Application of the finite analytic numerical method to a flowdependent variational data assimilation

An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.

Utility and Application of a Versatile Analytical Method for MMF Calculation in AC Machines

A versatile analytical method(VAM) for calculating the harmonic components of the magnetomotive force(MMF) generated by diverse armature windings in AC machines has been proposed, and the versatility of this method has been established in early literature. However, its practical applications and significance in advancing the analysis of AC machines need further elaboration. This paper aims to complement VAM by augmenting its theory, offering additional insights into its conclusions, as well as demonstrating its utility in assessing armature windings and its application of calculating torque for permanent magnet synchronous machines(PMSM). This work contributes to advancing the analysis of AC machines and underscores the potential for improved design and performance optimization.

Review on analytical technologies and applications in metabolomics

Over the past decade,the swift advancement of metabolomics can be credited to significant progress in technologies such as mass spectrometry,nuclear magnetic resonance,and multivariate statistics.Currently,metabolomics garners widespread application across diverse fields including drug research and development,early disease detection,toxicology,food and nutrition science,biology,prescription,and chinmedomics,among others.Metabolomics serves as an effective characterization technique,offering insights into physiological process alterations in vivo.These changes may result from various exogenous factors like environmental conditions,stress,medications,as well as endogenous elements including genetic and protein-based influences.The potential scientific outcomes gleaned from these insights have catalyzed the formulation of innovative methods,poised to further broaden the scope of this domain.Today,metabolomics has evolved into a valuable and widely accepted instrument in the life sciences.However,comprehensive reviews focusing on the sample preparation and analytical methodologies employed in metabolomics within the life sciences are surprisingly scant.This review aims to fill that gap,providing an overview of current trends and recent advancements in metabolomics.Particular emphasis is placed on sample preparation,sophisticated analytical techniques,and their applications in life science research.

Bi-Objective Optimization: A Pareto Method with Analytical Solutions

Multiple objectives to be optimized simultaneously are prevalent in real-life problems. This paper develops a new Pareto Method for bi-objective optimization which yields analytical solutions. The Pareto optimal front is obtained in closed-form, enabling the derivation of various solutions in a convenient and efficient way. The advantage of analytical solution is the possibility of deriving accurate, exact and well-understood solutions, which is especially useful for policy analysis. An extension of the method to include multiple objectives is provided with the objectives being classified into two types. Such an extension expands the applicability of the developed techniques.

Hydrodynamic Performance of a Newly-Designed Pelagic and Demersal Trawls Using Physical Modeling and Analytical Methods for Cameroonian Industrial Fisheries

This study proposed the newly-designed Pelagic and demersal trawls for the fishing vessels operating in Cameroonian waters in pelagic and demersal fishing grounds. The engineering performances of both trawls were investigated using physical modelling method and analytical method based on the predicted equations. In a flume tank, a series of physical model tests based on Tauti’s law were performed to investigate the hydrodynamic and geometrical performances of both trawls and to assess the applicability of the analytical methods based on predicted equations. The results showed that in model scale, the working towing speed and door spread for the pelagic trawl were 3.5 knots and 1.85 m, respectively, and for the bottom trawl net they were 4.0 knots and 1.8 m. At that speed and door spread, the drag force, net opening height, and wing-end spread of the pelagic model trawl were 36.73 N, 0.89 m, and 0.86 m, respectively, and the swept area was 0.76 m2. Bottom trawl speed and door spread were 30.43 N, 0.38 m, and 0.45 m, respectively, and the swept area was 0.25 m2. The maximum difference between the experimental and analytical results of hydrodynamic performances was less than 56.22% and 41.45%, respectively, for pelagic and bottom trawls, the results of the geometrical performances obtained using predicted equations were close to the experimental results in the flume tank with a maximum relative error less than 12.85%. The newly developed pelagic and bottom trawls had advanced engineering performance for high catch efficiency and selectivity and could be used in commercial fishing operations in Cameroonian waters.

Symplectic partitioned Runge-Kutta method based onthe eighth-order nearly analytic discrete operator and its wavefield simulations

We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.

