Variational-based data assimilation to simulate sediment concentration in the Lower Yellow River, China

The heavy sediment load of the Yellow River makes it difficult to simulate sediment concentration using classic numerical models. In this paper, on the basis of the classic one-dimensional numerical model of open channel flow, a variational-based data assimilation method is introduced to improve the simulation accuracy of sediment concentration and to estimate parameters in sediment carrying capacity. In this method, a cost function is introduced first to determine the difference between the sediment concentration distributions and available field observations. A one-dimensional suspended sediment transport equation, assumed as a constraint, is integrated into the cost function. An adjoint equation of the data assimilation system is used to solve the minimum problem of the cost function. Field data observed from the Yellow River in 2013 are used to test the proposed method. When running the numerical model with the data assimilation method, errors between the calculations and the observations are analyzed. Results show that (1) the data assimilation system can improve the prediction accuracy of suspended sediment concentration; (2) the variational inverse data assimilation is an effective way to estimate the model parameters, which are poorly known in previous research; and (3) although the available observations are limited to two cross sections located in the central portion of the study reach, the variational-based data assimilation system has a positive effect on the simulated results in the portion of the model domain in which no observations are available

Coexistence of spin glass and ferroelectricity in highly ordered Bi2FeMnO6 epitaxial thin film

Highly ordered Bi2FeMnO6 epitaxial thin films have been successfully grown on SrTiO3 substrate. Both synchrotron X-ray reciprocal space mapping and high resolution transmission electron microscopy confirmed the alternative alignment of Fe and Mn along [111] direction of Bi2FeMnO6 films. Magnetic and ferroelectric properties of Bi2FeMnO6 films are characterized and analyzed. The room-temperature ferroelectricity is well kept in Bi2FeMnO6 film as expected. However, it is very interesting that Bi2FeMnO6 film exhibits a typical spin-glass behavior and very weak magnetism rather than a ferri/ferromagnetism as generally believed. Our first-principles calculations suggest a spin frustration model for Bi2FeMnO6, which can well explain the intriguing magnetic property of Bi2FeMnO6 film.Comment: Main text: 30 pages and 14 figure

On the Lower Bound of Minimizing Polyak-{\L}ojasiewicz functions

Polyak-{\L}ojasiewicz (PL) [Polyak, 1963] condition is a weaker condition than the strong convexity but suffices to ensure a global convergence for the Gradient Descent algorithm. In this paper, we study the lower bound of algorithms using first-order oracles to find an approximate optimal solution. We show that any first-order algorithm requires at least ${\Omega}\left(\frac{L}{\mu}\log\frac{1}{\varepsilon}\right)$ gradient costs to find an $\varepsilon$-approximate optimal solution for a general $L$-smooth function that has an $\mu$-PL constant. This result demonstrates the optimality of the Gradient Descent algorithm to minimize smooth PL functions in the sense that there exists a ``hard'' PL function such that no first-order algorithm can be faster than Gradient Descent when ignoring a numerical constant. In contrast, it is well-known that the momentum technique, e.g. [Nesterov, 2003, chap. 2] can provably accelerate Gradient Descent to ${O}\left(\sqrt{\frac{L}{\hat{\mu}}}\log\frac{1}{\varepsilon}\right)$ gradient costs for functions that are $L$-smooth and $\hat{\mu}$-strongly convex. Therefore, our result distinguishes the hardness of minimizing a smooth PL function and a smooth strongly convex function as the complexity of the former cannot be improved by any polynomial order in general

A consistent analysis on QCD phase diagram and meson spectra in the improved soft-wall AdS/QCD

We present a consistent analysis on QCD phase diagram and meson spectra based on the improved soft-wall AdS/QCD. The equations of motion for the octet pseudoscalar, vector and axial-vector mesons with $2+1$ flavors are derived to calculate the octet meson spectra and relevant decay constants, by which the model parameters are determined. The chemical potential effects on chiral thermal transition are investigated, which enables us to obtain the QCD phase diagram in the $\mu-T$ plane. It is shown that the critical end point (CEP) linking the crossover transition with the first-order phase transition still exists and locates at $(\mu_B, T_c) \simeq (390 MeV, 145 MeV)$. The crossover line and the location of CEP resulted from the model agree with both the lattice result and the experimental analysis from relativistic heavy-ion collisions. We find that the improved soft-wall AdS/QCD model can provide a consistent description for both the chiral phase diagram and the main properties of low-energy hadron physics in the $2+1$ flavor case