Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

An approximate analytical model for unconventional reservoir considering variable matrix blocks and simultaneous matrix depletion

In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.

Analytical model for predicting time-dependent lateral deformation of geosynthetics-reinforced soil walls with modular block facing

To date,few models are available in the literature to consider the creep behavior of geosynthetics when predicting the lateral deformation(d)of geosynthetics-reinforced soil(GRS)retaining walls.In this study,a general hyperbolic creep model was first introduced to describe the long-term deformation of geosynthetics,which is a function of elapsed time and two empirical parameters a and b.The conventional creep tests with three different tensile loads(Pr)were conducted on two uniaxial geogrids to determine their creep behavior,as well as the a-Pr and b-Pr relationships.The test results show that increasing Pr accelerates the development of creep deformation for both geogrids.Meanwhile,a and b respectively show exponential and negatively linear relationships with Pr,which were confirmed by abundant experimental data available in other studies.Based on the above creep model and relationships,an accurate and reliable analytical model was then proposed for predicting the time-dependent d of GRS walls with modular block facing,which was further validated using a relevant numerical investigation from the previous literature.Performance evaluation and comparison of the proposed model with six available prediction models were performed.Then a parametric study was carried out to evaluate the effects of wall height,vertical spacing of geogrids,unit weight and internal friction angle of backfills,and factor of safety against pullout on d at the end of construction and 5 years afterwards.The findings show that the creep effect not only promotes d but also raises the elevation of the maximum d along the wall height.Finally,the limitations and application prospects of the proposed model were discussed and analyzed.

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.

Exploration of Ideological and Political Materials for the Course of Inorganic and Analytical Chemistry for Environmental and Ecological Engineering Major

Integrating ideological and political theories teaching into the whole process of classroom teaching construction is a new requirement for implementing the fundamental task of cultivating people by virtue and playing the role of collaborative education.In order to realize the seamless integration of inorganic and analytical chemistry courses and ideological and political education,this paper summarizes the current situation of ideological and political research on inorganic and analytical chemistry courses in three major databases in China(VIP,CNKI and Wanfang),and sorts out the knowledge points,ideological and political elements and educational goals according to the content of the course chapters,to provide a basic guarantee for the ideological and political education construction of the course.

GIS-Based Multi-Criteria Decision Analysis (MCDA) and Analytical Hierarchy Process (AHP) Techniques to Derive Flood Risks Management on Rice Productivity in Gishari Marshland

Floods are phenomenon with significant socio-economic implications mainly for human loss, agriculture, livestock, soil loss and land degradation, for which many researchers try to identify the most appropriate methodologies by analyzing their temporal and spatial development. This study therefore attempts to employ the GIS-based multi-criteria decision analysis and analytical hierarchy process techniques to derive the flood risks management on rice productivity in the Gishari Agricultural Marshland in Rwamagana district, Rwanda. Here, six influencing potential factors to flooding, including river slope, soil texture, Land Use Land Cover through Land Sat 8, rainfall, river distance and Digital Elevation Model are considered for the delineation of flood risk zones. Data acquisition like Landsat 8 images, DEM, land use land cover, slope, and soil class in the study area were considered. Results showed that if the DEM is outdated or inaccurate due to changes in the terrain, such as construction, excavation, or erosion, the predicted flood patterns might not reflect the actual water flow. This could result unexpected flood extents and depths, potentially inundating rice fields that were not previously at risk and this, expectedly explained that the increase 1 m in elevation would reduce the rice productivity by 0.17% due to unplanned flood risks in marshland. It was found that the change in rainfall distribution in Gishari agricultural marshland would also decrease the rice productivity by 0.0018%, which is a sign that rainfall is a major factor of flooding in rice scheme. Rainfall distribution plays a crucial role in flooding analysis and can directly impact rice productivity. Oppositely, another causal factor was Land Use Land Cover (LULC), where the Multivariate Logistic Regression Model Analysis findings showed that the increase of one unit in Land Use Land Cover would increase rice productivity by 0.17% of the total rice productivity from the Gishari Agricultural Marshland. Based on findings from these techniques, the Gishari Agricultural Marshlands having steeped land with grassland is classified into five classes of flooding namely very low, low, moderate, high, and very high which include 430%, 361%, 292%, 223%, and 154%. Government of Rwanda and other implementing agencies and major key actors have to contribute on soil and water conservation strategies to reduce the runoff and soil erosion as major contributors of flooding.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Understanding Pseudocapacitance Mechanisms by Synchrotron X-ray Analytical Techniques

Pseudocapacitive materials that store charges via reversible surface or near-surface faradaic reactions are capable of overcoming the capacity limitations of electrical double-layer capacitors.Revealing the structure–activity relationship between the microstructural features of pseudocapacitive materials and their electrochemical performance on the atomic scale is the key to build high-performance capacitor-type devices containing ideal pseudocapacitance effect.Currently,the high brightness(flux),and spectral and coherent nature of synchrotron X-ray analytical techniques make it a powerful tool for probing the structure–property relationship of pseudocapacitive materials.Herein,we report a comprehensive and systematic review of four typical characterization techniques(synchrotron X-ray diffraction,pair distribution function[PDF]analysis,soft X-ray absorption spectroscopy,and hard X-ray absorption spectroscopy)for the study of pseudocapacitance mechanisms.In addition,we offered significant insights for understanding and identifying pseudocapacitance mechanisms(surface redox pseudocapacitance,intercalation pseudocapacitance,and the extrinsic pseudocapacitance phenomenon in battery materials)by combining in situ hard XAS and electrochemical analyses.Finally,a perspective for further depth of understanding into the pseudocapacitance mechanism using synchrotron X-ray analytical techniques is proposed.

