Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior

In the light of the visual angle model (VAM), an improved car-following model considering driver's visual angle, anticipated time and stabilizing driving behavior is proposed so as to investigate how the driver's behavior factors affect the stability of the traffic flow. Based on the model, linear stability analysis is performed together with bifurcation analysis, whose corresponding stability condition is highly fit to the results of the linear analysis. Furthermore, the time-dependent Ginzburg-Landau (TDGL) equation and the modified Korteweg-de Vries (mKdV) equation are derived by nonlinear analysis, and we obtain the relationship of the two equations through the comparison. Finally, parameter calibration and numerical simulation are conducted to verify the validity of the theoretical analysis, whose results are highly consistent with the theoretical analysis.     

Chiral one‐dimensional hydrogen‐bonded architectures constructed from single‐enantiomer phosphoric triamides

The two single‐enantiomer phosphoric triamides N‐(2,6‐difluorobenzoyl)‐N′,N′′‐bis[(S)‐(−)‐α‐methylbenzyl]phosphoric triamide, [2,6‐F₂‐C₆H₃C(O)NH][(S)‐(−)‐(C₆H₅)CH(CH₃)NH]₂P(O), denoted L‐1 , and N‐(2,6‐difluorobenzoyl)‐N′,N′′‐bis[(R)‐(+)‐α‐methylbenzyl]phosphoric triamide, [2,6‐F₂‐C₆H₃C(O)NH][(R)‐(+)‐(C₆H₅)CH(CH₃)NH]₂P(O), denoted D‐1 , both C₂₃H₂₄F₂N₃O₂P, have been investigated. In their structures, chiral one‐dimensional hydrogen‐bonded architectures are formed along [100], mediated by relatively strong N—H…O(P) and N—H…O(C) hydrogen bonds. Both assemblies include the noncentrosymmetric graph‐set motifs R₂²(10), R₂¹(6) and C₂²(8), and the compounds crystallize in the chiral space group P1. Due to the data collection of L‐1 at 120 K and of D‐1 at 95 K, the unit‐cell dimensions and volume show a slight difference; the contraction in the volume of D‐1 with respect to that in L‐1 is about 0.3%. The asymmetric units of both structures consist of two independent phosphoric triamide molecules, with the main difference being seen in one of the torsion angles in the OPNHCH(CH₃)(C₆H₅) part. The Hirshfeld surface maps of these levo and dextro isomers are very similar; however, they are near mirror images of each other. For both structures, the full fingerprint plot of each symmetry‐independent molecule shows an almost asymmetric shape as a result of its different environment in the crystal packing. It is notable that NMR spectroscopy could distinguish between compounds L‐1 and D‐1 that have different relative stereocentres; however, the differences in chemical shifts between them were found to be about 0.02 to 0.001 ppm under calibrated temperature conditions. In each molecule, the two chiral parts are also different in NMR media, in which chemical shifts and P–H and P–C couplings have been studied.     

Promotion of a quality standard for Porana sinensis Hemsl. based on the efficacy-oriented Effect-Constituent Index

Multicompound determination for the quality control of traditional Chinese medicine (TCM) may often be inadequate, since these compounds may not be associated with, or fully represent, the clinical effects of TCM. Moreover, the individual contributions of each constituent to the pharmacological effect are often not considered. In China, Porana sinensis is widely used as a substitute for Erycibe sources to treat joint pain and rheumatoid arthritis. The existing quality control methods for P. sinensis neither consider the individual contributions of various compounds nor control the actual quality associated with different clinical efficacies. In the present study, a novel efficacy-oriented approach, named the effect-constituent index (ECI), was established for P. sinensis. Analyses of the spectrum–effect relationship and components in rat plasma were conducted to systematically and scientifically select quality markers. Quantitative analysis of multicomponents via a single marker method was introduced to enhance the practical application value of the established ECI. The established ECI shows a good ability to distinguish and predict the bioeffect-based quality of P. sinensis. The present study also provides a reference for the establishment and application of ECI as a quality control method for TCMs.     

Aeroelastic analysis of cantilever plates using Peters’ aerodynamic model,and the influence of choosing beam or plate theories as the structural model

In this paper, the aeroelastic analyses of a rectangular cantilever plate of varying aspect ratio is presented. The classical plate theory has been selected as the structural model. The main point that distinguishes this study from previously reported research is employing Peters’ theory to model aerodynamic effect which is not straightforward. The Peters’ aerodynamic model was originally developed to provide lift and moment, which is only applicable to the structural model based on the beam theories. In this study, using the basic concept of the Peters’ aerodynamic model in addition to utilizing the Fourier series, the pressure distribution is derived, which makes Peters’ model applicable to structural models based on plate theory. This combination provides a much simpler state–space aeroelastic model for plates in comparison to the prevalent panel methods, which could lead to a significant reduction in computational time. In addition, the aeroelastic response of the plate with respect to changes in the structural model from the beam theory to the plate theory is evaluated. By using data from an experiment carried out at Duke University, the theoretical results are evaluated. Furthermore, the differences in structural models obtained from the plate and beam theories can be divided into two distinct parts, which are responsible for differences in bending and torsional behaviors of the structure, separately. This approach enables us to measure the effects of differences of each behavior separately, which could provide with a new insight into the problem. It has been determined that the flutter speeds obtained from the beam and plate aeroelastic models are little affected by the difference in bending behavior, but rather is mainly caused by the difference in torsional frequencies.     

