Riemann积分的历史与发展

总结Riemann积分的发展历史、基本思想及其各种推广,介绍Riemann积分的局限性和缺陷,以及由此推动产生Lebesgue积分的过程.     

Entanglement Transfer Through Arrays of Cavities Coupled by Optical Fibers

We propose a scheme of entanglement transfer through two independent arrays of cavities coupled by optical fibers when each of the cavities contains a single two-level atom. We study the entanglement dynamics of the transferred states and find the explicit expression for the density matrix and concurrence. It is shown that the amount of the transferred entanglement has a direct connection with the target states and the lengths of the arrays of cavities. Moreover, the influence of the initial states and the length of the arrays of cavities on the phenomenon of entanglement sudden death is also investigated.     

Quantum Discord of Two Atoms Interacting with a Single-mode Thermal Field

This paper investigates the quantum discord and entanglement of two atoms when they simultaneously interact with a single-mode thermal field. The results show that, the two atoms which are initially in separate states can be entangled by a thermal field. However, with increase of the mean photon number, the value of the entanglement decreases and disappears when the temperature of the cavity is high enough (corresponding to the large value of the mean photon number). In stark contrast, the quantum discord does not decrease, but gradually reaches stable value at high temperature. In addition, when the two atoms are initially the Werner mixed state, we have found that, a large amount of quantum discord is exist even in the region where the entanglement is zero, which is a strong signature for the presence of non classical correlations. These results indicate that, the quantum discord is more resistant to the environment’s disturbance than the entanglement for higher temperatures.     

Structural transition of Ti3SiC2 under high hydrostatic pressure: A first-principles study

We theoretically studied the phase transformation, electronic and elastic properties of Ti₃SiC₂ ceramic by using the pseudopotential plane-wave method within the density functional theory. Our results demonstrate that there exists a structural phase transition from α‐Ti₃SiC₂ to β‐Ti₃SiC₂ under pressure up to 384 GPa, and α‐Ti₃SiC₂ is the most stable phase at zero pressure. The calculated electronic band structure and density of states reveal the metallic behavior for the polymorphs of Ti₃SiC₂. The mechanical stability of α‐Ti₃SiC₂ at zero pressure is confirmed by the elastic constants, and is analyzed in terms of electronic level. By analyzing the ratio between bulk and shear moduli, we conclude that α‐Ti₃SiC₂ is brittle in nature.     

Can climate sensitivity be estimated from short-term relationships of top-of-atmosphere net radiation and surface temperature?

Increasing the knowledge in climate radiative feedbacks is critical for current climate studies. This work focuses on short-term relationships between global mean surface temperature and top-of-atmosphere (TOA) net radiation. The relationships may be used to characterize the climate feedback as suggested by some recent studies. As those recent studies, an energy balance model with ocean mixed layer and both radiative and non-radiative heat sources is used here. The significant improvement of current model is that climate system memories are considered.Based on model simulations, short-term relationship between global mean surface temperature and TOA net radiation (or the linear striation feature as suggested by previous studies) might represent climate feedbacks when the system had no memories. However, climate systems with the same short-term feedbacks but different memories would have a similar linear striation feature. This linear striation feature reflects only fast components of climate feedbacks and may not represent the total climate feedback even when the memory length of climate systems is minimal. The potential errors in the use of short-term relationships in estimations of climate sensitivity could be big. In short time scales, fast climate processes may overwhelm long-term climate feedbacks. Thus, the climate radiative feedback parameter obtained from short-term data may not provide a reliable estimate of climate sensitivity. This result also suggests that long-term observations of global surface temperature and TOA radiation are critical in the understanding of climate feedbacks and sensitivities.     