Analytical Modeling and Mechanism Analysis of Time-Varying Excitation for Surface Defects in Rolling Element Bearings

Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.

Analytical model of 2D leakoff in waterflood-induced fractures

Waterflood-induced fractures,also known as self-induced fractures,spontaneously form at injection wells during waterflooding.These fractures propagate long distances through rock,allowing injected fluids to travel far away from a well,both within and outside the flooding layer.Essentially,the me-chanics of waterflood-induced fracture propagation is similar to that of hydraulic fractures,which are intentionally created for reservoir stimulation.Fracturing models developed for hydraulic fractures can also be applied to waterflood-induced fractures.However,waterflood-induced fractures are typically pumped with much larger volumes of water or brine and grow much longer in time.As a result,fluid leakoff from waterflood fractures into the formation is more extensive and two-dimensional(2D),a characteristic that is often ignored in a majority of modern fracturing simulators,making their appli-cation to waterflood fractures unreliable.In this work,we revisit the problem of leakoff for long-growing waterflood-induced fractures and develop a new analytical model for fluid leakoff that provides improved predictions of fracture geometry and can be easily implemented in fracturing simulators.We incorporate the developed solution into the classical Perkins-Kern-Nordgren(PKN)model of fracture growth,which shows that the choice of the Carter or a 2D leakoff model greatly impacts fracture ge-ometry at large time.The conducted parametric study shows while a toughness-dominated regime af-fects fracture evolution,most of fracture lifetime occurs in a viscosity-and-leakoff-dominated regime.We also develop an asymptotic solution for a leakoff profile in the limiting case of 2D leakoff domination(~~M and~~K).Finally,we study 3D fracture growth and out-of-zone injection with three layers and a complex structure of zones.The study shows that ignoring the 2D leakoff during simulation results in a significant overestimation of fracture geometry predictions.The present work,thus,plays an important role in improving waterflood fracture modelling,as it highlights the significance of 2D leakoff in waterflood-induced fractures and provides a reliable analytical model for fluid leakoff that can be incorporated into modern fracture simulators.

UV/Vis-based process analytical technology to improve monoclonal antibody and host cell protein separation

Process analytical technology(PAT) is gaining more interest in the biomanufacturing industry because of its potential to improve operational control and compliance through real-time quality assurance.Currently, biopharmaceutical producers mainly monitor chromatographic processes with ultraviolet/visible(UV/Vis) absorbance. However, this measurement has a very limited correlation with purity and quantity. The current study aims to determine the concentration of monoclonal antibody(mAb) and host cell proteins(HCPs) using a build-in UV/Vis monitoring during Protein A affinity chromatography and to optimize the separation conditions for high purity of mAb and minimizing the HCPs content. The eluate was analyzed through in-line UV/Vis at 280 and 410 nm, representing mAb and HCPs concentration,respectively. Each 0.1 column volume(CV) fraction of UV/Vis chromatogram peak area were calculated,and different separation conditions were then compared. The optimum conditions of mAb separation were found as 12 CV loading, elution at pH 3.5, and starting the collection at 0.5 CV point, resulting in high m Ab recovery of 95.92% and additional removal of 49.98% of HCP comparing with whole elution pool. This study concluded that UV/Vis-based in-line monitoring at 280 and 410 nm showed a high potential to optimize and real-time control Protein A affinity chromatography for mAb purification from HCPs.

An Approximate Analytical Method for a Slot Ring Radome

In this paper,an in-band and out-of-band microwave wireless power-transmission characteristic analysis of a slot ring radome based on an approximate analytical method is proposed.The main contribution of this paper is that,in the approximate analysis of the ring radome,a unified expression of the incident field on the radome surface is derived with E-plane and H-plane scanning,and the ring is approximated as 30 segments of straight strips.Solving the corresponding 60×60 linear equations yields the electric current distribution along the ring strip.The magnetic current along the complementary slot ring is obtained by duality.Thanks to the fully analytical format of the current distribution,the microwave wireless power-transmission characteristics are efficiently calculated using Munk’s scheme.An example of a slot ring biplanar symmetric hybrid radome is used to verify the accuracy and efficiency of the proposed scheme.The central processing unit(CPU)time is about 690 s using Ansys HFSS software versus 2.82 s for the proposed method.

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.

