Stochastic homogenization of nonlinear evolution equations with space-time nonlocality

In this paper we consider the homogenization problem of nonlinear evolution equations with space-time non-locality, the problems are given by Beltritti and Rossi [JMAA, 2017, 455: 1470-1504]. When the integral kernel $J(x,t;y,s)$ is re-scaled in a suitable way and the oscillation coefficient $\nu(x,t;y,s)$ possesses periodic and stationary structure, we show that the solutions $u^{\varepsilon}(x,t)$ to the perturbed equations converge to $u_{0}(x,t)$, the solution of corresponding local nonlinear parabolic equation as scale parameter $\varepsilon\rightarrow 0^{+}$. Then for the nonlocal linear index $p=2$ we give the convergence rate such that $||u^\varepsilon -u_{0}||_{_{L^{2}(\mathbb{R}^{d}\times(0,T))}}\leq C\varepsilon$. Furthermore, we obtain that the normalized difference $\frac{1}{\varepsilon}[u^{\varepsilon}(x,t)-u_{0}(x,t)]-\chi(\frac{x}{\varepsilon}, \frac{t}{\varepsilon^{2}}) \nabla_{x}u_{0}(x,t)$ converges to a solution of an SPDE with additive noise and constant coefficients. Finally, we give some numerical formats for solving non-local space-time homogenization.Comment: 24 pages, 1 figur

Semi-Supervised Text Simplification with Back-Translation and Asymmetric Denoising Autoencoders

Text simplification (TS) rephrases long sentences into simplified variants while preserving inherent semantics. Traditional sequence-to-sequence models heavily rely on the quantity and quality of parallel sentences, which limits their applicability in different languages and domains. This work investigates how to leverage large amounts of unpaired corpora in TS task. We adopt the back-translation architecture in unsupervised machine translation (NMT), including denoising autoencoders for language modeling and automatic generation of parallel data by iterative back-translation. However, it is non-trivial to generate appropriate complex-simple pair if we directly treat the set of simple and complex corpora as two different languages, since the two types of sentences are quite similar and it is hard for the model to capture the characteristics in different types of sentences. To tackle this problem, we propose asymmetric denoising methods for sentences with separate complexity. When modeling simple and complex sentences with autoencoders, we introduce different types of noise into the training process. Such a method can significantly improve the simplification performance. Our model can be trained in both unsupervised and semi-supervised manner. Automatic and human evaluations show that our unsupervised model outperforms the previous systems, and with limited supervision, our model can perform competitively with multiple state-of-the-art simplification systems

Homogenization of the distribution-dependent stochastic abstract fluid models

In this paper, we study the homogenization of the distribution-dependent stochastic abstract fluid models by combining the $two\!-\!scale$ convergence and martingale representative approach. A general framework of the homogenization research is established for stochastic abstract fluid models, which is the type of genuine-nonlinear partial differential equations including the (distribution-dependent) stochastic Navier-Stokes equations, stochastic magneto-hydrodynamic equations, stochastic Boussinesq equations, stochastic micropolar equations, stochastic Allen-Cahn equations.Comment: no comment

Intergenerational transmission of education in China: New evidence from the Chinese Cultural Revolution

This paper estimates the effect of parental education on children’s education by using instruments generated by the Chinese Cultural Revolution, and further explores the mechanisms of this causal relationship. Several important findings stand out from our empirical analyses. We find a larger intergenerational persistence in education for higher level in urban areas but for a lower level of education in rural areas. The main results from instrumental variable estimation show that the nurture effect is larger and more significant for fathers than for mothers. A deeper investigation of the mechanism behind this nurture effect informs us that a father’s education passes on to his children’s education partly through the income channel. Another notable finding is that even after controlling for fathers’ income, parental education still has a significantly positive effect on children’s education through the nurture effect. This indicates that beyond the income channel, there may exist other channels such as better home environment, which deserve to be explored in future research.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147763/1/rode12558_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147763/2/rode12558.pd

Microstructure of Perovskite Oxides Thin Films Grown on Miscut/Small Lattice-Mismatched Substrates.

Perovskite oxides exhibit a wide range of physical properties, such as high dielectric, piezoelectric, pyroelectric, ferroelectric/multiferroic, non-linear optical and high temperature superconducting properties. The unique combination of these properties makes possible the use of perovskite oxide thin films as core elements in the next generation devices for sensors and electric/electronic/optical circuits. Recent studies demonstrate that it is possible to tailor physical properties through controlling growth parameters during thin film deposition, for example, by choosing suitable substrates in certain oxide systems. This thesis is focused on the microstructural characterization of domain and strain engineered perovskite oxide thin films by transmission electron microscopy (TEM) and elucidation of the structure-property relationships in these thin films. The model systems studied in this thesis are ferroelectric domain engineered BiFeO3 by miscut SrTiO3 substrates, strain engineered BaTiO3 by small-lattice-mismatched substrates (GdScO3 and DyScO3) and crystallographic domain engineered PrScO3 via miscut SrTiO3 substrates. In detail, TEM results prove that the ferroelectric domain structures in multiferroic BiFeO3 thin films can be engineered by means of miscut SrTiO3 substrates. BiFeO3 thin films grown on low angle (<1°) miscut SrTiO3 substrates comprise 71° and 109° ferroelectric domains, while BiFeO3 thin films grown on 4° miscut SrTiO3 substrates comprise only 71° ferroelectric lamellae. Fully strained and partially strain-relaxed BaTiO3 thin films with coherent SrRuO3 bottom electrode can be grown on rare-earth scandate substrates (GdScO3 and DyScO3). Results corroborate that strain relaxation of the BaTiO3/SrRuO3 bilayer system is mainly determined by the lattice mismatch between each layer and the substrate, the thickness of each layer, and kinetics. Crystallographic domain structures in PrScO3 thin films can be engineered via miscut SrTiO3 substrates. PrScO3 thin films grown on high angle (≥1°) miscut SrTiO3 substrates comprise one type of crystallographic domain. In contrast, there are six types of crystallographic domains in PrScO3 thin films grown on low angle (<1°) miscut SrTiO3 substrates. These studies demonstrate that microstructure of perovskite oxide thin films can be engineered by means of miscut or small lattice-mismatched substrates. It, in turn, dramatically improves the physical properties of engineered perovskite oxide thin films.Ph.D.Materials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58528/1/yanbinc_1.pd