 90 using object-based design principles. The analysis portions of the code solve two equations. The first of these is the "innovation" equation, which is solved on the unstructured observation grid using a preconditioned conjugate gradient (CG) method. The "analysis" equation is a transformation from the observation grid back to a structured grid, and is solved by a direct matrix-vector multiplication. Use of a factored-operator formulation reduces the computational complexity of both the CG solver and the matrix-vector multiplication, rendering the matrix-vector multiplications as a successive product of operators on a vector. Sparsity is introduced to these operators by partitioning the observations using an icosahedral decomposition scheme. PSAS builds a large (approx. 128MB) run-time database of parameters used in the calculation of these operators. Implementing a message passing parallel computing paradigm into an existing yet developing computational system as complex as PSAS is nontrivial. One of the technical challenges is balancing the requirements for computational reproducibility with the need for high performance. The problem of computational reproducibility is well known in the parallel computing community. It is a requirement that the parallel code perform calculations in a fashion that will yield identical results on different configurations of processing elements on the same platform. In some cases this problem can be solved by sacrificing performance. Meeting this requirement and still achieving high performance is very difficult. Topics to be discussed include: current PSAS design and parallelization strategy; reproducibility issues; load balance vs. database memory demands, possible solutions to these problems.

Larson, J. W.↗

Co-Investigator Proposal for Enstrophy - - Filamentation of Auroral Currents

Cornell University provided three instruments for the Enstrophy experiment: an electric field meter, a plasma wave receiver, and a magnetometer for measuring FAC. The electric field meter consisted of a 6 m Weitzmann boom system with analog signal processing and 12 bit ADC, which yielded one electric field component instantaneously and a two dimensional electric field every half spin. The plasma wave receiver used the same sensing system with the addition of pre-amplifiers in the spheres to sense plasma waves up to and including the electron Langmuir frequency. Signal processing employed a variety of continuous and snap shot techniques depending on the frequency range and band width. The science magnetometer provided by Cornell University was a Billingsly design fluxgate previously used on spacecraft missions but without radiation hardening. The magnetometer was mounted on a one meter, stiff aluminum "flop-down" boom. The Enstrophy payload was launched on february 11, 1999. Because of a design flaw in the event timers, the magnetometer boom was deployed before the payload despun. As a result the magnetometer separated mechanically from the boom but maintained electrical connection. This was confirmed by the calculation of the scalar magnetic field from all three vector components of the magnetic field. However, the individual vector values had no scientific value. The electric field and plasma wave instrumentation worked as designed. The data from these instruments was provided to the University of New Hampshire and to the Principal Investigator, as proposed.

Kintner, Paul M.↗

Alignment between Filaments and Galaxy Spins from the MaNGA Integral-field Survey

Halos and galaxies acquire their angular momentum during the collapse of the surrounding large-scale structure. This process imprints alignments between galaxy spins and nearby filaments and sheets. Low-mass halos grow by accretion onto filaments, aligning their spins with the filaments, whereas high-mass halos grow by mergers along filaments, generating spins perpendicular to the filament. Here, we search for this alignment signal using filaments identified with the "Cosmic Web Reconstruction" algorithm applied to the Sloan Digital Sky Survey Main Galaxy Sample and galaxy spins from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) integral-field unit survey. MaNGA produces a map of the galaxy's rotational velocity, allowing direct measurement of the galaxy's spin direction, or unit angular momentum vector projected onto the sky. We find no evidence for alignment between galaxy spins and filament directions. We do find hints of a mass-dependent alignment signal, which is in 2σ–3σ tension with the mass-dependent alignment signal in the MassiveBlack-II and Illustris hydrodynamical simulations. However, the tension vanishes when galaxy spin is measured using the Hα emission line velocity rather than stellar velocity. Lastly, in simulations we find that the mass-dependent transition from aligned to anti-aligned dark matter halo spins is not necessarily present in stellar spins: we find a stellar spin transition in Illustris but not in MassiveBlack-II, highlighting the sensitivity of spin-filament alignments to feedback prescriptions and subgrid physics.

