Measured Strength Distributions Research Articles

Several QRPA method calculations of the Gamow–Teller strength distributions in $$^{62{-}72}$$Ge

Studies of exotic nuclei are currently one of the most prolific in nuclear physics. Weak rates in germanium isotopes have a fundamental role in the dynamics of supernovae. Electron capture and beta-decay of germanium isotopes, specified by Gamow–Teller transitions, importantly modify the lepton fraction of the stellar matter. In this study, Gamow–Teller Transitions (GT) for $$^{62{-}72}$$ Ge are calculated using QRPA methods. The GT strength distributions are calculated using eight different QRPA models. QRPA models, namely single quasi-particle (sqp), Pyatov method (PM) and the schematic model (SM), are further divided into four subcategories. Using these models, Gamow–Teller distribution, total GT strengths along electron capture direction ( $$\sum $$ B(GT) $$_+$$ ) and Ikeda sum rule are calculated. The results of sqp, PM, and SM are also compared with previous theoretical calculations and measured strength distributions wherever available. It is expected that this study of GT properties would gain favor and may help to a better understanding of the presupernova evolution of massive stars.

Level excursion analysis of probabilistic quasibrittle fracture

It has widely been acknowledged that no structures can be designed to be risk free, and therefore reliability analysis plays an essential role in the design of engineering structures. The recent focus has been placed on structures made of brittle heterogenous (a.k.a. quasibrittle) materials, such as ceramics, composites, concrete, rock, cold asphalt mixture, and many more at the microscale. This paper presents a level excursion model for the analysis of probabilistic failure of quasibrittle structures, in which the failure statistics is calculated as a first passage probability. The model captures both the spatial randomness of local material resistance and the random stress field induced by microstructures (e.g. randomly distributed flaws). The model represents a generalization of the classical weakest-link model at the continuum limit and it recovers the classical Weibull distribution as an asymptotic distribution function. The paper discusses two applications of the model. The model is first applied to the strength distribution of polycrystalline silicon (poly-Si) MEMS specimens. It is shown that the model agrees well with the experimentally measured strength distributions of poly-Si MEMS specimens of different sizes. The model predicts a complete size effect curve of the mean structural strength transitioning from a vanishing size effect at the small-size limit to the classical Weibull size effect at the large-size limit. The second application is concerned with the left tail of strength distribution of quasibrittle structures. By taking into account both random stress and strength fields, the model is used to investigate the origin of the power-law tail distribution of structural strength.

Effect of deformation, particle-hole and particle-particle interaction on Gamow-Teller transitions of 76Ge

Gamow-Teller (GT) transitions for 76Ge using QRPA methods in this article are calculated, which play an essential role in the supernovae. Three different QRPA models are used to the GT strength distributions. QRPA models namely single quasi-particle (sqp), Pyatov Method (PM) and the Schematic Model (SM). Gamow-Teller distribution, ΣB(GT)-, the centroid of energy, the width of energy and ISR are calculated by using these models. The effect of particle-particle interaction on spherical nuclei and deformed nuclei on Gamow-Teller transitions is wanted to show. Deformed Woods-Saxon potential is used in calculations of Single-particle energies and wave functions. The results are also compared with previous theoretical calculations and measured strength distributions wherever available. It is expected that the current study of GT features would be helpful and may guide to a better knowledge of the presupernova progression of massive stars.

A Renewal Weakest-Link Model of Strength Distribution of Polycrystalline Silicon MEMS Structures

Abstract Experimental data have made it abundantly clear that the strength of polycrystalline silicon (poly-Si) microelectromechanical systems (MEMS) structures exhibits significant variability, which arises from the random distribution of the size and shape of sidewall defects created by the manufacturing process. Test data also indicated that the strength statistics of MEMS structures depends strongly on the structure size. Understanding the size effect on the strength distribution is of paramount importance if experimental data obtained using specimens of one size are to be used with confidence to predict the strength statistics of MEMS devices of other sizes. In this paper, we present a renewal weakest-link statistical model for the failure strength of poly-Si MEMS structures. The model takes into account the detailed statistical information of randomly distributed sidewall defects, including their geometry and spacing, in addition to the local random material strength. The large-size asymptotic behavior of the model is derived based on the stability postulate. Through the comparison with the measured strength distributions of MEMS specimens of different sizes, we show that the model is capable of capturing the size dependence of strength distribution. Based on the properties of simulated random stress field and random number of sidewall defects, a simplified method is developed for efficient computation of strength distribution of MEMS structures.

