Evolution of probability measures associated with quantum systems

We derive the evolution equation for probability distributions and characteristic functions of the quantum tomograms associated with the linear and nonlinear evolutions of quantum states.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 365–370, February, 2005.     

Deposition pattern of drying droplets

The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.     

Effect of entanglement embedded in environment on quantum non-Markovianity based on collision model

By means of collision models(CMs) where the environment is simulated by a collection of ancillas consisting of two entangled qubits, we investigate the effects of entanglement in the environment on the non-Markovianity of an open quantum system. Two CMs are considered in this study, in the first one the open quantum system S directly collides with the environment,while in the second one the system interacts with two intermediate qubits which, in turn, are coupled to the environment. We show that it is possible to enhance the non-Markovianity by environment entanglement in both models. In particular, in the second model, we show that the initial state of the auxiliary qubits can also affect the non-Markovianity of the system and there exists the optimal combination of the initial environmental state and the initial state of auxiliary qubits. In this case, the non-Markovianity can be greatly enhanced.     

基于瑞利-索末菲积分的大衍射角衍射光学元件设计方法

针对现有的衍射光学元件设计方法只适用于小角度衍射的情况,本文提出了一种基于瑞利-索末菲衍射积分的设计方法,可以用来设计具有大衍射角的衍射光学元件。先对目标光场进行坐标变换和强度调整,再利用改进的Gerchberg-Saxton算法优化得到衍射光学元件的相位分布。分别采用本文方法和原有的基于夫琅禾费衍射积分的方法设计衍射光学元件实现线条结构光和不同角度方框图形的光场重构,结果表明:原有的设计方法只适用于衍射角全角小于25°的情况,当衍射角大于25°时,重构光场会出现显著的枕形畸变和不均匀的强度分布。而本文方法在小角度和大角度衍射下都能重构出准确的衍射角和较为均匀的强度分布.     

Nonlinear Channels of Werner States

We study the nonlinear positive map of the density matrix of two-qubit Werner states, called the nonlinear channel. The map ρ → Φ(ρ) is realized by the rational function Φ. We discuss the influence of the map on the entanglement properties of the transformed density matrix. We investigate the violation of the Bell inequality (CHSH inequality) for the two-qubit state Φ(ρ). The nonlinear channels under discussion create the entangled state from a separable Werner state. We study the quantum spin tomograms of the states.     

Accuracy and variability of acoustic measures of voicing onset

Five commonly used methods for determining the onset of voicing of syllable-initial stop consonants were compared. The speech and glottal activity of 16 native speakers of Cantonese with normal voice quality were investigated during the production of consonant vowel (CV) syllables in Cantonese. Syllables consisted of the initial consonants /ph/, /th/, /kh/, /p/, /t/, and /k/ followed by the vowel /a/. All syllables had a high level tone, and were all real words in Cantonese. Measurements of voicing onset were made based on the onset of periodicity in the acoustic waveform, and on spectrographic measures of the onset of a voicing bar (f0), the onset of the first formant (F1), second formant (F2), and third formant (F3). These measurements were then compared against the onset of glottal opening as determined by electroglottography. Both accuracy and variability of each measure were calculated. Results suggest that the presence of aspiration in a syllable decreased the accuracy and increased the variability of spectrogram-based measurements, but did not strongly affect measurements made from the acoustic waveform. Overall, the acoustic waveform provided the most accurate estimate of voicing onset; measurements made from the amplitude waveform were also the least variable of the five measures. These results can be explained as a consequence of differences in spectral tilt of the voicing source in breathy versus modal phonation.     

Parabolic Omori–Yau Maximum Principle for Mean Curvature Flow and Some Applications

We derive a parabolic version of Omori–Yau maximum principle for a proper mean curvature flow when the ambient space has lower bound on \(\ell \)-sectional curvature. We apply this to show that the image of Gauss map is preserved under a proper mean curvature flow in euclidean spaces with uniformly bounded second fundamental forms. This generalizes the result of Wang (Math Res Lett 10:287–299, 2003) for compact immersions. We also prove a Omori–Yau maximum principle for properly immersed self-shrinkers, which improves a result in Chen et al. (Ann Glob Anal Geom 46:259–279, 2014).     

Amphiphilic Core–Shell Nanocomposite Particles for Enhanced Magnetic Resonance Imaging

A scalable synthesis of magnetic core–shell nanocomposite particles, acting as a novel class of magnetic resonance (MR) contrast agents, has been developed. Each nanocomposite particle consists of a biocompatible chitosan shell and a poly(methyl methacrylate) (PMMA) core where multiple aggregated γ‐Fe₂O₃ nanoparticles are confined within the hydrophobic core. Properties of the nanocomposite particles including their chemical structure, particle size, size distribution, and morphology, as well as crystallinity of the magnetic nanoparticles and magnetic properties were systematically characterized. Their potential application as an MR contrast agent has been evaluated. Results show that the nanocomposite particles have good stability in biological media and very low cytotoxicity in both L929 mouse fibroblasts (normal cells) and HeLa cells (cervical cancer cells). They also exhibited excellent MR imaging performance with a T₂ relaxivity of up to 364 mM_Fe^?1 s^?1. An in vivo MR test performed on a naked mouse bearing breast tumor indicates that the nanocomposite particles can localize in both normal liver and tumor tissues. These results suggest that the magnetic core–shell nanocomposite particles are an efficient, inexpensive and safe T₂‐weighted MR contrast agent for both liver and tumor MR imaging in cancer therapy.     

Littlewood–Paley Operators on Spaces with Variable Exponent on Homogeneous Groups

In this paper,on homogeneous groups,we study the Littlewood–Paley operators in variable exponent spaces.First,we prove that the weighted Littlewood–Paley operators are controlled by the weighted Hardy–Littlewood maximal function,and obtain the vector-valued inequalities of the Littlewood–Paley operators,including the Lusin function,Littlewood–Paley g function and gλ* function.Second,we prove the boundedness of multilinear Littlewood–Paley gψ,λ* function.     

Study of shear transfer in Al/epoxy joint by digital photoelasticity

An improved six-step phase-shifting method is proposed for calculating full-field shear stress based on a four-step color phase-shifting method in digital photoelasticity. The method was verified using a disk under diametral compression and then applied to an aluminum alloy/epoxy joint for studying the shear transfer behavior. Experimental results revealed that the isochromatic fringe order and shear stress at the bonding interface are distributed continuously and increased with compression. In particular, an antisymmetric thermal residual shear stress appears at the bonding interface, because of the difference in the thermal expansion coefficients of Al and the resin. This indicates that the thermal residual shear stress at the bonding interface is self-balanced and reaches a peak at the edges of the bonding interface. The load transfer is realized by the shear band from the bonding interface to the bottom support. Basically, the bonding interfacial shear stress is balanced with the load.