Origin of sawtooth domain walls in ferroelectrics

Domains and domain walls are among the key factors that determine the performance of ferroelectric materials. In recent years, a unique type of domain walls, i.e., the sawtooth-shaped domain walls, has been observed in BiFeO$_{3}$ and PbTiO$_{3}$. Here, we build a minimal model to reveal the origin of these sawtooth-shaped domain walls. Incorporating this model into Monte-Carlo simulations shows that (i) the competition between the long-range Coulomb interaction (due to bound charges) and short-range interaction (due to opposite dipoles) is responsible for the formation of these peculiar domain walls and (ii) their relative strength is critical in determining the periodicity of these sawtooth-shaped domain walls. Necessary conditions to form such domain walls are also discussed

Relaxed 2-D Principal Component Analysis by LpL_p Norm for Face Recognition

A relaxed two dimensional principal component analysis (R2DPCA) approach is proposed for face recognition. Different to the 2DPCA, 2DPCA-$L_1$ and G2DPCA, the R2DPCA utilizes the label information (if known) of training samples to calculate a relaxation vector and presents a weight to each subset of training data. A new relaxed scatter matrix is defined and the computed projection axes are able to increase the accuracy of face recognition. The optimal $L_p$-norms are selected in a reasonable range. Numerical experiments on practical face databased indicate that the R2DPCA has high generalization ability and can achieve a higher recognition rate than state-of-the-art methods.Comment: 19 pages, 11 figure

Vacuum induced Berry phases in single-mode Jaynes-Cummings models

Motivated by the work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquire the photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even the filed is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with cavity quantum electrodynamics (QED) system is designed to detect the vacuum-induced Berry phase.Comment: 10 pages, 4 figures

A Unifying Framework for Strong Structural Controllability

This paper deals with strong structural controllability of linear systems. In contrast to existing work, the structured systems studied in this paper have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph theoretic condition for the full rank property of a given pattern matrix. This graph theoretic condition makes use of a new color change rule that is introduced in this paper. Based on these two results, we then establish a necessary and sufficient graph theoretic condition for strong structural controllability. Moreover, we relate our results to those that exists in the literature, and explain how our results generalize previous work.Comment: 11 pages, 6 Figure

Estimation of evapotranspiration in the Mu Us Sandland of China

Evapotranspiration (ET) was estimated from 1981–2005 over Wushen County located in the Mu Us Sandland, China, by applying the Advection-Aridity model, which is based on the complementary relationship hypothesis. We used National Oceanic and Atmospheric Administration (NOAA) Advanced Very High Resolution Radiometer (AVHRR), Moderate Resolution Imaging Spectroradiometer (MODIS), and meteorological data. Our results show that the estimated daily ET was about 4.5% higher than measurements using an Eddy Covariance (EC) system after forcing energy balance closure over an alfalfa field from 22 July 2004 to 23 August 2004. At a regional scale, the estimated monthly ET was about 8.7% lower than measurements using the EC system after forcing energy balance closure over an alfalfa field in August 2004. These results were about 3.0% higher than ET measurements by microlysimeter over sand dunes during June 1988. From 1981 to 2005, the average annual ET and precipitation levels were 287 mm and 336 mm, respectively, in Wushen County. The average annual ET varied from 230 mm in western parts of Wushen County to 350 mm in eastern parts of the county. Both inter-annual and seasonal variations in ET were substantial in Wushen County. The annual ET was 200–400 mm from 1981–2005, and the seasonal pattern of ET showed a single peak distribution. The cumulative ET during the June–September 2004 period was 250 mm, which was 87% of the total annual ET. The annual ET, precipitation, and the maximum Normalized Difference Vegetation Index (NDVI<sub>max</sub>) showed positive correlations temporally and spatially