Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium

Let $\mathcal{L}_\epsilon$ be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform $W^{1,p}$ estimate in a Lipschitz domain for solutions to the Dirichlet problem, where $(2n/(n+1)) -\delta<p<(2n/(n-1))+\delta$. The ranges of $p$'s are sharp for $n=2$ or 3

Anomalies in non-stoichiometric uranium dioxide induced by pseudo-phase transition of point defects

A uniform distribution of point defects in an otherwise perfect crystallographic structure usually describes a unique pseudo phase of that state of a non-stoichiometric material. With off-stoichiometric uranium dioxide as a prototype, we show that analogous to a conventional phase transition, these pseudo phases also will transform from one state into another via changing the predominant defect species when external conditions of pressure, temperature, or chemical composition are varied. This exotic transition is numerically observed along shock Hugoniots and isothermal compression curves in UO2 with first-principles calculations. At low temperatures, it leads to anomalies (or quasi-discontinuities) in thermodynamic properties and electronic structures. In particular, the anomaly is pronounced in both shock temperature and the specific heat at constant pressure. With increasing of the temperature, however, it transforms gradually to a smooth cross-over, and becomes less discernible. The underlying physical mechanism and characteristics of this type of transition are encoded in the Gibbs free energy, and are elucidated clearly by analyzing the correlation with the variation of defect populations as a function of pressure and temperature. The opportunities and challenges for a possible experimental observation of this phase change are also discussed.Comment: 11 pages, 5 figure

Efficient Privacy Preserving Viola-Jones Type Object Detection via Random Base Image Representation

A cloud server spent a lot of time, energy and money to train a Viola-Jones type object detector with high accuracy. Clients can upload their photos to the cloud server to find objects. However, the client does not want the leakage of the content of his/her photos. In the meanwhile, the cloud server is also reluctant to leak any parameters of the trained object detectors. 10 years ago, Avidan & Butman introduced Blind Vision, which is a method for securely evaluating a Viola-Jones type object detector. Blind Vision uses standard cryptographic tools and is painfully slow to compute, taking a couple of hours to scan a single image. The purpose of this work is to explore an efficient method that can speed up the process. We propose the Random Base Image (RBI) Representation. The original image is divided into random base images. Only the base images are submitted randomly to the cloud server. Thus, the content of the image can not be leaked. In the meanwhile, a random vector and the secure Millionaire protocol are leveraged to protect the parameters of the trained object detector. The RBI makes the integral-image enable again for the great acceleration. The experimental results reveal that our method can retain the detection accuracy of that of the plain vision algorithm and is significantly faster than the traditional blind vision, with only a very low probability of the information leakage theoretically.Comment: 6 pages, 3 figures, To appear in the proceedings of the IEEE International Conference on Multimedia and Expo (ICME), Jul 10, 2017 - Jul 14, 2017, Hong Kong, Hong Kon

Transport coefficients of a unitarized pion gas

The latest experimental results in relativistic heavy-ion collisions show that the matter there produced requires transport coefficients because of the important collective properties found. We review the theoretical calculation of these transport coefficients in the hadron side at low temperatures by computing them in a gas composed of low energy pions. The interaction of these pions is taken from an effective chiral theory and further requiring scattering unitarity. The propagation of D and D* mesons in the thermalized pion gas is also studied in order to extract the heavy quark diffusion coefficients in the system.Comment: 7 pages, 3 figures, contribution to the International School of Nuclear Physics, 33rd Course: From Quarks and Gluons to Hadrons and Nuclei, Erice-Sicily: 16-24 September 201