Analytical Solutions for Testing of Baroclinic and Wind-Driven Three-Dimensional Hydrodynamic Models

It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.

Three-dimensional analytical solution of acoustic emission source location for cuboid monitoring network without pre-measured wave velocity

To find analytical solutions of nonlinear systems for locating the acoustic emission/microseismic（AE/MS） source without knowing the wave velocity of structures, the sensor location coordinates were simplified as a cuboid monitoring network. Different locations of sensors on upper and lower surfaces were considered and used to establish nonlinear equations. Based on the proposed functions of time difference of arrivals, the analytical solutions were obtained using five sensors under three networks. The proposed analytical solutions were validated using authentic data of numerical tests and experiments. The results show that located results are consistent with authentic data, and the outstanding characteristics of the new solution are that the solved process is not influenced by the wave velocity knowledge and iterated algorithms.

Three-dimensional analytical solution of acoustic emission or microseismic source location under cube monitoring network

To find the analytical solution of the acoustic emission/microseismic(AE/MS) source location coordinates, the sensor location coordinates were optimized and simplified. A cube monitoring network of sensor location was selected, and the AE/MS source localization equations were established. A location method with P-wave velocity by analytical solutions (P-VAS) was obtained with these equations. The virtual location tests show that the relocation results of analytical method are fully consistent with the actual coordinates for events both inside and outside the monitoring network; whereas the location error of traditional time difference method is between 0.01 and 0.03 m for events inside the sensor array, and the location errors are larger, which is up to 1080986 m for events outside the sensor array. The broken pencil location tests were carried out in the cross section of 100 mm×98 mm, 350 mm-length granite rock specimen using five AE sensors. Five AE sources were relocated with the conventional method and the P-VAS method. For the four events outside monitoring network, the positioning accuracy by P-VAS method is higher than that by the traditional method, and the location accuracy of the larger one can be increased by 17.61 mm. The results of both virtual and broken pencil location tests show that the proposed analytical solution is effective to improve the positioning accuracy. It can locate the coordinates of AE/MS source only using simple four arithmetic operations, without determining the fitting initial value and iterative calculation, which can be solved by a conventional calculator or Microsoft Excel.

Kangfuxin solution alleviates esophageal stenosis after endoscopic submucosal dissection:A natural ingredient strategy

BACKGROUND Esophageal stricture ranks among the most significant complications following endoscopic submucosal dissection(ESD).Excessive fibrotic repair is a typical pathological feature leading to stenosis after ESD.AIM To examine the effectiveness and underlying mechanism of Kangfuxin solution(KFX)in mitigating excessive fibrotic repair of the esophagus post-ESD.METHODS Pigs received KFX at 0.74 mL/kg/d for 21 days after esophageal full circumferential ESD.Endoscopic examinations occurred on days 7 and 21 post-ESD.In vitro,recombinant transforming growth factor(TGF)-β1(5 ng/mL)induced a fibrotic microenvironment in primary esophageal fibroblasts(pEsF).After 24 hours of KFX treatment(at 1.5%,1%,and 0.5%),expression ofα-smooth muscle actin-2(ACTA2),fibronectin(FN),and type collagen I was assessed.Profibrotic signaling was analyzed,including TGF-β1,Smad2/3,and phosphor-smad2/3(p-Smad2/3).RESULTS Compared to the Control group,the groups treated with KFX and prednisolone exhibited reduced esophageal stenosis,lower weight loss rates,and improved food tolerance 21 d after ESD.After treatment,Masson staining revealed thinner and less dense collagen fibers in the submucosal layer.Additionally,the expression of fibrotic effector molecules was notably inhibited.Mechanistically,KFX downregulated the transduction levels of fibrotic functional molecules such as TGF-β1,Smad2/3,and p-Smad2/3.In vitro,pEsF exposed to TGF-β1-induced fibrotic microenvironment displayed increased fibrotic activity,which was reversed by KFX treatment,leading to reduced activation of ACTA2,FN,and collagen I.The 1.5%KFX treatment group showed decreased expression of p-Smad 2/3 in TGF-β1-activated pEsF.CONCLUSION KFX showed promise as a therapeutic option for post-full circumferential esophageal ESD strictures,potentially by suppressing fibroblast fibrotic activity through modulation of the TGF-β1/Smads signaling pathway.

AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot＇s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot＇s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Exact analytical solutions of three-dimensional Gross-Pitaevskii equation with time-space modulation

By the generalized sub-equation expansion method and symbolic computation, this paper investigates the （3＋1）dimensional Gross-Pitaevskii equation with time-and space-dependent potential, time-dependent nonlinearity, and gain or loss. As a result, rich exact analytical solutions are obtained, which include bright and dark solitons, Jacobi elliptic function solutions and Weierstrass elliptic function solutions. With computer simulation, the main evolution features of some of these solutions are shown by some figures. Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management.

Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching of the plate

In this communication a generalized three- dimensional steady flow of a viscous fluid between two infinite parallel plates is considered. The flow is generated due to uniform stretching of the lower plate in x- and y-directions. It is assumed that the upper plate is uniformly porous and is subjected to constant injection. The governing system is fully coupled and nonlinear in nature. A complete analytic solution which is uniformly valid for all values of the dimensionless parameters β Re and λ is obtained by using a purely analytic technique, namely the homotopy analysis method. Also the effects of the parameters β Re and λ on the velocity field are discussed through graphs.

Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion

The problem of a transversely isotropic functionally graded material （FGM） plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional （3D） general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.

Exact Solution of Terzaghi’s Consolidation Equation and Extension to Two/Three-Dimensional Cases

The differential equation by Terzaghi and Fr?hlich, better known as Terzaghi’s one-dimensional consolidation equation, simulates the visco-elastic behaviour of soils depending on the loads applied as it happens, for example, when foundations are laid and start carrying the weight of the structure. Its application is traditionally based on Taylor’s solution that approximates experimental results by introducing non-dimensional variables that, however, contradict the actual behaviour of soils. The proposal of this research is an exact solution consisting in a non-linear equation that can be considered correct as it meets both mathematical and experimental requirements. The solution proposed is extended to include differential equations relating to two/three dimensional consolidation by adopting a transversally isotropic model more consistent with the inner structure of soils.

Analytical Solution for Three-dimensional Forging Taking into Account Bulging of Sides by Mean Yield Criterion

Currently, for some complex plastic deformations, the analytical solution can not be obtained by using Mises yield criterion, because Mises yield criterion is nine dimensions, the velocity field is complex, and the solving methods are not innovative. Corresponding solutions of these problems are that yield criterion is linearized to reduce the variable numbers, and the velocity field and the solving methods are reasonably simplified, respectively. In this paper, a new linear yield criterion--mean yield（MY） criterion and inner-product of strain rate vector are used to analytically solve 3D forging taking into account bugling of sides. The velocity field is expressed as a vector in three dimensions, and rotation and divergence are applied to confirm that the velocity field is kinematically admissible. Then, the corresponding strain rate tensor of the velocity field is transformed into principal one by making the determinant of coefficients of the tensor cubic equation be zero. By using MY criterion, the plastic power is term by term integrated and summed according to inner-product of strain rate vector. An upper bound analytical solution is obtained for the forging, and verified by a pure lead press test. The test result turns out that the total pressure calculated by MY criterion is higher by 2.5%-15% than measuring value. In addition, a measuring formula of bulging parameter （a） is proposed, but the values of a measured by the formula are lower than those optimized by the golden section search. The total pressure calculated by MY criterion is compared with the ones by twin shear, Trasca yield, and Mises yield criterion. The comparing result shows that the total pressure calculated by MY criterion is slightly higher than the mean value of that by twin shear and Trasca yield criterion, and lower than that by Mises yield criterion, but more close to that by Mises yield criterion compared with that by other two. The proposed analytical solving methods can be effectively used to other complex plastic deformation, simplifying the solving process and obtaining the reasonable results.

Air Pollution Steady-State Advection-Diffusion Equation: The General Three-Dimensional Solution

Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation as- suming turbulence parameterization for realistic physical scenarios. We present the general steady three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.