Investigation of Gamow Teller transition properties in [formula omitted]Ni isotopes using QRPA methods

Weak rates in nickel isotopes play an integral role in the dynamics of supernovae. Electron capture and β-decay of nickel isotopes, dictated by Gamow–Teller transitions, significantly alter the lepton fraction of the stellar matter. In this paper we calculate Gamow–Teller (GT) transitions for isotopes of nickel, Ni56–64, using QRPA methods. The GT strength distributions were calculated using four different QRPA models. Our results are also compared with previous theoretical calculations and measured strength distributions wherever available. Our investigation concluded that amongst all RPA models, the pn-QRPA(C) model best described the measured GT distributions (including total GT strength and centroid placement). It is hoped that the current investigation of GT properties would prove handy and may lead to a better understanding of the presupernova evolution of massive stars.

A first passage based model for probabilistic fracture of polycrystalline silicon MEMS structures

Experiments have shown that the failure loads of Microelectromechanical Systems (MEMS) devices usually exhibit a considerable level of variability, which is believed to be caused by the random material strength and the geometry-induced random stress field. Understanding the strength statistics of MEMS devices is of paramount importance for the device design guarding against a tolerable failure risk. In this study, we develop a continuum-based probabilistic model for polycrystalline silicon (poly-Si) MEMS structures within the framework of first passage analysis. The failure of poly-Si MEMS structures is considered to be triggered by fracture initiation from the sidewalls governed by a nonlocal failure criterion. The model takes into account an autocorrelated random field of material tensile strength. The nonlocal random stress field is obtained by stochastic finite element simulations based on the information of the uncertainties of the sidewall geometry. The model is formulated within the contexts of both stationary and non-stationary stochastic processes for MEMS structures of various geometries and under different loading configurations. It is shown that the model agrees well with the experimentally measured strength distributions of uniaxial tensile poly-Si MEMS specimens of different gauge lengths. The model is further used to predict the strength distribution of poly-Si MEMS beams under three-point bending, and the result is compared with the Monte Carlo simulation. The present model predicts strong size effects on both the strength distribution and the mean structural strength. It is shown that the mean size effect curve consists of three power-law asymptotes in the small, intermediate, and large-size regimes. By matching these three asymptotes, an approximate size effect equation is proposed. The present model is shown to be a generalization of the classical weakest-link statistical model, and it provides a physical interpretation of the material length scale used in the weakest-link model.

Dipole response of the odd-proton nucleus 205Tl up to the neutron-separation energy

The low-lying electromagnetic dipole strength of the odd-proton nuclide 205Tl has been investigated up to the neutron separation energy exploiting the method of nuclear resonance fluorescence. In total, 61 levels of 205Tl have been identified. The measured strength distribution of 205Tl is discussed and compared to those of even–even and even–odd mass nuclei in the same mass region as well as to calculations that have been performed within the quasi-particle phonon model.

A statistical model for the unconfined compressive strength of deep-mixed columns

The strength of soil improved by deep mixing processes often exhibits significant spatial variability. This paper presents a statistical model for strength distribution in deep-mixed columns, based on the assumption that spatial variation in strength arises from spatial variation in binder mass fraction. The statistical inputs of the model are the probability density function and coefficient of variation of the binder distribution, both of which were obtained from centrifuge model data and were assumed to be independent of the amount of the binder introduced into the ground. The theoretical framework of the model is first developed, followed by an assessment of the probability density function for the binder distribution. The variation of binder mass fraction within a deep mixing column is fitted by a truncated normal distribution. The model is benchmarked against core strength data from three phases of deep mixing operation in a construction project. The simplicity of the model precludes consideration of the effects of detailed mixing blade configuration, in situ variation in soil properties as well as workmanship. In spite of this, the computed histograms of strength distribution gave a reasonable reflection of the measured strength distribution. This suggests that despite the variety and complexity of deep mixing processes, one may still be able to develop a simple and workable model of the strength distribution taking into account just a few important factors.

