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This study formulates the reduction effects of a sandy berm on irregular wave runup over a dune-berm coast. The numerical experiments by Park and Cox (2016) are closely re-examined to develop an empirical formula describing the variability of reduction effects of a sandy berm over a broad range of conditions. Based on a sequence of regression analyses, the reduction effects are expressed as a reduction factor in terms of normalized berm width, normalized surge level, and wave steepness in deep water. The comparison with the numerical experiments demonstrates that the regression formula can satisfactorily reproduce the variability of the reduction effects over the range of numerical experiments. The analysis of prediction uncertainty demonstrated that the derived formula reproduced the reduction effects observed in the numerical experiments with negligible bias and a 90% confidence interval of approximately ±20% relative error. In addition, conversion formulas between representative runup values based on different statistical definitions are derived to enable consistent comparisons between them. The proposed reduction formula is implemented into three empirical runup models that are applicable to the quick estimations of irregular wave runup on a dune-berm coast: the models by Park and Cox (2016), Stockdon et al. (2006), and Mase et al. (2013). Consistent comparisons were conducted among the empirical predictions and numerical experiments based on the statistical conversion formulas. Combined with the proposed reduction formula, all three models well reproduced the normalized 2% runup in the numerical experiments over a wide range of conditions. On the other hand, the uncertainty in the runup prediction appeared in different forms depending on the selected model. When the proposed reduction formula was implemented in the modified Park and Cox (2016) and modified Stockdon et al. (2006) models, the uncertainty was described by a log-normal distribution of the error ratio between the empirical predictions and numerical experiments. Quantitatively, these two models predicted 90% of the normalized runup on a dune within a range of relative error of less than approximately 20–30%. When the proposed reduction formula was combined with the model by Mase et al. (2013), the uncertainty followed a normal distribution of the residual error between the empirical predictions and numerical experiments. On the normalized runup, the model prediction indicated a small conservative bias (+0.05) and a root-mean-square error of 0.13.
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Measurement of Cross Sections and Momentum Distributions of Proton-Rich Radioactive Isotopes Produced from a 345-MeV/Nucleon 78Kr Beam
Abstract We measured the production cross sections and momentum distributions of proton-rich radioactive isotopes (RIs) whose atomic numbers were 18–37. These isotopes were produced by the projectile fragmentation of a 345-MeV/nucleon $$^{78}$$Kr beam impinged on a 5-mm Be target. The cross sections close to the stability region were reproduced fairly well by the semi-empirical formulas, EPAX3.1a and FRACS1.1. However, these formulas tend to overestimate the cross sections of the RIs near the proton drip line, sometimes by as much as 100-fold. The Abrasion–Ablation model in the LISE$$^{++}$$ package was employed, using different mass table variations, to describe the experimental results in this region. The best agreement was achieved when the Weizsäcker-Skyrme microscopic-macroscopic mass formula (WS4$$_{\mathrm{RBF}}$$) and a version of the nonrelativistic Hartree–Fock–Bogoliubov mass model (HFB22) were used. The momentum distribution was represented well by an asymmetric Gaussian distribution. The width of the high-momentum side of the distribution was reproduced fairly well by the Goldhaber model, whereas the width of the low-momentum side was 1.1 times larger than that of the high-momentum side. Moreover, an exponential-shaped low-momentum tail was observed, which began from a height of approximately 1/100–1/1000 of the momentum peak. The momentum means were not reproduced well by Morrissey’s empirical formula: additional velocity loss to the formula was observed. The yield of $$^{68}$$Br was smaller than the expected yield, as estimated from the yield systematics of its neighboring RIs. Assuming an in-flight decay in the separator, the half-life of $$^{68}$$Br was estimated to be $$105^{+62}_{-25}$$ ns.
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- Award ID(s):
- 2310078
- PAR ID:
- 10590137
- Author(s) / Creator(s):
- ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Progress of Theoretical and Experimental Physics
- Volume:
- 2025
- Issue:
- 5
- ISSN:
- 2050-3911
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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