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At least 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

An analytical approach to evaluation of space radiation effects on materials for long-life missions

An analytical model was developed which quantifies effects on organic composite matrix materials of high energy electrons and of UV as well as interactions between the two radiations. Literature data on polyethylene were used to construct a degradation kinetics scheme corresponding to an Earth orbit at L=3. Analysis of the model showed that steady state concentrations of radicals put limits on accelerated test conditions. These conclusions were validated by an experimental study on polymethylmethacrylate using UV laser excitation. Relationships for balancing electron and UV radiations to equal acceleration factors are derived. Pulse radiolysis using an electron-beam along with time-resolved spectroscopy is shown to be able to separate primary form secondary reactions. Implications of these reactions to changes in engineering material properties are indicated. The use of mechanistic studies is discussed in the context of general test strategies for evaluating materials for space applications.

Moacanin, J.↗
NASA NTRS1996

Performance Evaluation in Network-Based Parallel Computing

Network-based parallel computing is emerging as a cost-effective alternative for solving many problems which require use of supercomputers or massively parallel computers. The primary objective of this project has been to conduct experimental research on performance evaluation for clustered parallel computing. First, a testbed was established by augmenting our existing SUNSPARCs' network with PVM (Parallel Virtual Machine) which is a software system for linking clusters of machines. Second, a set of three basic applications were selected. The applications consist of a parallel search, a parallel sort, a parallel matrix multiplication. These application programs were implemented in C programming language under PVM. Third, we conducted performance evaluation under various configurations and problem sizes. Alternative parallel computing models and workload allocations for application programs were explored. The performance metric was limited to elapsed time or response time which in the context of parallel computing can be expressed in terms of speedup. The results reveal that the overhead of communication latency between processes in many cases is the restricting factor to performance. That is, coarse-grain parallelism which requires less frequent communication between processes will result in higher performance in network-based computing. Finally, we are in the final stages of installing an Asynchronous Transfer Mode (ATM) switch and four ATM interfaces (each 155 Mbps) which will allow us to extend our study to newer applications, performance metrics, and configurations.

Dezhgosha, Kamyar↗
NASA NTRS2005

Effects of Control Mode and R-Ratio on the Fatigue Behavior of a Metal Matrix Composite

Composite Because of their high specific stiffness and strength at elevated temperatures, continuously reinforced metal matrix composites (MMC's) are under consideration for a future generation of aeropropulsion systems. Since components in aeropropulsion systems experience substantial cyclic thermal and mechanical loads, the fatigue behavior of MMC's is of great interest. Almost without exception, previous investigations of the fatigue behavior of MMC's have been conducted in a tension-tension, load-controlled mode. This has been due to the fact that available material is typically less than 2.5-mm thick and, therefore, unable to withstand high compressive loads without buckling. Since one possible use of MMC's is in aircraft skins, this type of testing mode may be appropriate. However, unlike aircraft skins, most engine components are thick. In addition, the transient thermal gradients experienced in an aircraft engine will impose tension-compression loading on engine components, requiring designers to understand how the MMC will behave under fully reversed loading conditions. The increased thickness of the MMC may also affect the fatigue life. Traditionally, low-cycle fatigue (LCF) tests on MMC's have been performed in load control. For monolithic alloys, low-cycle fatigue tests are more typically performed in strain control. Two reasons justify this choice: (1) the critical volume from which cracks initiate and grow is generally small and elastically constrained by the larger surrounding volume of material, and (2) load-controlled, low-cycle fatigue tests of monolithics invariably lead to unconstrained ratcheting and localized necking--an undesired material response because the failure mechanism is far more severe than, and unrelated to, the fatigue mechanism being studied. It is unknown if this is the proper approach to composite testing. However, there is a lack of strain-controlled data on which to base any decisions. Consequently, this study addresses the isothermal, LCF behavior of a [0]_32 MMC tested under strain- and load-controlled conditions for both zero-tension and tension-compression loading conditions. These tests were run at 427 C on thick specimens of SiC-reinforced Ti-15-3. For the fully-reversed tests, no difference was observed in the lives between the load- and strain-controlled tests. However, for the zero-tension tests, the strain-controlled tests had longer lives by a factor of 3 in comparison to the load-controlled tests. This was due to the fact that under strain-control the specimens cyclically softened, reducing the cracking potential. In contrast, the load-controlled tests ratcheted toward larger tensile strains leading to an eventual overload of the fibers. Fatigue tests revealed that specimens tested under fully-reversed conditions had lives approximately an order of magnitude longer than for those specimens tested under zero tension. When examined on a strain-range basis, the fully reversed specimens had similar, but still shorter lives than those of the unreinforced matrix material. However, the composite had a strain limitation at short lives because of the limited strain capacity of the brittle ceramic fiber. The composite also suffered at very high lives because of the lack of an apparent fatigue limit in comparison to the unreinforced matrix. The value of adding fibers to the matrix is apparent when the fatigue lives are plotted as a function of stress range. Here, the composite is far superior to the unreinforced matrix because of the additional load-carrying capacity of the fibers.