Mass spectrometry imaging of latent fingerprints using titanium oxide development powder as an existing matrix

Recent research has focused on increasing the evidentiary value of latent fingerprints through chemical analysis. Although researchers have optimized the use of organic and metal matrices for matrix‐assisted laser desorption/ionization‐mass spectrometry imaging (MALDI‐MSI) of latent fingerprints, the use of development powders as matrices has not been fully investigated. Carbon forensic powder (CFP), a common nonporous development technique, was shown to be an efficient one‐step matrix; however, a high‐resolution mass spectrometer was required in the low mass range due to carbon clusters. Titanium oxide (TiO₂) is another commonly used development powder, especially for dark nonporous surfaces. Here, forensic TiO₂ powder is utilized as a single‐step development and matrix technique for chemical imaging of latent fingerprints without the requirement of a high‐resolution mass spectrometer. All studied compounds were successfully detected when TiO₂ was used as the matrix in positive mode, although, generally, the overall ion signals were lower than the previously studied CFP. TiO₂ provided quality mass spectrometry (MS) images of endogenous and exogenous latent fingerprint compounds. The subsequent addition of traditional matrices on top of the TiO₂ powder was ineffective for universal detection of latent fingerprint compounds. Forensic TiO₂ development powder works as an efficient single‐step development and matrix technique for MALDI‐MSI analysis of latent fingerprints in positive mode and does not require a high‐resolution mass spectrometer for analysis.     

Statistical structure of the velocity field in cavitating flow around a 2D hydrofoil

Transformation of flow turbulence structure with cavitation occurrence, determination of the flow conditions favorable for nucleation of cavitation bubbles, influence of the statistical structure of turbulence on this process and the inverse effect of cavitation on the flow dynamics are challenging problems in modern fluid mechanics. The paper reports on the results of statistical processing of the velocity fields measured by a PIV technique in cavitating flow over a 2D symmetric hydrofoil for four flow conditions, starting from a cavitation-free regime and finishing by unsteady cloud cavitation. We analyze basic information on the statistical structure of velocity fluctuations in the form of histograms and Q-Q diagrams along with profiles of the mean velocity and turbulent kinetic energy. The research reveals that the flow turbulence pattern and distributions of turbulent fluctuations change significantly with the cavitation development. Under unsteady cloud cavitation conditions, the probability density function of the fluctuating velocity has a two-mode distribution, which indicates switching of two alternating flow conditions in a region above the hydrofoil aft part due to periodic passing of cavitation clouds. Behaviors of the mean and most probable velocities unexpectedly appear to be different with a monotonous increase of the incoming flow velocity. This finding must be caused by modification of the skewness coefficient of the fluctuating velocity.     

在线社交网络控制实验的现状与展望

在线社交网络已发展成为一个独特的电子生态系统，其应用深刻影响着人们生活的方方面面。由于在线社交网络特性复杂，分析在线社交网络形成和变化中的规律成为当前计算机科学、社会学和物理学的一项挑战。传统上，在线社交网络实证研究主要采用计算机辅助的被动数据获取和分析方式。近年来，在真实大规模在线社交网络上直接进行控制实验从而主动获取数据并开展分析研究的方式广受关注。评述了这一领域的研究进展，包括：社交网络控制实验的主要研究模式；控制实验方法在社交网络结构、信息传播、行为和心理学等领域取得的主要成果以及主要实验工具的适用条件和局限性。最后，展望了人工智能技术在社交网络控制实验中的应用潜力，分析了智能算法对降低实验成本和提高实验效率的作用。     

Effect of nitrogen plasma treatment on the crystallinity and self‐bonding of polyetheretherketone (PEEK) for biomedical applications

Polyetheretherketone (PEEK) is a thermoplastic material with outstanding properties and high potential for biomedical applications, including hermetic encapsulation of active implantable devices. Different biomedical grade PEEK films with initial degree of crystallinity ranging from 8% to 32% (with or without mineral filling) were inspected. PEEK surfaces were treated with nitrogen RF plasma and the effects on materials crystallinity and self‐bonding were evaluated. In particular, the relationship between auto‐adhesive properties and crystalline content of PEEK before and after plasma treatment was examined. PEEK samples showed different bonding strength depending on their degree of crystallinity, with higher self‐bonding performance of mineral‐filled semi‐crystalline films. XRD did not show any modification of the PEEK microstructure as a result of plasma treatment, excluding a significant influence of crystallinity on the self‐bonding mechanisms. Nevertheless, plasma surface treatment successfully improved the self‐bonding strength of all the PEEK films tested, with larger increase in the case of semi‐crystalline unfilled materials. This could be interpreted to the increase in chain mobility that led to interfacial interpenetration of the amorphous phase.