Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

Tuning Emission Wavelength of Polymorphous Crystal via Controllable Alkyl Chain Stacking and Its Vapor- and Thermo-Responsive Fluorescence

Tuning fluorescence colour of solid-state materials has become a topic of increasing interest for both fundamental mechanism study and practical applications such as sensors, optical recording and security printing. In this work, a fluorescent colour tuneable molecule BA-C16 is rationally designed and facilely synthesized by attaching flexible long alkyl chains to 2-hydroxybenzophenone azine ( BA ), which shows both aggregation-induced emission (AIE) and excited-state intramolecular proton transfer (ESIPT) characteristics. Compared to BA , the simple introduction of long alkyl chains in BA-C16 leads to an emission wavelength redshift from 542 to 558 nm. This strategy of extending emission wavelength is rarely reported, and is ascribed to the enlarged through-space π-conjugation between interplanar molecules in the aggregate of BA-C16 . Three crystals of BA-C16 are obtained with green, yellowish green and yellow emission. According to characterization by X-ray crystallography, X-ray powder diffraction and differential scanning calorimetry, alkyl chains play an important role in inducing different stacking modes of the three crystals, which further leads to polymorph-dependent fluorescence colour. BA-C16 exhibits tuneable solid-state fluorescence upon vapor fumigation, or annealing based on a transition between a “near-monomer” crystalline state and a “dimer” crystalline state. BA-C16 is further applied for rewritable fluorescence printing tuned by vapor- and thermal-treatment.     

Qualitative and quantitative determination of Atractylodes rhizome using ultra‐performance liquid chromatography coupled with linear ion trap–Orbitrap mass spectrometry with data‐dependent processing

A quick and effective workflow based on ultra‐performance liquid chromatography coupled with electron spray ionization and LTQ‐Orbitrap mass spectrometry (UPLC‐LTQ‐Orbitrap MS) was established for compositional analysis and screening of the characteristic compounds of three species of Atractylodes rhizome for quality evaluation. This technique was employed to determine the seven main components in Atractylodes rhizome samples. Ultimately, 78 constituents were identified; of these, seven characteristic compounds were selected for species discrimination, comprising atractylodin (63), atractylenolide I (43), atractylenolide II (49), atractylenolide III (53), atractylon (69), methyl‐atractylenolide II (54) and (4E,6E,12E)‐tetradecadecatriene‐8,10‐diyne‐1,3‐diacetate (59). The seven main compounds, including six characteristic compounds, were simultaneously determined in 29 batches of Atractylodes rhizome samples. Thus, the method validation showed acceptable results. Quantitative analysis showed significantly different contents of the seven main components among the three species of Atractylodes rhizome, which indicates possible distinctions in the pharmacological effects. This established method can simultaneously provide qualitative and quantitative results for compositional characterization of Atractylodes rhizomes and for quality control.     

Dose‐dependent exposure profile and metabolic characterization of notoginsenoside R1 in rat plasma by ultra‐fast liquid chromatography–electrospray ionization–tandem mass spectrometry

Notoginsenoside R₁ (NGR₁), a diagnostic protopanaxatriol‐type (ppt‐type) saponin in Panax notoginseng, possesses potent biological activities including antithrombotic, anti‐inflammatory, neuron protection and improvement of microcirculation, yet its pharmacokinetics and metabolic characterization as an individual compound remain unclear. The aim of this study was to investigate the exposure profile of NGR₁ in rats after oral and intravenous administration and to explore the metabolic characterization of NGR₁. A simple and sensitive ultra‐fast liquid chromatographic–tandem mass spectrometric method was developed and validated for the quantitative determination of NGR₁ and its major metabolites, and for characterization of its metabolic profile in rat plasma. The blood samples were precipitated with methanol, quantified in a negative multiple reaction monitoring mode and analyzed within 6.0 min. Validation parameters (linearity, precision and accuracy, recovery and matrix effect, stability) were within acceptable ranges. After oral administration, NGR₁ exhibited dose‐independent exposure behaviors with t_1/2 over 8.0 h and oral bioavailability of 0.25–0.29%. A total of seven metabolites were characterized, including two pairs of epimers, 20(R)‐notoginsenoside R₂/20(S)‐notoginsenoside R₂ and 20(R)‐ginsenoside Rh₁/20(S)‐ginsenoside Rh₁, with the 20(R) form of saponins identified for the first time in rat plasma. Five deglycometabolites were quantitatively determined, among which 20(S)‐notoginsenoside R₂, ginsenoside Rg₁, ginsenoside F₁ and protopanaxatriol displayed relatively high exploration, which may partly explain the pharmacodynamic diversity of ginsenosides after oral dose.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.     