Source record↗
DOE OSTI2018

Complex Electric Modulus Spectroscopy of (MnFe{sub 2}O{sub 4}){sub x}/CuTl-1223 Nanoparticles-Superconductor Composites

Manganese ferrite (MnFe{sub 2}O{sub 4}) nanoparticles and Cu{sub 0.5}Tl{sub 0}.{sub 5}Ba{sub 2}Ca{sub 2}Cu{sub 3}O{sub 10−δ}(CuTl-1223) superconducting phase were synthesized by sol-gel and solid-state reaction methods, respectively. Different contents of MnFe{sub 2}O{sub 4} nanoparticles were added in CuTl-1223 superconducting matrix to get (MnFe{sub 2}O{sub 4}){sub x}/CuTl-1223; x = 0∼2.0 wt% nanoparticles-superconductor composites. Complex electric modulus spectroscopy measurements of (MnFe{sub 2}O{sub 4}){sub x}/CuTl-1223 composites were carried out at different test frequencies from 20 Hz to 10 MHz and at different operating temperatures from 78 to 253 K to analyze and interpret the dynamical aspects of electrical transport phenomena (i.e., such as carrier hopping rate, conductivity, and blocking factor). The complex electric modulus spectra showed the effects of both grains and grain-boundaries on electrical properties. The capacitance of grain-boundaries was found higher than that of grains. The capacitive behavior of grains was increased and that of grain-boundaries was decreased with increasing operating temperature for all these samples. Blocking factor of these composites was increased with increasing contents of MnFe{sub 2}O{sub 4} nanoparticles. Shifting of peaks in imaginary part of modulus spectra towards lower frequency with increasing contents of these nanoparticles showed non-Debye type relaxation phenomenon in the material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Λ c → Λ l + ν l Form Factors and Decay Rates from Lattice QCD with Physical Quark Masses

The first lattice QCD calculation of the form factors governing $Λ_c→Λℓ+ν_ℓ$ decays is reported. The calculation was performed with two different lattice spacings and includes one ensemble with a pion mass of 139(2) MeV. The resulting predictions for the $Λ_c→Λe+ν_e$ and $Λc→Λμ+ν_μ$ decay rates divided by $|V_{cs}|$2 are 0.2007(71)(74) and $0.1945(69)(72)ps^{-1}$, respectively, where the two uncertainties are statistical and systematic. Taking the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cs}|$ from a global fit and the $Λ_c$ lifetime from experiments, this translates to branching fractions of $\mathscr{B} (Λ_c→Λe+ν_e)=0.0380(19)_{LQCD}(11)_{τ_{Λ_c}}$ and $\mathscr{B}(Λc→Λμ+ν_μ)=0.0369(19)_{LQCD}(11)_{τ_{Λ_c}}$. These results are consistent with, and two times more precise than, the measurements performed recently by the BESIII Collaboration. Using instead the measured branching fractions together with the lattice calculation to determine the CKM matrix element gives $|V_{cs}|=0.949(24)_{LQCD}(14)_{τ_{Λ_c}}(49)_{\mathscr{B}}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