Three-dimensional time-of-flight magnetic resonance angiography combined with high resolution T2-weighted imaging in preoperative evaluation of microvascular decompression

BACKGROUND Neurovascular compression(NVC) is the main cause of primary trigeminal neuralgia(TN) and hemifacial spasm(HFS). Microvascular decompression(MVD) is an effective surgical method for the treatment of TN and HFS caused by NVC. The judgement of NVC is a critical step in the preoperative evaluation of MVD, which is related to the effect of MVD treatment. Magnetic resonance imaging(MRI) technology has been used to detect NVC prior to MVD for several years. Among many MRI sequences, three-dimensional time-of-flight magnetic resonance angiography(3D TOF MRA) is the most widely used. However, 3D TOF MRA has some shortcomings in detecting NVC. Therefore, 3D TOF MRA combined with high resolution T2-weighted imaging(HR T2WI) is considered to be a more effective method to detect NVC.AIM To determine the value of 3D TOF MRA combined with HR T2WI in the judgment of NVC, and thus to assess its value in the preoperative evaluation of MVD.METHODS Related studies published from inception to September 2022 based on PubMed, Embase, Web of Science, and the Cochrane Library were retrieved. Studies that investigated 3D TOF MRA combined with HR T2WI to judge NVC in patients with TN or HFS were included according to the inclusion criteria. Studies without complete data or not relevant to the research topics were excluded. The Quality Assessment of Diagnostic Accuracy Studies checklist was used to assess the quality of included studies. The publication bias of the included literature was examined by Deeks’ test. An exact binomial rendition of the bivariate mixed-effects regression model was used to synthesize data. Data analysis was performed using the MIDAS module of statistical software Stata 16.0. Two independent investigators extracted patient and study characteristics, and discrepancies were resolved by consensus. Individual and pooled sensitivities and specificities were calculated. The I_(2) statistic and Q test were used to test heterogeneity. The study was registered on the website of PROSERO(registration No. CRD42022357158).RESULTS Our search identified 595 articles, of which 12(including 855 patients) fulfilled the inclusion criteria. Bivariate analysis showed that the pooled sensitivity and specificity of 3D TOF MRA combined with HR T2WI for detecting NVC were 0.96 [95% confidence interval(CI): 0.92-0.98] and 0.92(95%CI: 0.74-0.98), respectively. The pooled positive likelihood ratio was 12.4(95%CI: 3.2-47.8), pooled negative likelihood ratio was 0.04(95%CI: 0.02-0.09), and pooled diagnostic odds ratio was 283(95%CI: 50-1620). The area under the receiver operating characteristic curve was 0.98(95%CI: 0.97-0.99). The studies showed no substantial heterogeneity(I2 = 0, Q = 0.001 P = 0.50).CONCLUSION Our results suggest that 3D TOF MRA combined with HR T2WI has excellent sensitivity and specificity for judging NVC in patients with TN or HFS. This method can be used as an effective tool for preoperative evaluation of MVD.

Anorectal dysfunction in patients with mid-low rectal cancer after surgery: A pilot study with three-dimensional high-resolution manometry

BACKGROUND The quality of life in patients who develop low anterior resection syndrome(LARS)after surgery for mid-low rectal cancer is seriously impaired.The underlying pathophysiological mechanism of LARS has not been fully investigated.AIM To assess anorectal function of mid-low rectal cancer patients developing LARS perioperatively.METHODS Patients diagnosed with mid-low rectal cancer were included.The LARS score was used to evaluate defecation symptoms 3 and 6 mo after anterior resection or a stoma reversal procedure.Anorectal functions were assessed by threedimensional high resolution anorectal manometry preoperatively and 3-6 mo after surgery.RESULTS The study population consisted of 24 patients.The total LARS score was decreased at 6 mo compared with 3 mo after surgery(P<0.05),but 58.3%(14/24)lasted as major LARS at 6 mo after surgery.The length of the high-pressure zone of the anal sphincter was significantly shorter,the mean resting pressure and maximal squeeze pressure of the anus were significantly lower than those before surgery in allpatients (P < 0.05), especially in the neoadjuvant therapy group after surgery (n = 18). The focalpressure defects of the anal canal were detected in 70.8% of patients, and those patients had higherLARS scores at 3 mo postoperatively than those without focal pressure defects (P < 0.05). Spasticperistaltic contractions from the new rectum to anus were detected in 45.8% of patients, whichwere associated with a higher LARS score at 3 mo postoperatively (P < 0.05).CONCLUSIONThe LARS score decreases over time after surgery in the majority of patients with mid-low rectalcancer. Anorectal dysfunctions, especially focal pressure defects of the anal canal and spasticperistaltic contractions from the new rectum to anus postoperatively, might be the majorpathophysiological mechanisms of LARS.