Temperature Field in Laser Line Scanning Thermography: Analytical Calculation and Experiment

The temperature field in laser line scanning thermography is investigated comprehensively in this work,including analytical calculation and experiment.Firstly,the principle of laser line scanning thermography is analyzed.On this basis,a physical laser line scanning model is proposed.Afterwards,based on Fourier transform(FT)and segregation variablemethod(SVM),the heat conduction differential equation in laser line scanning thermography is derived in detail.The temperature field of the composite-based coatings model with defects is simulated numerically.The results show that the laser line scanning thermography can effectively detect the defects in the model.The correctness of the analytical calculation is verified by comparing the surface temperature distribution obtained by analytical calculation and numerical simulation.Additionally,an experiment is carried out and the changeable surface temperature obtained by analytical calculation is compared with the experimental results.It shows that the error of maximum temperature obtained by analytical calculation and by experiment is 8%with high accuracy,which proves the correctness of analytical calculation and enriches the theoretical foundation of laser line scanning thermography.

Experimental investigation and analytically modeling of hysteretic behavior of rigid bus-flexible connectors of 220 kV electrical substations

This paper describes the quasi-static testing and analytical modelling of the hysteretic behavior of aluminum alloy rigid bus-flexible connectors of 220 kV electrical substations.The main objective of the study is to experimentally investigate the hysteretic behavior of six different types of rigid bus-flexible connectors 220 kV electrical substations when subjected to cyclic loading.Another objective is to theoretically study the flexibility and effectiveness of a previously proposed analytical model in fitting the experimental hysteresis loops of the tested rigid bus-flexible connectors.The experimental investigation indicates that the tested rigid bus-flexible connectors exhibit highly asymmetric hysteresis behavior along with tension stiffening effect.The theoretical study demonstrates that the generalized Bouc-Wen model has high flexibility and is effective in fitting the experimental hysteresis resisting force-displacement curves of the six tested rigid bus-flexible connectors.

Revisiting the analytical solutions for ultimate bearing capacity of pile embedded in rocks

This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified HoekeBrown failure criterion.Although this criterion is considered a reference value for empirical and numerical calculations,some limitations of its basic simplifications have not been clarified yet.This research compares the analytical results obtained from the novel discontinuity layout optimization(DLO)method and the numerical solutions from the finite difference method(FDM).The limitations of the analytical solution are considered by comparing different DLO failure modes,thus allowing for the first time a critical evaluation of its scope and conditioning for implementation.Errors of up to 40%in the bearing capacity and unrealistic failure modes are the main issues in the analytical solution.The main aspects of the DLO method are also analyzed with an emphasis on the linearization of the rock failure criterion and the accuracy resulting from the discretization size.The analysis demonstrates DLO as a very efficient and accurate tool to address the pile tip bearing capacity,presenting considerable advantages over other methods.

Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

In this paper, the axial-flux permanent magnet driver is modeledand analyzed in a simple and novel way under three-dimensional cylindricalcoordinates. The inherent three-dimensional characteristics of the deviceare comprehensively considered, and the governing equations are solved bysimplifying the boundary conditions. The axial magnetization of the sectorshapedpermanent magnets is accurately described in an algebraic form bythe parameters, which makes the physical meaning more explicit than thepurely mathematical expression in general series forms. The parameters of theBessel function are determined simply and the magnetic field distribution ofpermanent magnets and the air-gap is solved. Furthermore, the field solutionsare completely analytical, which provides convenience and satisfactoryaccuracy for modeling a series of electromagnetic performance parameters,such as the axial electromagnetic force density, axial electromagnetic force,and electromagnetic torque. The correctness and accuracy of the analyticalmodels are fully verified by three-dimensional finite element simulations and a15 kW prototype and the results of calculations, simulations, and experimentsunder three methods are highly consistent. The influence of several designparameters on magnetic field distribution and performance is studied and discussed.The results indicate that the modeling method proposed in this papercan calculate the magnetic field distribution and performance accurately andrapidly, which affords an important reference for the design and optimizationof axial-flux permanent magnet drivers.

Application of GIS based analytical hierarchy process and multicriteria decision analysis methods to identify groundwater potential zones in Jedeb Watershed, Ethiopia

The hydrogeological situation of the study area requires the identification of groundwater potential.Remote sensing and satellite data have proven to be reliable tools for understanding various factors that affect groundwater occurrence and movement.This study employed weighted overlay analysis based on satellite imagery and secondary data to create a thematic map for characterizing groundwater potentials in the study area located within Abbay Basin,Ethiopia.Remote sensing(RS)and GIS-based Fuzzy-Analytical Hierarchy Process methods were utilized to classify groundwater potential(GWP)zones into five categories:Very good,good,moderate,poor,and very poor.The central and eastern parts of the study area were identified as having high(33.186%)and very high(2.351%)groundwater potentials,while the western part exhibited poor and very poor potential areas.The groundwater potential map delineated higher and moderate potentials,suitable for installing shallow and production bores.This research demonstrates the effectiveness of RS and GIS techniques for delineating groundwater potential zones,which can aid in the planning and management of groundwater resources.The research findings have the potential to contribute to the formulation of improved groundwater management programs in the study area.