spdlayers

Symmetric Positive Definite (SPD) enforcement layers for PyTorch. Regardless of the input, the output of these layers will always be a SPD tensor! The `Cholesky` layer uses a cholesky factorization to enforce SPD, and the `Eigen` layer uses an eigendecomposition to enforce SPD. Both layers take in some tensor of shape `[batch_size, input_shape]` and output a SPD tensor of shape`[batch_size, output_shape, output_shape]`. The relationship between input and output is defined by the following. ```python input_shape = sum([i for i in range(output_shape + 1)]) ``` The layers have no learnable parameters, and merely serve to transform a vector space to a SPD matrix space.

Jekel, CharlesF.↗
DOE OSTI2024

Exploring the fragmentation efficiency of proteins analyzed by MALDI-TOF-TOF tandem mass spectrometry using computational and statistical analyses

Matrix-assisted laser desorption/ionization time-of-flight-time-of-flight (MALDI-TOF-TOF) tandem mass spectrometry (MS/MS) is a rapid technique for identifying intact proteins from unfractionated mixtures by top-down proteomic analysis. MS/MS allows isolation of specific intact protein ions prior to fragmentation, allowing fragment ion attribution to a specific precursor ion. However, the fragmentation efficiency of mature, intact protein ions by MS/MS post-source decay (PSD) varies widely, and the biochemical and structural factors of the protein that contribute to it are poorly understood. With the advent of protein structure prediction algorithms such as Alphafold2, we have wider access to protein structures for which no crystal structure exists. In this work, we use a statistical approach to explore the properties of bacterial proteins that can affect their gas phase dissociation via PSD. We extract various protein properties from Alphafold2 predictions and analyze their effect on fragmentation efficiency. Our results show that the fragmentation efficiency from cleavage of the polypeptide backbone on the C-terminal side of glutamic acid (E) and asparagine (N) residues were nearly equal. In addition, we found that the rearrangement and cleavage on the C-terminal side of aspartic acid (D) residues that result from the aspartic acid effect (AAE) were higher than for E- and N-residues. From residue interaction network analysis, we identified several local centrality measures and discussed their implications regarding the AAE. We also confirmed the selective cleavage of the backbone at D-proline bonds in proteins and further extend it to N-proline bonds. Finally, we note an enhancement of the AAE mechanism when the residue on the C-terminal side of D-, E- and N-residues is glycine. To the best of our knowledge, this is the first report of this phenomenon. Our study demonstrates the value of using statistical analyses of protein sequences and their predicted structures to better understand the fragmentation of the intact protein ions in the gas phase.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1984

The characterization of Mode I delamination failure in non-woven, multidirectional laminates

The uniform double cantilever beam test and SEM are presently used for the characterization of Mode I delamination behavior in fiber-reinforced epoxy laminates. Delamination failure assumes forms that depend on ply orientation, test specimen geometry, and matrix toughness, but the calculated fracture energy is noted to be heavily dependent on fracture surface morphology. A material property concept that is independent of both test specimen geometry and the orientation of the plies constituting the delaminating interface is elucidated, through the definition of interlaminar fracture solely in terms of an interlaminar separation that includes no fiber breakage or pull-out. This value, which dissipates the lowest possible amount of energy during crack growth, is the controlling factor for laminate toughness.

Chai, H.↗
NASA NTRS2001

Notch Sensitivity of Woven Ceramic Matrix Composites Under Tensile Loading: An Experimental, Analytical, and Finite Element Study

