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Howes et al. Reply to Comment on Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas arXiv:0711.4355
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In a comment on arXiv:1006.5070v1, Drechsler et al. present new band-structure calculations suggesting that the frustrated ferromagnetic spin-1/2 chain LiCuVO4 should be described by a strong rather than weak ferromagnetic nearest-neighbor interaction, in contradiction with their previous calculations. In our reply, we show that their new results are at odds with the observed magnetic structure, that their analysis of the static susceptibility neglects important contributions, and that their criticism of the spin-wave analysis of the bound-state dispersion is unfounded. We further show that their new exact diagonalization results reinforce our conclusion on the existence of a four-spinon continuum in LiCuVO4, see Enderle et al., Phys. Rev. Lett. 104 (2010) 237207.
In a comment on arXiv:1006.5070v2, Drechsler et al. claim that the frustrated ferromagnetic spin-1/2 chain LiCuVO4 should be described by a strong rather than weak ferromagnetic nearest-neighbor interaction, in contradiction with their previous work. Their comment is based on DMRG and ED calculations of the magnetization curve and the magnetic excitations. We show that their parameters are at odds with the magnetic susceptibility and the magnetic excitation spectrum, once intensities are taken into account, and that the magnetization curve cannot discriminate between largely different parameter sets within experimental uncertainties. We further show that their new exact diagonalization results support the validity of the RPA-approach, and strongly reinforce our conclusion on the existence of a four-spinon continuum in LiCuVO4, see Enderle et al., Phys. Rev. Lett. 104 (2010) 237207.
The preceding Comment by Xu et al. (Phys. Rev. Lett. 122, 059803 (2019); arXiv:1808.05390) erroneously applies the entropic stress expression in our Letter (T.C. OConnor et al., Phys. Rev. Lett. 121, 047801 (2018); arXiv:1806.09509) to transient stress. In addition, the authors only apply this expression at extreme extension rates where we clearly showed deviations from the entropic stress expression for steady-state extensional flow. Hence the surprisingly minor discrepancies noted in the Comment between observed and predicted stress are entirely expected and have no bearing on the discussion or conclusions in our Letter.
We demonstrate that the concerns expressed by Garcia et al. are misplaced, due to (1) a misreading of our findings in [1]; (2) a widespread failure to examine and present words in support of asserted summary quantities based on word usage frequencies; and (3) a range of misconceptions about word usage frequency, word rank, and expert-constructed word lists. In particular, we show that the English component of our study compares well statistically with two related surveys, that no survey design influence is apparent, and that estimates of measurement error do not explain the positivity biases reported in our work and that of others. We further demonstrate that for the frequency dependence of positivity---of which we explored the nuances in great detail in [1]---Garcia et al. did not perform a reanalysis of our data---they instead carried out an analysis of a different, statistically improper data set and introduced a nonlinearity before performing linear regression.
Estimating population models from uncertain observations is an important problem in ecology. Perretti et al. observed that standard Bayesian state-space solutions to this problem may provide biased parameter estimates when the underlying dynamics are chaotic. Consequently, forecasts based on these estimates showed poor predictive accuracy compared to simple model-free methods, which lead Perretti et al. to conclude that Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data. However, a simple modification of the statistical methods also suffices to remove the bias and reverse their results.
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