Modeling of Probabilistic Failure of Polycrystalline Silicon MEMS Structures

Microelectromechanical Systems (MEMS) devices typically need to be designed against a very low failure probability, which is on the order of or lower. Experimental determination of the target strength for such a low failure probability requires testing of tens of thousands of specimens, which can be cost prohibitive for the design process. Therefore, understanding the probabilistic failure of MEMS devices is of paramount importance for design. Currently available probabilistic models for predicting the strength statistics of MEMS structures are based on classical Weibull statistics. Significant advances in experimental techniques for measuring the strength of MEMS devices have produced data that have unambiguously demonstrated that the strength distributions consistently deviate from the Weibull distribution. Such deviations can be explained by the fact that the Weibull distributions are derived based on extreme value statistics, which is inapplicable to MEMS devices where the dimensions of the material microstructure are not negligible compared to the characteristic structural dimensions. This paper presents a robust probabilistic model for strength distribution of polycrystalline silicon (poly‐Si) MEMS structures that could be extended to other brittle materials at the microscale. The overall failure probability of the structure is related to the failure probability of each material element along its sidewalls through a weakest‐link statistical model. The failure statistics of the material element is determined by both the intrinsic random material strength as well as the random stress field induced by the sidewall geometry. Different from the classical Weibull statistics, the present model is designed to account for structures consisting of a finite number of material elements, and it predicts a scale effect on their failure statistics. It is shown that the model agrees well with the measured strength distributions of poly‐Si MEMS specimens of different sizes, and the calibrated mean strength of the material element is consistent with the theoretical strength of silicon. Meanwhile, it is shown that the two‐parameter and three‐parameter Weibull distributions cannot provide optimum and consistent fits of the observed size‐dependent strength distributions, and thus have very limited prediction capability. The present model explicitly relates the strength statistics to the size effect on the mean structural strength, and therefore provides an efficient means of determining the failure statistics of MEMS structures.

NUCLEAR WEAK RESPONSE FROM THE COMBINED STUDY OF β-DECAY AND CHARGE-EXCHANGE REACTION

Studying the weak nuclear response, especially the Gamow-Teller (GT) transitions, of stable as well as unstable pf-shell nuclei, is one of the key issues in nuclear and astro-nuclear physics. We study the decay half-lives and the GT transitions starting from Tz = ±1 and ±2 mirror nuclei, respectively, by means of β decays and complementary hadronic (3 He , t) charge-exchange reactions. Under the assumption that isospin is a good quantum number, symmetry is expected for mirror nuclei and the GT transitions starting from the mirror nuclei. The half-lives and branching ratios and the measured strength distributions of GT transitions are compared and also combined for the understanding of the nuclear structure of pf-shell nuclei far-from-stability.

Gamow-Teller strength distribution in the beta-decay of100Ag from total-absorption gamma spectrometry

The EC/β+-decay of the odd-odd nucleus100Ag was studied by means of total absorptionγ-ray spectrometry. Most of the Gamow-Teller strength was found to be concentrated at an excitation energy of 5.6 MeV in100Pd, the FWHM of this resonance being 1.5 MeV. The measured strength distribution which is interpreted within the BCS approximation as being due to the dominant population of four-quasiparticle excitations, resembles the distribution predicted by an advanced shell-model calculation for the98Ag →98Cd decay.

Combined Effect of Flaw Distribution and Diameter Variation on the Statistics of Glass Fiber Strength

This paper examines the combined effects of flaw‐severity distribution and fiber diameter distribution on the fracture statistics of glass fibers. The approach adopted is to assume specific forms (Gaussian and Weibull) for the diameter distribution, a Weibull distribution for the true strength, and then to calculate the measured strength distributions. Exact analytical results are obtained in the cases of flawless fibers, uniform size flaws, and when true strength and fiber diameter are Weibull distributed. Approximate analytical expressions have been derived for the general case. A procedure is described to obtain the parameters of the true strength distribution from the knowledge of measured strength distribution and the coefficient of variation of fiber diameters. Implications of these results for the fracture statistics of high‐strength glass fibers are discussed.