Development of analytical methods for polycyclic aromatic hydrocarbons (PAHs) in airborne particulates: A review

In the present work, the different sample collection, pretreatment and analytical methods for polycyclic aromatic hydrocarbons （PAHs） in airborne particulates is systematacially reviewed, and the applications of these pretreatment and analytical methods for PAHs are compared in detail. Some comments on the future expectation are also presented.

Methods of analytical mechanics for solving differential equations of first order

A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton-Noether method, the Lagrange-Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics.

Analytical methods for investigating in vivo fate of nanoliposomes:A review

Nanoliposomes are considered to be the most successful nanoparticle drug delivery system, but their fate in vivo has not been fully understood due to lack of reliable bioanalytical methods, which seriously limits the development of liposomal drugs. Hence, an overview of currently used bioanalytical methods is imperative to lay the groundwork for the need of developing a bioanalytical method for liposome measurements in vivo. Currently, major analytical methods for nanoliposomes measurement in vivo include fluorescence labeling, radiolabeling, magnetic resonance imaging（MRI）, mass spectrometry and computed tomography. In this review, these bioanalytical methods are summarized, and the advantages and disadvantages of each are discussed. We provide insights into the applicability and limitations of these analytical methods in the application of nanoliposomes measurement in vivo, and highlight the recent development of instrumental analysis techniques. The review is devoted to providing a comprehensive overview of the investigation of nanoliposomes design and associated fate in vivo, promoting the development of bioanalytical techniques for nanoliposomes measurement, and understanding the pharmacokinetic behavior, effectiveness and potential toxicity of nanoliposomes in vivo.

The Working Mechanism and An Analytic Method of the Deep Embedded Large Cylinder Structure

The large cylinder is a new-type structure that has been applied to harbor and offshore engineering. An analytic method of the relationship between loads and the structure displacement is developed based on the failure mode of deep embedded large cylinder structures. It can be used to calculate directly the soil resistance and the ultimate bearing capacity of the structure under usage. A new criterion of the large cylinder structure, which discriminates the deep embedded cylinder from the shallow embedded cylinder, is defined. Model tests prove that the proposed method is feasible for the analysis of deep embedded large cylinder structures.

Efficient and rapid accuracy estimation of the Earth's gravitational field from next-generation GOCE Follow-On by the analytical method

Firstly, a new analytical error model of the cumulative geoid height using the three-dimensional diagonal tensors of satellite gravity gradiometry （SGG） is introduced based on the variance-covariance matrix principle. Secondly, a study for the requirements demonstration on the next-generation GOCE Follow-On satellite gravity gradiometry system is developed using different satellite orbital altitudes and measurement accuracies of satellite gravity gradiometer by the new analytical error model of SGG. The research results show that it is preferable to design satellite orbital altitudes of 300 km–400km and choose the measurement accuracies of 10-13/s2 –10-15/s2 from satellite gravity gradiometer. Finally, the complementarity of the four-stage satellite gravity missions, including past CHAMP, current GRACE, and GOCE, and next-generation GOCE Follow-On, is contrastively demonstrated for precisely recovering the Earth’s full-frequency gravitational field with high spatial resolution.

Impedance Analytical Method of Wave Run-up and Reflection from A Slotted-Wall Caisson Breakwater

An impedance analytical method （IAM） is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of flow resistance. A set of algebraic expressions are obtained for free surface elevation inside and outside chamber, and reflection coefficient. The prediction of the reflection coefficients shows that the relative widths of the chamber inducing the minimum reflection coefficient for a slotted-wall caisson breakwater are in a range of 0.10～0.20, which are smaller than that （0.15～0.25） for a perforated-wall caisson breakwater. The reflection coefficients and free surface elevation obtained by the present model are compared with that of laboratory experiments carried out by previous researchers.

Analytical methods for determination of terbinafine hydrochloride in pharmaceuticals and biological materials

Terbinafine is a new powerful antifungal agent indicated for both oral and topical treatment of myco- sessince. It is highly effective in the treatment of determatomycoses. The chemical and pharmaceutical analysis of the drug requires effective analytical methods for quality control and pharmacodynamic and pharmacokinetic studies. Ever since it was introduced as an effective antifungal agent, many methods have been developed and validated for its assay in pharmaceuticals and biological materials. This article reviews the various methods reported during the last 25 years.