79 ASTRONOMY AND ASTROPHYSICS↗

Planar Doppler Velocimetry for Large-Scale Wind Tunnel Testing

Recently, Planar Doppler Velocimetry (PDV) has been shown by several laboratories to offer an attractive means for measuring three-dimensional velocity vectors everywhere in a light sheet placed in a flow. Unlike other optical means of measuring flow velocities, PDV is particularly attractive for use in large wind tunnels where distances to the sample region may be several meters, because it does not require the spatial resolution and tracking of individual scattering particles or the alignment of crossed beams at large distances. To date, demonstrations of PDV have been made either in low speed flows without quantitative comparison to other measurements, or in supersonic flows where the Doppler shift is large and its measurement is relatively insensitive to instrumental errors. Moreover, most reported applications have relied on the use of continuous-wave lasers, which limit the measurement to time-averaged velocity fields. This work summarizes the results of two previous studies of PDV in which the use of pulsed lasers to obtain instantaneous velocity vector fields is evaluated. The objective has been to quantitatively define and demonstrate PDV capabilities for applications in large-scale wind tunnels that are intended primarily for the production testing of subsonic aircraft. For such applications, the adequate resolution of low-speed flow fields requires accurate measurements of small Doppler shifts that are obtained at distances of several meters from the sample region. The use of pulsed lasers provides the unique capability to obtain not only time-averaged fields, but also their statistical fluctuation amplitudes and the spatial excursions of unsteady flow regions such as wakes and separations. To accomplish the objectives indicated, the PDV measurement process is first modeled and its performance evaluated computationally. The noise sources considered include those related to the optical and electronic properties of Charge-Coupled Device (CCD) arrays and to speckle effects associated with coherent illumination from pulsed lasers. The signal noise estimates are incorporated into the PDV signal analysis process and combined with computed scattering signals using a Mie scattering theory for polydisperse smoke particles. The relevant parameters incorporate a range of practical aerodynamic test conditions and facility sizes. The results define the optimum instrument configurations, show that the expected signal levels from a practical PDV system are sufficiently large to allow its useful application in large facilities, and show that the expected velocity measurement uncertainties are small compared to the mean velocities of interest for most subsonic, large-scale wind tunnel testing. Experimental studies using several experimental bench-top setups are then described that validate the physics of the PDV model and to calibrate its computed results. The validated model allows estimates of the uncertainties of PDV measurements and a complete definition of the PDV capabilities to be made with sufficient confidence to decide the viability of PDV for large-scale wind tunnel applications.

McKenzie, Robert L.↗

Guaranteeing Pointing Performance of the SDO Sun-Pointing Controllers in Light of Nonlinear Effects

The Solar Dynamics Observatory (SDO) mission is the first Space Weather Research Network mission, part of NASA s Living With a Star program.1 This program seeks to understand the changing Sun and its effects on the Solar System, life, and society. To this end, the SDO spacecraft will carry three Sun-observing instruments to geosynchronous orbit: Helioseismic and Magnetic Imager (HMI), led by Stanford University; Atmospheric Imaging Assembly (AIA), led by Lockheed Martin Space and Astrophysics Laboratory; and Extreme Ultraviolet Variability Experiment (EVE), led by the University of Colorado. Links describing the instruments in detail may be found through the SDO web site.2 The basic mission goals are to observe the Sun for a very high percentage of the 5-year mission (10-year goal) with long stretches of uninterrupted observations and with constant, high-data-rate transmission to a dedicated ground station. These goals guided the design of the spacecraft bus that will carry and service the three-instrument payload. At the time of this publication, the SDO spacecraft bus is well into the integration and testing phase at the NASA Goddard Space Flight Center (GSFC). A three-axis stabilized attitude control system (ACS) is needed both to point at the Sun accurately and to keep the roll about the Sun vector correctly positioned. The ACS has four reaction wheel modes and 2 thruster actuated modes. More details about the ACS in general and the control modes in particular can be found in Refs. [3-6]. All four of SDO s wheel-actuated control modes involve Sun-pointing controllers, as might be expected from such a mission. Science mode, during which most science data is collected, uses specialized guide telescopes to point accurately at the Sun. Inertial mode has two sub-modes, one tracks a Sun-referenced target orientation, and another maintains an absolute (star-referenced) target orientation, that both employ a Kalman filter to process data from a digital Sun sensor and two star trackers. However, this paper is concerned only with the other two modes: Safe Hold (SH) and Sun Acquisition (SA).