Azobenzene‐Functionalized Cage Silsesquioxanes as Inorganic–Organic Hybrid,Photoresponsive, Nanoscale,Building Blocks

Mono‐ and octa‐azobenzene‐functionalized cage silsesquioxanes were easily synthesized by the reaction of 4‐bromoazobenzene with monovinyl‐substituted octasilsesquioxane and cubic octavinylsilsesquioxane through the Heck coupling reaction. Excited‐state energies obtained from time‐dependent density functional theory (TDDFT) and the CAM‐B3LYP functional correlate very well with experimental trans–cis photoisomerization results from UV/Vis spectroscopy. These azobenzene‐functionalized cages exhibit good thermal stability and are fluorescent with maximum emission at approximately 400 nm, making them potential materials for blue‐light emission.     

Strongly localized states in a single carbon nanotube with polymer molecules

A single-walled carbon nanotube (SWCNT) with conjugated polymer molecules is analyzed via optical spectroscopy. The presence of strongly localized excitonic states in the SWCNT is confirmed using time-integrated photoluminescence (PL). The PL spectrum exhibits extremely narrow width (~0.8 meV) which is attributed to the strong confinement of the states by polymer molecules. In addition, I observed that the excited states are gradually filled as a function of the excitation power, which supports the localized excitonic behavior. Only the ground excitonic state is observed at low excitation powers, but three additional PL peaks appear as the excitation power is increased. Especially, the power-dependent PL spectrum shows a blueshift and increased width, which can be elucidated in terms of quantum confined stark effect and the screening of induced electric fields. Overall, I demonstrate that the presence of polymer molecules induces several localized states in a single SWCNT.     

Characteristic material parameters of CIGS solar cell related with device performance

CIGS solar cells with power conversion efficiency (PCE) in the range of 1.82%–12.30% were obtained by using two-step process, and were further analyzed through various measurement techniques. Material parameters showed diverse values and some trends depending on the device performance. The lower performance device showed small integrated PL intensity, short minority life time, larger defect density and lower activation energy, whereas the higher performance device showed opposite values. We investigated relationship between material parameters and PCE of solar cells, and found that some physical parameters such as integrated PL intensity, minority life time, defect density, and difference between band gap and activation energy (E_g-E_a), which all reflect defect states in bulk and at pn interface, are strongly related with PCE and would be used as a good indicator to evaluate device performance quickly.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Particle size effects in Fischer-Tropsch synthesis by Co catalyst supported on carbon nanotubes

The effect of Co particle size on the Fischer-Tropsch synthesis (FTS) activity of carbon nanotube (CNT)-supported Co catalysts was investigated. Microemulsion (using water-to-surfactant molar ratios of 2 to12) and impregnation techniques were used to prepare catalysts with different Co particle sizes. Kinetic studies were performed to understand the effect of Co particle size on catalytic activity. Size-dependent kinetic parameters were developed using a thermodynamic method, to evaluate the structural sensitivity of the CNT-supported Co catalysts. The size-independent FTS reaction rate constant and size-independent adsorption parameter increased with increasing reac-tion temperature. The Polani parameter also depended on catalyst particle size, because of changes in the catalyst surface coverage.