The stress concentrations associated with circular notches and subjected to uniform tensile loading in woven ceramic matrix composites (CMCs) have been investigated for high-efficient turbine engine applications. The CMC's were composed of Nicalon silicon carbide woven fabric in SiNC matrix manufactured through polymer impregnation process (PIP). Several combinations of hole diameter/plate width ratios and ply orientations were considered in this study. In the first part, the stress concentrations were calculated measuring strain distributions surrounding the hole using strain gages at different locations of the specimens during the initial portion of the stress-strain curve before any microdamage developed. The stress concentration was also calculated analytically using Lekhnitskii's solution for orthotropic plates. A finite-width correction factor for anisotropic and orthotropic composite plate was considered. The stress distributions surrounding the circular hole of a CMC's plate were further studied using finite element analysis. Both solid and shell elements were considered. The experimental results were compared with both the analytical and finite element solutions. Extensive optical and scanning electron microscopic examinations were carried out for identifying the fracture behavior and failure mechanisms of both the notched and notched specimens. The stress concentration factors (SCF) determined by analytical method overpredicted the experimental results. But the numerical solution underpredicted the experimental SCF. Stress concentration factors are shown to increase with enlarged hole size and the effects of ply orientations on stress concentration factors are observed to be negligible. In all the cases, the crack initiated at the notch edge and propagated along the width towards the edge of the specimens.

Haque, A.↗
DOE OSTI2017

Temperature compensated transfer function for probability of detection (POD) in high temperature ultrasonic NDE using low temperature signals - 249

Ultrasonic piezoelectric based transducers offer the potential for in-coolant NDT measurements and imaging required at high temperature for the safe operation of advanced small modular reactors (SMRs). Current work estimates a significant 97% reduction in the probability of detection (POD) for an artificial flaw size of 2{lambda} due to degradation of the transducer performance at elevated temperature. The source of variability for POD in the current work is the temperature dependence of material matrix of piezoelectric material PZT-5A used in the sensor. The physics based model developed using finite element method quantifies reduction in the scattering amplitude for the side drilled hole (SDH) from 15 C to 195 C. Using model assisted probability of detection (MAPOD) approach, sensor temperature effect on the POD is demonstrated for SDHs in the low carbon steel specimen. Scattering amplitudes for the room temperature simulated data is validated with the experimental data. A temperature correction factor and transfer factors are reported to transform the simulated temperature effect from physics based model to the experimental data for estimation of high temperature POD using low temperature ultrasonic measurements. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2019

Interlayer correlated fractional quantum Hall state in the ν = 4 / 5 bilayer system

We perform exact diagonalization studies for fractional quantum Hall states at filling factor 4/5 in a bilayer system, on a torus with various aspect ratios and angles. In this work we find that in the absence of tunneling, two weakly coupled 2/5 layers undergo a phase transition into an interlayer-correlated regime, which is also Abelian with the fivefold degeneracy on the torus. In the limit of zero layer separation, this phase becomes a singlet in the pseudospin variable describing the layer degree of freedom. By studying the Chern-number matrix, we show that the K matrix describing the interlayer-correlated regime requires a matrix dimension larger than two and this regime is in particular not described by a Halperin state. A detailed analysis of possible 4 × 4 K matrices having the requisite symmetries and quantum numbers shows that there is only one equivalence class of such matrices. A model wave function representing this universality class is constructed. The role of separate particle number conservation in both layers is discussed, and it is argued that this additional symmetry allows for the further distinction of two different symmetry-protected Abelian phases in the interlayer correlated regime. Interlayer tunneling breaks this symmetry and can drive the system into a single-layer regime when strong enough. A qualitative phase diagram in the tunneling-layer separation parameter space is proposed based on our numerical results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Towards maintaining canine training aid integrity: Effects of environmental factors and operational use on the triacetone triperoxide polymer odor capture‐and‐release system

