Multivariate localization methods for ensemble Kalman filtering

In ensemble Kalman filtering (EnKF), the small number of ensemble members that is feasible to use in a practical data assimilation application leads to sampling variability of the estimates of the background error covariances. The standard approach to reducing the effects of this sampling variability, which has also been found to be highly efficient in improving the performance of EnKF, is the localization of the estimates of the covariances. One family of localization techniques is based on taking the Schur (element-wise) product of the ensemble-based sample covariance matrix and a correlation matrix whose entries are obtained by the discretization of a distance-dependent correlation function. While the proper definition of the localization function for a single state variable has been extensively investigated, a rigorous definition of the localization function for multiple state variables that exist at the same locations has been seldom considered. This paper introduces two strategies for the construction of localization functions for multiple state variables. The proposed localization functions are tested by assimilating simulated observations experiments into the bivariate Lorenz 95 model with their help

The Chiral Fermion Meson Model at Finite Temperature

We study the chiral fermion meson model which is the well known linear sigma model of Gell-Mann-and-Levy at finite temperature.A modified self-consistent resummation (MSCR) which resums higher order terms in the perturbative expansion is proposed. It is shown that with the MSCR the problem of tachyonic masses is solved, the renormalization of the gap equations is carried out and the Goldstone's theorem is verified. We also apply the method to investigate another known case at high temperature and compare with results found in the literature.Comment: 31 pages, 9 EPS figures. Final version with extended Concluding Remarks section, accepted for publication in Phys. Rev.

Rotational coherence of encapsulated ortho and para water in fullerene-C₆₀ revealed by time-domain terahertz spectroscopy

We resolve the real-time coherent rotational motion of isolated water molecules encapsulated in fullerene-C60 cages by time-domain terahertz (THz) spectroscopy. We employ single-cycle THz pulses to excite the low-frequency rotational motion of water and measure the subsequent coherent emission of electromagnetic waves by water molecules. At temperatures below ~ 100 K, C60 lattice vibrational damping is mitigated and the quantum dynamics of confined water are resolved with a markedly long rotational coherence, extended beyond 10 ps. The observed rotational transitions agree well with low-frequency rotational dynamics of single water molecules in the gas phase. However, some additional spectral features with their major contribution at ~2.26 THz are also observed which may indicate interaction between water rotation and the C60 lattice phonons. We also resolve the real-time change of the emission pattern of water after a sudden cooling to 4 K, signifying the conversion of ortho-water to para-water over the course of 10s hours. The observed long coherent rotational dynamics of isolated water molecules confined in C60 makes this system an attractive candidate for future quantum technology

Terahertz underdamped vibrational motion governs protein-ligand binding in solution

Low-frequency collective vibrational modes in proteins have been proposed as being responsible for efficiently directing biochemical reactions and biological energy transport. However, evidence of the existence of delocalized vibrational modes is scarce and proof of their involvement in biological function absent. Here we apply extremely sensitive femtosecond optical Kerr-effect spectroscopy to study the depolarized Raman spectra of lysozyme and its complex with the inhibitor triacetylchitotriose in solution. Underdamped delocalized vibrational modes in the terahertz frequency domain are identified and shown to blue-shift and strengthen upon inhibitor binding. This demonstrates that the ligand-binding coordinate in proteins is underdamped and not simply solvent-controlled as previously assumed. The presence of such underdamped delocalized modes in proteins may have significant implications for the understanding of the efficiency of ligand binding and protein–molecule interactions, and has wider implications for biochemical reactivity and biological function