A normalized solitary wave solution of the Maxwell-Dirac equations

We prove the existence of a $L^2$-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the mean-field limit, we prove the existence of the (positive) energy minimizer.     

Design,synthesis and evaluation of novel dehydroabietic acid-dithiocarbamate hybrids as potential multi-targeted compounds for tumor cytotoxicity

In the present study, novel representatives of the important group of biologically-active, dehydroabietic acid-bearing dithiocarbamate moiety, were synthesized and characterized by ¹H NMR, ¹³C NMR, HR-MS. The in vitro antiproliferative activity evaluation (MTT) indicated that these compounds exhibited potent inhibitory activities in various cancer cell lines (HepG-2, MCF-7, HeLa, T-24, MGC-803). Particularly, compound III-b possessed extraordinary cytotoxicity with low micromolar IC₅₀ values ranging from 4.07 to 38.84 µM against tested cancer cell lines, while displayed weak cytotoxicity on two normal cell lines (LO-2 and HEK 293 T). Subsequently, the potential mechanisms of representative compound III-b were elementarily investigated by Transwell experiment, which showed III-b can inhibit cancer cells migration. Annexin-V/PI dual staining showed that the compound can induce HepG-2 cells apoptosis in a dose-dependent manner. Meanwhile this apoptosis may be related to the upregulated protein expression of cleaved-caspase 3, cleaved-caspase 9, Bax and downregulated of Bcl-2 indicated by Western Blot. Later study further confirmed that ROS levels in HepG-2 cells increased significantly with the rise of concentrations. In addition, through the network pharmacology data analyzing, the core targets and signaling pathways of compound III-b for treatment of liver neoplasms were forecasted. Molecular docking model showed that compound III-b had high affinity with hub targets (CASP3, EGFR, HSP90AA1, MAPK1, ERBB2, MDM2), suggesting that compound III-b might target the hub protein to modulate signaling activity. Taken together, these data indicated that dehydroabietic acid structural modification following the “Molecular hybridization” principle is a feasible way to discover the potential multi-targeted antitumor compounds.     

Optical Trapping with Focused Surface Waves

Near-field optical trapping can be realized with focused evanescent waves that are excited at the water–glass interface due to the total internal reflection, or with focused plasmonic waves excited on the water–gold interface. Herein, the performance of these two kinds of near-field optical trapping techniques is compared using the same optical microscope configuration. Experimental results show that only a single-micron polystyrene bead can be trapped by the focused evanescent waves, whereas many beads are simultaneously attracted to the center of the excited region by focused plasmonic waves. This difference in trapping behavior is analyzed from the electric field intensity distributions of these two kinds of focused surface waves and the difference in trapping behavior is attributed to photothermal effects due to the light absorption by the gold film.     

Electrodynamics of Magnetoelectric Media and Magnetoelectric Fields

The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the electromagnetic (EM) field in a magnetoelectric (ME) medium is not a trivial problem. The question of whether electromagnetism and magnetoelectricity can coexist without an extension of Maxwell's theory arises when the effects of EM energy propagation are studied and the group velocity of the waves in an ME medium is considered. The energy balance equation reveals unusual topological structure of fields in ME materials. Together with certain constraints on the constitutive parameters of a medium, definite constraints on the local field structure should be imposed. Analyzing the EM phenomena inside an ME material, the question “what kind of the near fields arising from a sample of such a material can be measured?” should be answered. The visualization of the ME states requires an experimental technique that is based on an effective coupling to the violation of spatial as well as temporal inversion symmetry. To observe the ME energy in a subwavelength region, it is necessary to assume the existence of first-principle near fields—the ME fields. These are non-Maxwellian near fields with specific properties of violation of spatial and temporal inversion symmetry. A particular interest to the ME fields arises in studies of metamaterials with “artificial-atoms” ME elements.     

Global stability of rarefaction waves for a viscous radiative and reactive gas with temperature-dependent viscosity

We study the nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional viscous radiative and reactive gas when the viscosity and heat conductivity coefficients depend on both density and absolute temperature. Our main idea is to use the smallness of the strength of the rarefaction waves to control the possible growth of its solutions induced by the nonlinearity of the system and the interactions of rarefaction waves from different families. The proof is based on some detailed analysis on uniform positive lower and upper bounds of the specific volume and the absolute temperature.     

空化可压缩流动空穴溃灭激波特性研究

为深入研究空化可压缩流动中空泡/空泡团溃灭过程中激波产生、传播及其与空穴相互作用规律,本文采用数值模拟方法对空化可压缩流动空穴溃灭激波特性展开了研究.数值计算基于OpenFOAM开源程序,综合考虑蒸汽相和液相的压缩性,通过在原无相变两相可压缩求解器的控制方程中耦合模拟空化汽液相间质量交换的源项,实现了对空化流动的非定常可压缩计算.利用上述考虑汽/液相可压缩性的空化流动求解器,对周期性云状空化流动进行了数值模拟,并重点研究了空穴溃灭激波特性.结果表明:上述数值计算方法可以准确捕捉到空穴非定常演化过程及大尺度脱落空泡云团溃灭激波现象,大尺度脱落空泡云团溃灭过程分为3个阶段:(1) U型空泡团形成; (2) U型空泡团头部溃灭; (3) U型空泡团腿部溃灭.在U 型空泡团腿部溃灭瞬间,观察到激波产生,并向上游和下游传播,向上游传播的激波与空穴相互作用,导致水翼吸力面新生的附着型片状空穴回缩,直至完全溃灭.并且空穴溃灭激波存在回弹现象, 抑制了下一周期的空化发展.      

Jordan–Cattaneo waves: Analogues of compressible flow

We review work of Jordan on a hyperbolic variant of the Fisher–KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee–Infante equation. Extension of Jordan’s ideas to a model for traffic flow are also mentioned. We also examine a diffusive susceptible–infected (SI) model, and generalizations of diffusive Lotka–Volterra equations, including a Lotka–Volterra–Bass competition model with diffusion. For all cases we show how a Jordan–Cattaneo wave may be analysed and we indicate how to find the wavespeeds and the amplitudes. Finally we present details of a fully nonlinear analysis of acceleration waves in a Cattaneo–Christov poroacoustic model.