Wave propagation characterization and design of two-dimensional elastic chiral metacomposite

In this work, a chiral metacomposite is proposed by integrating two-dimensional periodic chiral lattice with elastic metamaterial inclusions for low-frequency wave applications. The plane harmonic wave propagation in the proposed metacomposite is investigated through the finite element technique and Bloch's theorem. Band diagrams are obtained to illustrate wave properties of the chiral metacomposite. Effective dynamic properties of the chiral metacomposite are numerically calculated to explain low-frequency bandgap behavior in the chiral metacomposite. Interestingly doubly negative effective density and modulus of the chiral metacomposite are found in a specific frequency range, where a pass band with negative group velocity is observed. Tuning of the resulting low-frequency bandgaps is then discussed by adjusting microstructure parameters of the metamaterial inclusion and lattice geometry. Specifically design of a metacomposite beam structure for the broadband low-frequency vibration suppression is demonstrated.     

On Perturbations of Generalized Landau-Lifshitz Dynamics

We consider deterministic and stochastic perturbations of dynamical systems with conservation laws in ℝ³. The Landau-Lifshitz equation for the magnetization dynamics in ferromagnetics is a special case of our system. The averaging principle is a natural tool in such problems. But bifurcations in the set of invariant measures lead to essential modification in classical averaging. The limiting slow motion in this case, in general, is a stochastic process even if pure deterministic perturbations of a deterministic system are considered. The stochasticity is a result of instabilities in the non-perturbed system as well as of existence of ergodic sets of a positive measure. We effectively describe the limiting slow motion.     

Effects of laser power density on the microstructure and microhardness of Ni–Al alloyed layer by pulsed laser irradiation

Laser alloying of Ni–P electroless deposited layer with aluminum substrate was carried out by Nd–YAG pulsed laser. The phase composition and microstructure of the alloyed layers produced by different laser power densities were identified by X-ray diffractionary (XRD), scanning electron microscope (SEM) accompanied by energy dispersion X-ray analysis (EDS) and transmission electron microscope (TEM). Furthermore, the surface roughness of the alloyed layers was characterised by confocal laser scanning microscope (CLSM). The results showed that the characteristic dendritic or lamellar microstructures were observed in the alloyed layers. The phase constituents of the alloyed zones were intermetallic compounds of nickel–aluminum NiAl, Al₃Ni and Al₃Ni₂, as well as some non-equilibrium phases and amorphous phases depending on the employed laser power density. As a result, the microhardness of the alloyed layer with Ni–P amorphous phases formed at laser power density 5.36×10⁹ W/m² reached to HV_0.1 390.     

Structure and photoluminescence properties of ZnS films grown on porous Si substrates

ZnS films were deposited on porous silicon (PS) substrates with different porosities. With the increase of PS substrate porosity, the XRD diffraction peak intensity decreases and the surface morphology of the ZnS films becomes rougher. Voids appear in the films, due to the increased roughness of PS structure. The photoluminescence (PL) spectra of the samples before and after deposition of ZnS were measured to study the effect of substrate porosity on the luminescence properties of ZnS/PS composites. As-prepared PS substrates emit strong red light. The red PL peak of PS after deposition of ZnS shows an obvious blueshift. As PS substrate porosity increases, the trend of blueshift increases. A green emission at about 550 nm was also observed when the porosity of PS increased, which is ascribed to the defect-center luminescence of ZnS. The effect of annealing time on the structural and luminescence properties of ZnS/PS composites were also studied. With the increase of annealing time, the XRD diffraction peak intensity and the self-activated luminescence intensity of ZnS increase, and, the surface morphology of the ZnS films becomes smooth and compact. However, the red emission intensity of PS decreases, which was associated with a redshift. White light emission was obtained by combining the luminescence of ZnS with the luminescence of PS.     

Set covering-based surrogate approach for solving sup-{\mathcal{T}} equation constrained optimization problems

This work considers solving the sup-T{\mathcal{T}} equation constrained optimization problems from the integer programming viewpoint. A set covering-based surrogate approach is proposed to solve the sup-T{\mathcal{T}} equation constrained optimization problem with a separable and monotone objective function in each of the variables. This is our first trial of developing integer programming-based techniques to solve sup-T{\mathcal{T}} equation constrained optimization problems. Our computational results confirm the efficiency of the proposed method and show its potential for solving large scale sup-T{\mathcal{T}} equation constrained optimization problems.