Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.     

Comparative molecular field analysis of chromatographic hydrophobicity indices for some coumarin analogs

The chromatographic hydrophobicity index (CHI) is an HPLC‐based parameter that provides reliable guidance in optimization of pharmacological efficiency and adsorption, distribution, metabolism and exertion (ADME) profile of drug candidates. In the present work, classical and three‐dimensional quantitative structure–property relationship (QSPR) models were developed for prediction of CHI values of some 4‐hydroxycoumarin analogs on immobilized artificial membrane column. Comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) as 3D–QSPR methods were performed to gain insight into the key structural factors affecting on the chromatographic hydrophobicity of interested chemicals. The calculated parameters of Q ², R ² and standard error were 0.545, 0.996 and 0.773 for CoMFA model and 0.815, 0.986 and 1.44 for CoMSIA model, respectively. The contour maps for steric fields of the CoMFA model illustrate that the hydrophobicity of chemicals will be higher when the positions of R6, R7 and R8 in the 4‐hydroxycuomarin ring are substituted by alkyl groups. Moreover, by the analysis of the plots of electrostatic fields, it was concluded that the CHI value greatly increases if one hydrogen on coumarin ring is substituted by the F, Cl, Br, OH or OCH₃ group.     

Improvement charge injection in P-type polymer field-effect transistors with low-cost molybdenum electrodes through dodecanoic acid self assembled monolayer

Most of the merit of organic thin film transistors (OTFTs) is that they can be manufactured using cost effective processes. However, expensive gold (Au) electrodes have usually been used as a source/drain (S/D), due to their benign energy level matching, high air stability, and easy patternability. In this article, we report a simple method for improving the charge injection from a low cost molybdenum (Mo) electrode to organic semiconductors in OTFTs by incorporating a dodecanoic acid (DA)–based self-assembled monolayer (SAM). The OTFT performance is remarkably improved when compared to the devices with a pristine Au electrode. The hole carrier mobilities (hole μ_FET) were ～0.13 (rr-P3HT), ～0.55 (PC12TV12T) and ～0.72 (P2100) cm²/V·sec.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).     

Zinc sulfide nanosheets as a novel solid‐phase extraction material for flavonoids

As a novel solid‐phase extraction material, zinc sulfide nanosheets were prepared by a simple method and were used to extract flavonoids. We used scanning electron microscopy to show its nanosheet morphology and energy dispersive X‐ray spectroscopy and powder X‐ray diffraction to confirm its chemical and phase compositions. Coupled to a high‐performance liquid chromatography, the zinc sulfide nanosheets were packed into a microcolumn and were used to extract four model flavonoids to examine their extraction ability. The parameters of sample loading and elution were investigated. Under optimized conditions, the analytical method for flavonoids was established. For the method, wide linearities from 1 to 250 μg/L and low limits of detection from 0.25 to 0.5 μg/L were obtained. The relative standard deviations for single column repeatability and column to column reproducibility were less than 7.7 and 10.4%, respectively. The established method was also used to analyze two real samples and the recoveries from 88.7 to 98.2% further proved the reliability of the method. Moreover, the zinc sulfide nanosheets have good stability and that in one column can be reused for more than 50 times. This work proves that the prepared zinc sulfide nanosheets are a good candidate as the flavonoids sorbent.     

Experiment on relationship between the magnetic gradient of low-carbon steel and its stress

In geomagnetic field, a series of tensile experiments on the low-carbon steel sticks were carried out. A special homemade detector was used to measure the magnetic gradient on the material surface. The results showed that the relationship between the magnetic gradient and the stress varied with different conditions of measurement. There was no obvious correlation between the magnetic gradient and the tensile stress if the sample remained on the material test machine. If the sample was taken off from the machine, the measured magnetic gradient was linear with the prior maximum stress. In Nanjing, PR China, a place of 32°N latitude, the slope of the linear relationship was about 67 (uT/m)/MPa. This offered a new method of non-destructive stress testing by measuring the magnetic gradient on the ferromagnetic component surface. The prior maximum applied stress of the sample could be tested by measuring the present surface magnetic gradient. Actually this phenomenon was the metal magnetic memory (MMM). The magnetic gradient near the stress concentration zone of the sample, the necking point, was much larger than other area. Thus, the hidden damage in the ferromagnetic component could be detected early by measuring the magnetic gradient distribution on its surface. In addition, the magnetic memory signal gradually weakened as the sample was taken off and laid aside. Therefore, it was effective for a given period of time to detect the stress or stress concentration based on the MMM testing.     

On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

Dynamics of Robertson–Walker spacetimes with diffusion

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.     

Emergent geometry experienced by fermions in graphene in the presence of dislocations

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect.