Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom

High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).

Numerical Modelling of Ore-forming Dynamics of Fractal Dispersive Fluid Systems

Based on an analysis of the fractal structures and mass transport mechanism of typical shear-fluid-ore formation system, the fractal dispersion theory of the fluid system was used in the dynamic study of the ore formation system. The model of point-source diffusive illuviation of the shear-fluid-ore formation system was constructed, and the numerical simulation of dynamics of the ore formation system was finished. The result shows that: (1) The metallogenic system have nested fractal structure. Different fractal dimension values in different systems show unbalance and inhomogeneity of ore-forming processes in the geohistory. It is an important parameter to symbolize the process of remobilization and accumulation of ore-forming materials. Also it can indicate the dynamics of the metallogenic system quantitatively to some extent. (2) In essence, the fractal dispersive ore-forming dynamics is a combination of multi-processes dominated by fluid dynamics and supplemented by molecule dispersion in fluids and fluid-rock interaction. It changes components and physico-chemical properties of primary rocks and fluids, favouring deposition and mineralization of ore-forming materials. (3) Gold ore-forming processes in different types of shear zones are quite different. (1) In a metallogenic system with inhomogeneous volumetric change and inhomogeneous shear, mineralization occurs in structural barriers in the centre of a shear zone and in geochemical barriers in the shear zone near its boundaries. But there is little possibility of mineralization out of the shear zone. (2) As to a metallogenic system with inhomogeneous volumetric change and simple shear, mineralization may occur only in structural barriers near the centre of the shear zone. (3) In a metallogenic system with homogeneous volumetric change and inhomogeneous shear, mineralization may occur in geochemical barriers both within and out of the shear zone.

Novel method for the determination of five carbamate pesticides in water samples by dispersive liquid-liquid microextraction combined with high performance liquid chromatography

A novel method for the determination of five carbamate pesticides （metolcarb, carbofuran, carbaryl, isoprocard and diethofencard） in water samples was developed by dispersive liquid-liquid microextraction （DLLME） coupled with high performance liquid chromatography-diode array detector （HPLC-DAD）. Some experimental parameters that influence the extraction efficiency were studied and optimized to obtain the best extraction results. Under the optimum conditions for the method, the calibration curve was linear in the concentration range from 5 to 1000 ng mL^-1 for all the five carbamate pesticides, with the correlation coefficients （r^2） varying from 0.9984 to 0.9994. Good enrichment factors were achieved ranging from 80 to 177- fold, depending on the compound. The limits of detection （LODs） （S/N = 3） were ranged from 0.1 to 0.5 ng mL^-1. The method has been successfully applied to the analysis of the pesticide residues in environmental water samples.

Folded localized excitations in the (2+1)-dimensional modified dispersive water-wave system

By using a mapping approach and a linear variable separation approach, a new family of solitary wave solutions with arbitrary functions for the （2＋1）-dimensional modified dispersive water-wave system （MDWW） is derived. Based on the derived solutions and using some multi-valued functions, we obtain some novel folded localized excitations of the system.

Ionic liquid based dispersive liquid-liquid microextraction of aromatic amines in water samples

In this work, a new microextraction method termed ionic liquid based dispersive liquid-liquid microextraction （IL-DLLME） was demonstrated for the extraction of 2-methylaniline, 4-chloroaniline, 1-naphthylamine and 4-aminobiphenyl in aqueous matrices. After extraction the ionic liquid （IL） phase was injected directly into the high performance liquid chromatography （HPLC） system for determination. Some parameters that might affect the extraction efficiency were optimized. Under the optimum conditions, good linear relationship, sensitivity and reproducibility were obtained. The limits of detection （LOD, S/N = 3） for the four analytes were in the range of 0.45-2.6 μg L^-1. The relative standard deviations （R.S.D., n = 6） were in the range of 6.2-9.8%. This method was applied for the analysis of the real water samples. The recoveries ranged from 93.4 to 106.4%. The main advantages of the method are high speed, high recovery, good repeatability and volatile organic solvent-free.

Fast determination of multi-mycotoxins in corn by dispersive solid-phase extraction coupled with ultra-performance liquid chromatography with tandem quadrupole time-of-flight mass spectrometry

A fast analytical method for the simultaneous determination of 9 mycotoxins, including alfatoxins （B1, B2, G1, and G2）, fumonisins （B1, B2 and B3）, zearalenone, and deoxynivalenol in corn using dispersive solid-phase extraction method and ultra-performance liquid chromatography coupled to tandem quadrupole time-of-lfight mass spectrometry （UPLC-Q-TOF-MS） was developed and validated. Samples were extracted with acetonitrile-water （84：16, v：v, containing 1% acetic acid） using ultrasonic extraction. The extracts were puriifed with a dispersive SPE method using C18 as a cleaning agent. The ifnal clear extracts were dried by nitrogen blowing and subsequently redissolved in methanol-water （5：5, v：v）. The samples were then analyzed by UPLC-Q-TOF-MS with 0.1% formic acid in ammonium acetate-methanol as mobile phase. The mean recoveries were ranged from 68.0 to 120.0%, and the relative standard deviation （RSD） ranged from 0.18 to 6.29%. Limits of detections ranged from 0.05 to 50 μg kg？1, and limits of quantiifcation ranged from 0.1 to 200 μg kg？1, which were below the legal limits set by the European Union for the legislated mycotoxins. The developed method was applied to 130 corn samples. Among the mycotoxins studied, alfatoxins B1 and fumonisins B1, B2 and B3 were the most predominant mycotoxins, and their concentrations were 0–593.12, 0–2.01×104, 0–6.94×103 and 0–3.05×103 μg kg–1, respectively.

Exact travelling wave solutions for （1＋ 1）-dimensional dispersive long wave equation

A complete discrimination system for the fourth order polynomial is given. As an application, we have reduced a （1＋1）-dimensional dispersive long wave equation with general coefficients to an elementary integral form and obtained its all possible exact travelling wave solutions including rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions double periodic solutions. This method can be also applied to many other similar problems.

Three kinds of nonlinear dispersive waves in elastic rods with finite deformation

On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.

Dispersive Liquid-liquid Microextraction Combined with High-performance Liquid Chromatography for the Determination of Clozapine and Chlorpromazine in Urine

A simple method has been proposed for the determination of clozapine （CLZ） and chlorpromazine （CPZ） in human urine by dispersive liquid-liquid microextraction （DLLME） in combination with high-performance liquid chromatography-ultraviolet detector （HPLC-UV）. All important variables influencing the extraction efficiency, such as pH, types of the extraction solvent and the disperser solvent and their volume, ionic strength and centrifugation time were investigated and optimized. Under the optimal conditions, the limit of detection （LODs） and quantification （LOQs） of the method were 13 and 39 ng/mL for CLZ, and 2 and 6 ng/mL for CPZ, respectively. The relative standard deviations （RSDs） of the targets were less than 5.1% （C=0.100 μg/mL, n=9）. Good linear behaviors over the tested concentration ranges were obtained with the values of R20.999 for the targets. The absolute extraction efficiencies of CLZ and CPZ from the spiked blank urine samples were 98.3% and 97.8%, respectively. The applicability of the technique was validated by analyzing urine samples and the mean recoveries for spiked urine samples ranged from 93.3% to 105.0%. The method was successfully applied for the determination of CLZ and CPZ in real human urine.

Determination of Amitraz in the Honey Samples by Dispersive Liquid-Liquid Microextraction Followed by Gas Chromatography—Flame Ionization Detection

Dispersive liquid-liquid microextraction (DLLME) followed by gas chromatography–flame ionization detection (GC-FID), as a simple, rapid and efficient method, was developed for the determination of amitraz in honey samples. This method involves the use of an appropriate mixture of the extraction and disperser solvents for the formation of a cloudy solution in 5.0 mL aqueous sample containing amitraz. After extraction, phase separation was performed by centrifugation and the concentrated amitraz in the sedimented phase was determined by gas chromatography—flame ionization detection (GC-FID). Some important parameters such as the type and volume of extraction and disperser solvents, and the effect of pH and salt on the extraction recovery of amitraz were investigated. Under the optimum conditions (13 μL of carbon tetrachloride as an extraction solvent, 1 mL of acetonitrile as a disperser solvent, no salt addition and pH 6) preconcentration factor and the extraction recovery were 955 and 95.5%, respectively. The linear range was 0.01 - 1.0 mg?kg–1 and the limit of detection was 0.0015 mg?kg–1. The relative standard deviation (RSD, n = 4) for 0.1 mg?kg–1 of amitraz was 3.2%. The recoveries of amitraz from honey samples at the spiking levels of 0.1 mg?kg-1 were 78.8 and 98.2%. The results indicated that DLLME is an efficient technique for the extraction of amitraz in honey samples.

Perfectly matched layer implementation for ADI-FDTD in dispersive media

Alternating direction implicit finite difference time domain （ADI-FDTD） method is unconditionally stable and the maximum time step is not limited by the Courant stability condition, but rather by numerical error. Compared with the conventional FDTD method, the time step of ADI-FDTD can be enlarged arbitrarily and the CPU cost can be reduced. 2D perfectly matched layer （PML） absorbing boundary condition is proposed to truncate computation space for ADI-FDTD in dispersive media using recursive convolution（RC） method and the 2D PML formulations for dispersive media are derived. ADI-FDTD formulations for dispersive media can be obtained from the simplified PML formulations. The scattering of target in dispersive soil is simulated under sine wave and Gaussian pulse excitations and numerical results of ADI-FDTD with PML are compared with FDTD. Good agreement is observed. At the same time the CPU cost for ADI-FDTD is obviously reduced.

Impact of Fiber Dispersion on Performance of Entanglement-Based Dispersive Optics Quantum Key Distribution

Dispersive optics quantum key distribution(DO-QKD)based on energy-time entangled photon pairs is an important QKD scheme.In DO-QKD,the arrival time of photons is used in key generation and security analysis,which would be greatly affected by fiber dispersion.In this work,we establish a theoretical model of the entanglement-based DO-QKD system,considering the protocol,physical processes(such as fiber transmission and single-photon detection),and the analysis of security tests.Based on this theoretical model,we investigate the influence of chromatic dispersion introduced by transmission fibers on the performance of DO-QKD.By analyzing the benefits and costs of dispersion compensation,the system performance under G.652 and G.655 optical fibers are shown,respectively.The results show that dispersion compensation is unnecessary for DO-QKD systems in campus networks and even metro networks.Whereas,it is still required in DO-QKD systems with longer fiber transmission distances.

Dispersive Nonlinearity in Er-Doped Optical Fiber

Optical dispersive nonlinearities in Er-doped optical fiber are discussed and measured at the third window wavelength 1.55 μm for optical communications firstly. The experimental method, which is developed by us, is based on dynamic scanning for fixed-point-interference (DSFPI) of two fiber beams. The real part and complex value of the third-order susceptibility at the wavelength are also obtained from the measured Kerr coefficient and nonlinear-absorption coefficient reported elsewhere.

Degradation Dynamics and Residue Analysis of Flubendiamide in Cabbage and Soil by Liquid Chromatography-Tandem Mass Spectrometry with Dispersive Solid Phase Extraction

To formulate a scientific basis for a reasonable spray dose and safe interval period of 20% flubendiamide water dispersible granule (WDG) on controlling vegetable pests, degradation dynamics of flubendiamide in cabbage and soil was analyzed in this study. Dissipation and residue of flubendiamide in 20% flubendiamide WDG in cabbage and soil under field conditions were investigated by liquid chromatography-tandem mass spectrometry with dispersive solid phase extraction. Results showed that the degradation dynamic equations of flubendiamide in cabbage and soil were based on the first-order reaction dynamic equations. The half-lives of the degradation of flubendiamide were 3.51 d to 3.96 d and 3.43 d to 3.87 d in the cabbage of Yangzhou and Jingzhou, respectively, and 4.42 d to 5.13 d and 4.37 d to 4.99 d in the soil of Yangzhou and Jingzhou, respectively. The terminal residues of flubendiamide in the cabbage of Yangzhou and Jingzhou were 0.0247 mg·kg-1 to 0.0393 mg·kg-1 and 0.0225 mg·kg-1 to 0.0273 mg·kg-1, respectively, when 20% flubendiamide WDG was applied at a dose of0.050g·m-2. Flubendiamide is safe to be applied in cabbage fields at the recommended dose.