Abstract There are many factors that may affect the longevity of or guide the use of canine training aids. Literature to date has mainly focused on identifying the headspace volatiles associated with training aids or odors and only minimal research exists into how different variables may alter those volatiles. The current study examines several factors affecting canine training aids: humidity, air flow, transportation, and operational deployment, using the triacetone triperoxide polymer odor capture‐and‐release canine training aid (TATP POCR) as the target. The TATP POCR is an absorption‐based canine training aid developed to be used to safely train canines to detect the odor of the explosive TATP in operational settings. Comparisons of the TATP POCR to neat TATP are made throughout the manuscript. First, humidity increased the background components of the POCR matrix, as well as the amount of TATP recovered was above the POCR. Humidity thus affected the amount of TATP detected but did not prevent detection. Second, air flow lessened the lifetime of the TATP POCR. Third, the practice of using primary and secondary containment successfully prevented contamination, cross‐contamination, and significant target loss, thereby maintaining kit integrity. Finally, the absorption of background odors from training environments was not observed. TATP headspace concentrations between a Deployed and Control POCR kit were not significantly different at time 0 (i.e., upon opening), which suggests that the operational use does not affect the function of the TATP POCR system. This information provides pivotal evidence for explosives detection canine handlers or trainers who utilize the TATP POCR.

Legal Medicine↗
NASA NTRS1977

Implicit approximate-factorization schemes for the efficient solution of steady transonic flow problems

Implicit approximate-factorization algorithms (AF) are developed for the solution of steady-state transonic flow problems. The performance of the AF solution method is evaluated relative to that of the standard solution method for transonic flow problems, successive line over-relaxation (SLOR). Both methods are applied to the solution of the nonlinear, two-dimensional transonic small-disturbance equation. Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for a transonic flow field. This increase in computational efficiency is achieved with no appreciable increase in computer storage or coding complexity.

Ballhaus, W. F.↗
NASA NTRS2006

BLIMPK/Streamline Surface Catalytic Heating Predictions on the Space Shuttle Orbiter

This paper describes the results of an analysis of localized catalytic heating effects to the U.S. Space Shuttle Orbiter Thermal Protection System (TPS). The analysis applies to the High-temperature Reusable Surface Insulation (HRSI) on the lower fuselage and wing acreage, as well as the critical Reinforced Carbon-Carbon on the nose cap, chin panel and the wing leading edge. The object of the analysis was to use a modified two-layer approach to predict the catalytic heating effects on the Orbiter windward HRSI tile acreage, nose cap, and wing leading edge assuming localized highly catalytic or fully catalytic surfaces. The method incorporated the Boundary Layer Integral Matrix Procedure Kinetic (BLIMPK) code with streamline inputs from viscous Navier-Stokes solutions to produce heating rates for localized fully catalytic and highly catalytic surfaces as well as for nominal partially catalytic surfaces (either Reinforced Carbon-Carbon or Reaction Cured Glass) with temperature-dependent recombination coefficients. The highly catalytic heating results showed very good correlation with Orbiter Experiments STS-2, -3, and -5 centerline and STS-5 wing flight data for the HRSI tiles. Recommended catalytic heating factors were generated for use in future Shuttle missions in the event of quick-time analysis of damaged or repaired TPS areas during atmospheric reentry. The catalytic factors are presented along the streamlines as well as a function of stagnation enthalpy so they can be used for arbitrary trajectories.