Starin, Scott R.↗

Accelerating high-order continuum kinetic plasma simulations using multiple GPUs

Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in configuration space. The immense computational cost of evolving high-dimensional variables, and their large number of degrees of freedom, often limits the utility of continuum kinetic simulations and presents a challenge when it comes to accurately simulating real-world physical phenomena. To address this challenge, we present techniques that accelerate and minimize the computational work required for a scalable Vlasov-Poisson solver. We show theoretical hardware compute and communication bounds for solving a fourth-order finite-volume Vlasov-Poisson system. These bounds are then used to inform and evaluate the design of performance portable algorithms for a multiple graphics processing unit (GPU) accelerated version of the Vlasov-Poisson solver VCK-CPU [1]. We demonstrate that the multi-GPU Vlasov solver implementation, VCK-GPU, simultaneously minimizes required inter-process data transfer while also being bounded by the machine network performance limits. This results in an overall strong scaling speedup per timestep of up to 40x in three-dimensional phase space (one position, two velocity coordinates) and 54x in four dimensional phase space (two position, two velocity coordinates) and a 341x increase in simulation throughput of the GPU accelerated code over the existing CPU code. The GPU code is also able to weak scale up to 256 compute nodes and 1024 GPUs. In conclusion, we demonstrate that the improved compute performance enables exploring configurations which were previously computationally infeasible, including resolving fine-scale distribution function filamentation and multi-species dynamics with realistic electron-proton mass ratios.

Continuum kinetics↗

First Principles Nonadiabatic Excited-State Molecular Dynamics in NWChem

Computational simulation of non-adiabatic molecular dynamics is an indispensable tool for understanding complex photoinduced processes such as internal conversion, energy transfer, charge separation, and spatial localization of excitons, to name a few. Here, we report an implementation of the fewest-switches surface hopping algorithm in the NWChem computational chemistry program. Here the surface hopping method is combined with linear-response time-dependent density functional theory calculations of adiabatic excited state potential energy surfaces. To treat quantum transitions between arbitrary electronic Born{Oppenheimer states, we have implemented both numerical and analytical differentiation schemes for derivative non-adiabatic couplings. A numerical approach for the time-derivative non-adiabatic couplings together with an analytical method for calculating non-adiabatic coupling vectors is an efficient combination for surface hopping approaches. Additionally, electronic decoherence schemes and a state reassigned unavoided crossings algorithm are also implemented to improve the accuracy of the simulated dynamics and to handle trivial unavoided crossings. We apply our code to study the ultrafast decay of photoexcited benzene, including a detailed analysis of the potential energy surface, population decay time scales, and vibrational coordinates coupled to the excitation dynamics. The development presented in this work is a baseline for future implementations of more sophisticated frameworks for simulating of non-adiabatic molecular dynamics in NWChem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimizing the hit finding algorithm for liquid argon TPC neutrino detectors using parallel architectures

Neutrinos are particles that interact rarely, so identifying them requires large detectors which produce lots of data. Processing this data with the computing power available is becoming even more difficult as the detectors increase in size to reach their physics goals. Liquid argon time projection chamber (LArTPC) neutrino experiments are expected to grow in the next decade to have 100 times more wires than in currently operating experiments, and modernization of LArTPC reconstruction code, including parallelization both at data- and instruction-level, will help to mitigate this challenge. The LArTPC hit finding algorithm is used across multiple experiments through a common software framework. In this paper we discuss a parallel implementation of this algorithm. Using a standalone setup we find speedup factors of two times from vectorization and 30–100 times from multi-threading on Intel architectures. The new version has been incorporated back into the framework so that it can be used by experiments. On a serial execution, the integrated version is about 10 times faster than the previous one and, once parallelization is enabled, more speedups comparable to the standalone program are achieved.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