Optical strong coupling in hybrid metal-graphene metamaterial for terahertz sensing

We propose a terahertz hybrid metamaterial composed of subwavelength metallic slits and graphene plasmonic ribbons for sensing application. This special design can cause the interaction between the plasmon resonances of the metallic slits and graphene ribbons, giving rise to a strong coupling effect and Rabi splitting. Intricate balancing in the strong coupling region can be perturbed by the carrier concentration of graphene, which is subject to the analyte on its surface. Thereby, the detection of analyte can be reflected as a frequency shift of resonance in terahertz transmission spectra. The result shows that this sensor can achieve a theoretical detection limit of 325 electrons or holes per square micrometer. Meanwhile, it also works well as a refractive index sensor with the frequency sensitivity of 485 GHz/RIU. Our results may contribute to design of ultra-micro terahertz sensors.     

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

The self-consistent mean field approximation of the two-flavor NJL model,with a free parameter a to reflect the competition between the "direct" channel and the "exchange" channel,is employed to study the QCD phase structure at finite iso spin chemical potential μ_I,finite bary on chemical potential μ_B and finite temperature T,and especially to study the location of the QCD critical point.Our results show that in order to match the corresponding lattice results of iso spin density and energy density,the contributions of the "exchange" channel need to be considered in the framework of the NJL model,and a weighting factor α=0.5 should be taken.It is also found that for fixed isospin chemical potentials,the lower temperature of the phase transition is obtained with increasing a in the T-μ_I plane,and the largest difference of the phase transition temperature with different a's appears at μ_I~1.5 mπ.At μ_I=0 the temperature of the QCD critical end point(CEP) decreases with increasing a,while the critical baryon chemical potential increases.At high isospin chemical potential(μ_I=500 MeV),the temperature of the QCD tricritical point(TCP) increases with increasing a,and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as μ_B increases.At low density,the critical temperature of the QCD phase transition with different a's rapidly increases with μ_I at the beginning,and then increases smoothly around μ_I 300 MeV.In the high baryon density region,the increase of the iso spin chemical potential will raise the critical baryon chemical potential of the phase transition.     

Effects of electron correlation on superconductivity in the Hatsugai–Kohmoto model

Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm. We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space. The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory. The self-consistent equation for the pair potential is derived and solved. Somewhat contrary to expectation, a weak attractive U comparable to the pair potential can destroy the superconductivity, whereas for weak to intermediate repulsive U, the pair potential can be enhanced. The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation. We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors, in contrast to the uncorrelated BCS limit.     

Creation and annihilation phenomena of electron and positron pairs in an oscillating field

The combination of an oscillating and a static field is used to study the creation and annihilation phenomena during the pair creation process. The time evolution, spatial density and momentum distribution of the created particles for a fermionic system are presented, which demonstrate that with the increasing static field intensity, the number of the created particles experiences a distinguishable decrease in every period of the oscillating field, which is caused by the annihilation phenomena between the created electrons and positrons.     

Semi‐strong and strong solutions for variable density asymmetric fluids in unbounded domains

We establish the existence of local in time semi‐strong solutions and global in time strong solutions for the system of equations describing flows of viscous and incompressible asymmetric fluids with variable density in general three‐dimensional domains with boundary uniformly of class C³. Under suitable assumptions, uniqueness of local semi‐strong solutions is also proved. Copyright © 2016 John Wiley & Sons, Ltd.     

Global regularity for a two‐dimensional nonlinear Boussinesq system

In this paper, we first utilize the vanishing diffusivity method to prove the existence of global quasi‐strong solutions and get some higher order estimates, and then prove the global well‐posedness of the two‐dimensional Boussinesq system with variable viscosity for H³ initial data. Copyright © 2016 John Wiley & Sons, Ltd.     

Convergence of over-relaxed contraction-proximal point algorithm in Hilbert spaces

The proximal point algorithm (PPA) is a classical method for finding zeros of maximal monotone operators. It is known that the algorithm only has weak convergence in a general Hilbert space. Recently, Wang, Wang and Xu proposed two modifications of the PPA and established strong convergence theorems on these two algorithms. However, these two convergence theorems exclude an important case, namely, the over-relaxed case. In this paper, we extend the above convergence theorems from under-relaxed case to the over-relaxed case, which in turn improve the performance of these two algorithms. Preliminary numerical experiments show that the algorithm with over-relaxed parameter performs better than that with under-relaxed parameter.     

一类随机非自伴波方程的半离散有限元近似

本文研究了由白噪音驱动的随机非自伴波方程的有限元近似,由于线性算子A非自伴,不能应用A的特征值和特征向量,从而得到的结果更具有一般性.空间离散上采用标准的有限元法,并借助强连续算子函数的性质,得到了该方程的强收敛误差估计.本文方法也适用于多维情况的分析.最后用数值算例验证了理论分析的正确性.     

Representation and approximation of convex dynamic risk measures with respect to strong–weak topologies

We provide a representation for strong-weak continuous dynamic risk measures from L^p into L^p_t spaces where these spaces are equipped respectively with strong and weak topologies and p is a finite number strictly larger than one. Conversely, we show that any such representation that admits a compact (with respect to the product of weak topologies) sub-differential generates a dynamic risk measure that is strong--weak continuous. Furthermore, we investigate sufficient conditions on the sub-differential for which the essential supremum of the representation is attained. Finally, the main purpose is to show that any convex dynamic risk measure that is strong-weak continuous can be approximated by a sequence of convex dynamic risk measures which are strong--weak continuous and admit compact sub-differentials with respect to the product of weak topologies. Throughout the arguments, no conditional translation invariance or monotonicity assumptions are applied.