Three-Dimensional Exact Solution for Dynamic Damped Response of Plates with Two Free Edges

A three-dimensional state space method has been developed for the calculation of dynamic response of plates with two free edges and two simply supported edges.A complex damping model was introduced, then the exact solutions which satisfy all the governing equations and boundary conditions were obtained.In order to overcome the difficulty of satisfying all the stress conditions at free edges, the displacement functions of free edges were assumed.The boundary conditions were strictly satisfied when the convergence rate was good.The computing time was evidently less than that of finite element method.The comparison of the solution with those of finite element method show that there is an excellent agreement for displacements.When the imaginary parts of normal stress deviated, the finite element results showed existence of shear stresses at top and bottom surfaces, and the boundary conditions of FEM model were not strictly satisfied.

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method （SSDQM）. The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model （ALM） is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.

THE THREE-DIMENSIONAL FUNDAMENTAL SOLUTION TO STOKES FLOW IN THE OBLATE SPHEROIDAL COORDINATES WITH APPLICATIONS TO MULTIPLES SPHEROID PROBLEMS

A new three-dimensional fundamental solution to the Stokes flow was proposed by transforming the solid harmonic functions in Lamb's solution into expressions in terms Of the oblate spheroidal coordinates. These fundamental solutions are advantageous in treating flows past an arbitrary number of arbitrarily positioned and oriented oblate spheroids. The least squares technique was adopted herein so that the convergence difficulties often encountered in solving three-dimensional problems were completely avoided. The examples demonstrate that present approach is highly accurate, consistently stable and computationally efficient. The oblate spheroid may be used to model a variety of particle shapes between a circular disk and a sphere. For the first time, the effect of various geometric factors on the forces and torques exerted on two oblate spheroids were systematically studied by using the proposed fundamental solutions. The generality of this approach was illustrated by two problems of three spheroids.

Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing

Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.

Three-dimensionally ordered macroporous SnO_2-based solid solution catalysts for effective soot oxidation

A series of three‐dimensionally ordered macroporous(3DOM)SnO2‐based catalysts modified by the cations Ce4+,Mn3+,and Cu2+have been prepared by using a colloidal crystal templating method and tested for soot combustion under loose contact condition.XRD and STEM mapping results confirm that all the secondary metal cations have entered the lattice matrix of tetragonal rutile SnO2 to form non‐continuous solid solutions,thus impeding crystallization and improving the surface areas and pore volumes of the modified catalysts.In comparison with regular SnO2 nanoparticles,the 3DOM SnO2 displays evidently improved activity,testifying that the formation of the 3DOM structure can anchor the soot particulates in the macro‐pores,which ensures that the contact of the soot particles with the active sites on the 3DOM skeleton is more easily formed,thus benefiting the target reaction.With the incorporation of the secondary metal cations,the activity of the catalyst can be further improved due to the formation of more abundant mobile oxygen species.In summary,these effects are believed to be the major factors responsible for the activity of the catalyst.

Determination of Three-Dimensional Structures of Oridonin in Solution by NOESY Spectrum and Molecular Mechanics Calculation

The phase sensitive NOESY spectrum of oridonin was treated using Full Relaxation Matrix Analysis(FRMA) approach, and the cross relaxation rates of proton pairs were obtained by diagonalizing the NOE matrix of oridonin. The inter proton distances were calculated according to 1/r6 ij ∝σij. The three-dimensional structure of oridonin in solution was calculated by the combination of WUPH, WUPH-S method with molecular mechanics minimization on the basis of NMR experiment.