Marichalar, Jeremiah J.↗
DOE OSTI2018

ZKSCAN3 promotes breast cancer cell proliferation, migration and invasion

Highlights: • ZKSCAN3 is upregulated in breast cancer tissue and cell lines. • Knocking down ZKSCAN3 suppresses breast cancer cell proliferation, enhances cell apoptosis and blocks cell cycle. • Knocking down ZKSCAN3 significantly inhibits breast cancer cell migration and invasion. • Knocking down ZKSCAN3 significantly inhibits breast tumor growth in vivo. • Knocking down ZKSCAN3 reduces activity of the Akt/mTOR pathway. ZKSCAN3, a zinc-finger transcription factor, which has been shown to be upregulated in several human cancer. However, the expression level, function and mechanism of ZKSCAN3 in breast cancer remains unknown. In the current study, immunohistochemistry, western blot and quantitative real time polymerase chain reaction (qRT-PCR) results showed that ZKSCAN3 was overexpressed in breast cancer tissue compared with normal breast tissue. Through analyzing the clinicopathological characteristics, we demonstrated that positive ZKSCAN3 expression predicted poor prognosis of patients with breast cancer. The expression level of ZKSCAN3 protein/mRNA in breast cancer cells (MCF-7 and MDA-MB-231) was higher than its expression in normal breast cells (HBL-100). Knocking down ZKSCAN3 via its short hairpin RNA (shRNA) in MCF-7 and MDA-MB-231 inhibited cell viability, migration and invasion. Western blot analysis showed that ZKSCAN3 silencing lead to significant decreases in the expression of Cyclin D1, B-cell lymphoma-2 (Bcl-2), and matrix metalloproteinase (MMP)-2/MMP-9, as well as increases in the expression of Bcl2 Associated X Protein (Bax) in breast cancer cells. Additionally, ZKSCAN3-shRNA expression markedly suppressed tumor growth in breast cancer xenograft mice. Finally, we demonstrated that silencing of ZKSCAN3 was able to inhibit Akt/mTOR signaling pathway by blocking p-Akt and p-mTOR protein expression in breast cancer cells. These results demonstrate that ZKSCAN3 plays a significant role in the progression of breast cancer. Therefore, ZKSCAN3 is a potential therapeutic target for breast cancer.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

CMPLE: Correlation Modeling to Decode Photosynthesis Using the Minorize–Maximize Algorithm

In plant genomic experiments, correlations among various biological traits (phenotypes) give new insights into how genetic diversity may have tuned biological processes to enhance fitness under diverse conditions. Consequently, knowing how the correlations are affected by genetic (G) and environmental (E) factors helps develop climate-resilient plants. However, the current literature lacks any method for assessing the effect of predictors on pairwise correlations among multiple phenotypes together with easily interpretable model parameters. To address this need, we propose to model pairwise correlations directly in terms of G and E and develop a computationally efficient inference procedure. Two major novelties in our methodology are (1) the use of a composite pairwise likelihood method to avoid the positive definiteness restriction on the correlation matrix and (2) the use of a novel Minorize–Maximize (MM) algorithm for the efficient estimation of a large number of parameters. The proposed method shows excellent numerical performance on synthetic datasets. Here, the analysis of the motivating data on cowpea reveals that the rates of solar energy storage by photosynthesis (the aggregate trait) are differentially affected by different genetic loci through two distinct processes: “photoinhibition” which results from photodamage caused by excess light, and “photoprotection” which protects plants from photodamage but also results in energy loss.

Correlation modeling↗
DOE OSTI2017

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the anti-bound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen–Morse II potentials. We have computed the Wigner reflection and transmission time delays for the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case. - Highlights: • The scattering matrix of hyperbolic step potential is studied. • The scattering matrix has a branch cut and an infinite number of poles. • The poles are associated to anti-bound states. • Susy partners using antibound states are computed. • Wigner time delays for the hyperbolic step and partner potentials are compared.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Determining g A / g V with High-Resolution Spectral Measurements Using a LiInSe 2 Bolometer

Neutrinoless double beta decay (0νββ) processes sample a wide range of intermediate forbidden nuclear transitions, which may be impacted by quenching of the axial vector coupling constant (g A /g V ), the uncertainty of which plays a pivotal role in determining the sensitivity reach of 0νββ experiments. Here we present measurements performed on a high-resolution LiInSe 2 bolometer in a “source = detector” configuration to measure the spectral shape of the fourfold forbidden β decay of 115 In . The value of g A /g V is determined by comparing the spectral shape of theoretical predictions to the experimental β spectrum taking into account various simulated background components as well as a variety of detector effects. We find evidence of quenching of g A /g V at >5 σ with a model-dependent quenching factor of 0.655 ± 0.002 as compared to the free-nucleon value for the interacting shell model. We also measured the 115 In half-life to be [5.18 ± 0.06(stat) $^{+0.005}_{- 0.015}$(sys)] x 10 14 yr within the interacting shell model framework. This Letter demonstrates the power of the bolometeric technique to perform precision nuclear physics single-β decay measurements, which along with improved nuclear modeling can help reduce the uncertainties in the calculation of several decay nuclear matrix elements including those used in 0νββ sensitivity calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