Multiple Soliton Solutions of the Dispersive Long-Wave Equations

Using a simple homogeneous balance method,which is very concise and primary,we find the multiple soliton solutions of the dispersive long-wave equations.The method can be generalized to deal with the higher dimensional dispersive long-wave equations and other class of nonlinear equation.

Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation

A general solution, including three arbitrary functions, is obtained for a （2~l）-dimensional modified dispersive water-wave （MDWW） equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.

Frequency-Dependent FDTD Method Using DSP for Arbitrary Dispersive Media

A new frequency dependent finite difference time domain (FD FDTD) method using digital signal processing (DSP) is proposed. The dispersive media is characterized as an infinite impulse response (IIR) filter, directly leading to FDTD equations. The representation of a dispersive medium is therefore converted to a problem of digital IIR design. It is shown that the numerical results are consistent with analytic solution.

Utilization of Dispersive Liquid-Liquid Microextraction Coupled with HPLC-UV as a Sensitive and Efficient Method for the Extraction and Determination of Oleanolic Acid and Ursolic Acid in Chinese Medicinal Herbs

Isomeric triterpenic acids of oleanolic acid (OA) and ursolic acid (UA) both have very low ultraviolet absorption and always exist in the same plant, so the separation and simultaneous determination of them have been a difficult task. In this study, a sensitive method combining dispersive liquid-liquid microextraction (DLLME) with HPLC-UV was developed for the extraction and determination of OA and UA in traditional Chinese medicinal herbs (CMHs). Variables influencing DLLME such as type and volume of extraction solvent, volume of dispersive solvent, ionic strength, aqueous phase pH, extraction time, centrifugation speed and time, and sample volume were investigated and optimized. Under the optimum conditions, both OA and UA attained favorable extraction efficiencies with enrichment factors 1378 and 933, respectively. The linear dynamic ranges of 0.07 - 30.4 μg?mL–1 for OA and 0.08 - 33.6 μg?mL–1 for UA were obtained with square correlation coefficients of 0.9963. The detection limits of OA and UA were both 0.02 μg?mL–1. The method recoveries ranged between 88.2% - 116.2% for OA and 85.7% - 108.2% for UA with the RSDs (n = 5) lower than 8.6%. The proposed method was successfully applied to concentrate and simultaneously determine these two triterpenic acids in Hedyotis diffusa and Eriobotrya japonica samples.

Dispersive liquid-liquid microextraction,an effective tool for the determination of synthetic cannabinoids in oral fluid by liquid chromatography-tandem mass spectrometry

In the present work,dispersive liquid-liquid microextraction(DLLME)was used to extract six synthetic cannabinoids(JWH-018,JWH-019,JWH-073,JWH-200,or WIN 55,225,JWH-250,and AM-694)from oral fluids.A rapid baseline separation of the analytes was achieved on a bidentate octadecyl silica hydride phase(Cogent Bidentate C18;4.6 mm×250 mm,4μm)maintained at 37℃,by eluting in isocratic conditions(water:acetonitrile(25:75,V/V)).Detection was performed using positive electrospray ionization-tandem mass spectrometry.The parameters affecting DLLME(pH and ionic strength of the aqueous phase,type and volume of the extractant and dispersive solvent,vortex and centrifugation time)were optimized for maximizing yields.In particular,using 0.5 mL of oral fluid,acetonitrile(1 mL),was identified as the best option,both as a solvent to precipitate proteins and as a dispersing solvent in the DLLME procedure.To select an extraction solvent,a low transition temperature mixture(LTTM;composed of sesamol and chlorine chloride with a molar ratio of 1:3)and dichloromethane were compared;the latter(100μL)was proved to be a better extractant,with recoveries ranging from 73%to 101%by vortexing for 2 min.The method was validated according to the guidelines of Food and Drug Administration bioanalytical methods:intra-day and inter-day precisions ranged between 4%and 18%depending on the spike level and analyte;limits of detection spanned from 2 to 18 ng/mL;matrixmatched calibration curves were characterized by determination coefficients greater than 0.9914.Finally,the extraction procedure was compared with previous methods and with innovative techniques,presenting superior reliability,rapidity,simplicity,inexpensiveness,and efficiency.