High-pressure phonon dispersion of copper by using the modified analytic embedded atom method

By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three high symmetry directions and four oft-symmetry directions, and then simulate the phonon dispersion curves of Cu at high pressures of 50, 100, and 150 GPa. The results show that the shapes of dispersion curves at high pressures are very similar to that at zero pressure. All the vibration frequencies of Cu in all vibration branches at high pressures are larger than the results at zero pressure, and increase correspondingly as pressure reaches 50, 100, and 150 GPa sequentially. Moreover, on the basis of phonon dispersion, we calculate the values of specific heat of Cu at different pressures. The prediction of thermodynamic quantities lays a significant foundation for guiding and judging experiments of thermodynamic properties of solids under high pressures.

Pioglitazone:A review of analytical methods

Pioglitazone is an oral anti-hyperglycemic agent. It is used for the treatment of diabetes mellitus type 2. It selectively stimulates nuclear receptor peroxisome proliferator-activated receptor gamma （PPAR-gamma）. It was the tenth-best-selling drug in the U.S. in 2008. This article examines published analytical methods reported so far in the literature for the determination of pioglitazone in biological samples and pharmaceutical formulations. They include various techniques like electrochemical methods, spectrophotometry, capillary electrophoresis, high-performance liquid chromatography, liquid chromatography-electrospray ionization-tandem mass spectrometry and high-performance thin layer chromatography.

Evaluation of bioefficacy ofα-cypermethrin in long lasting impregnated net(Interceptor~) using analytical method

Objective:To evaluate relationship betweenα-cypermethrin residues in Interceptor~? nets by using HPTLC methods and mortality percentage in standard WHO’s method 'cone test' after repeated washings.Methods:Interceptor~? containingα-cypermethrin was provided by BASF Company.The washing procedure and bioassay tests were carried out according to the WHO-recommended methods.Malaria vector,An.stephensi was exposed to impregnated bed net for three minutes and then mortality measured after 24 hour recovery period.Chemical analysis was carried out in chemical laboratory by using high performance thin layer chromatography method.Results:Result of cone bioassay method showed that washing reduced the efficacy of Interceptor~? bed net from 100%in unwashed nets to 15%at 20 washes.After 20 washes,nets contain(61.2±2.8) mg/m^2 resulting 15%mortality in cone test.Killing activity was reduced when nets were washed.Conclusions:Results will provide an essential clue for monitoring and evaluation of bioefficacy of any long lasting impregnated bed net for quality control.Findings of this study will be useful for WHO.local investigators and people who wish to use pyrethroid-impregnated bed nets for malaria vector control.

Analytical method of radiation by a wave energy device with dual rectangular floating bodies

The system with one floating rectangular body on the free surface and one submerged rectangular body has been applied to a wave energy conversion device in water of finite depth. The radiation problem by this device on a plane incident wave is solved by the use of an eigenfunction expansion method, and a new analytical expression for the radiation velocity potential is obtained. The wave excitation force is calculated via the known incident wave potential and the radiation potential with a theorem of Haskind employed. To verify the correctness of this method, an example is computed respectively through the bound element method and analytical method. Results show that two numerical methods. are in good agreement, which shows that the present method is applicable. In addition, the trends of hydrodynamic coefficients and wave force are analyzed under different conditions by use of the present analytical method.

Application of the state space model to the system of wave energy conversion Analytical method for wave forces on singleoscillating rectangular buoy

A new analytical method is proposed to analyze the force acting on a rectangular oscillating buoy due to linear waves.In the method a new analytical expression for the diffraction velocity potential is obtained first by use of theeigenfunction expansion method and then the wave excitation force is calculated by use of the known incident wavepotential and the diffraction potential. Compared with the classical analytical method, it can be seen that the presentmethod is simpler for a two-dimensional problem due to the comparable effort needed for the computation ofdiffraction potential and for that of radiated potential. To verify the correctness of the method, a classical example inthe reference is recomputed and the obtained results are in good accordance with those by use of other methods,which shows that the present method is correct.

Similarity solutions of vertical plane wall plume based on finite analytic method

The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.

AN ANALYTICAL METHOD FOR A MIXED BOUNDARY VALUE PROBLEM OF CIRCULAR PLATES UNDER ARBITRARY LATERAL LOADS

In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.