Three‐dimensional(3D)‐printed MXene high‐voltage aqueous micro‐supercapacitors with ultrahigh areal energy density and low‐temperature tolerance

The rapid advancement in the miniaturization,integration,and intelligence of electronic devices has escalated the demand for customizable microsupercapacitors(MSCs)with high energy density.However,efficient microfabrication of safe and high‐energy MXene MSCs for integrating microelectronics remains a significant challenge due to the low voltage window in aqueous electrolytes(typically≤0.6 V)and limited areal mass loading of MXene microelectrodes.Here,we tackle these challenges by developing a highconcentration(18mol kg^(−1))“water‐in‐LiBr”(WiB)gel electrolyte for MXene symmetric MSCs(M‐SMSCs),demonstrating a record high voltage window of 1.8 V.Subsequently,additive‐free aqueous MXene ink with excellent rheological behavior is developed for three‐dimensional(3D)printing customizable all‐MXene microelectrodes on various substrates.Leveraging the synergy of a highvoltage WiB gel electrolyte and 3D‐printed microelectrodes,quasi‐solid‐state MSMSCs operating stably at 1.8 V are constructed,and achieve an ultrahigh areal energy density of 1772μWhcm^(−2) and excellent low‐temperature tolerance,with a long‐term operation at−40℃.Finally,by extending the 3D printing protocol,M‐SMSCs are integrated with humidity sensors on a single planar substrate,demonstrating their reliability in miniaturized integrated microsystems.

Three-dimensional(3D)parametric measurements of individual gravels in the Gobi region using point cloud technique

Gobi spans a large area of China,surpassing the combined expanse of mobile dunes and semi-fixed dunes.Its presence significantly influences the movement of sand and dust.However,the complex origins and diverse materials constituting the Gobi result in notable differences in saltation processes across various Gobi surfaces.It is challenging to describe these processes according to a uniform morphology.Therefore,it becomes imperative to articulate surface characteristics through parameters such as the three-dimensional(3D)size and shape of gravel.Collecting morphology information for Gobi gravels is essential for studying its genesis and sand saltation.To enhance the efficiency and information yield of gravel parameter measurements,this study conducted field experiments in the Gobi region across Dunhuang City,Guazhou County,and Yumen City(administrated by Jiuquan City),Gansu Province,China in March 2023.A research framework and methodology for measuring 3D parameters of gravel using point cloud were developed,alongside improved calculation formulas for 3D parameters including gravel grain size,volume,flatness,roundness,sphericity,and equivalent grain size.Leveraging multi-view geometry technology for 3D reconstruction allowed for establishing an optimal data acquisition scheme characterized by high point cloud reconstruction efficiency and clear quality.Additionally,the proposed methodology incorporated point cloud clustering,segmentation,and filtering techniques to isolate individual gravel point clouds.Advanced point cloud algorithms,including the Oriented Bounding Box(OBB),point cloud slicing method,and point cloud triangulation,were then deployed to calculate the 3D parameters of individual gravels.These systematic processes allow precise and detailed characterization of individual gravels.For gravel grain size and volume,the correlation coefficients between point cloud and manual measurements all exceeded 0.9000,confirming the feasibility of the proposed methodology for measuring 3D parameters of individual gravels.The proposed workflow yields accurate calculations of relevant parameters for Gobi gravels,providing essential data support for subsequent studies on Gobi environments.

基于Three.js的虚拟模型3D交互展示研究及实现

WebGL的开源框架Three.js是轻量级的3D库,该技术的易用性降低三维空间技术的学习成本,并且极大程度上提高3D显示性能,故被广泛使用。经研究,可以应用Three.js技术实现虚拟数字模型的网页3D展示效果,以交互热点为索引将虚拟模型嵌入至Pano2VR制作的实景漫游系统,实现在网页实景VR里进行虚拟模型3D交互展示,多维度丰富虚拟模型的视觉展示效果。

Laboratory observation of electron energy distribution near three-dimensional magnetic nulls

The acceleration of electrons near three-dimensional(3D)magnetic nulls is crucial to the energy conversion mechanism in the 3D magnetic reconnection process.To explore electron acceleration in a 3D magnetic null topology,we constructed a pair of 3D magnetic nulls in the PKU Plasma Test(PPT)device and observed acceleration of electrons near magnetic nulls.This study measured the plasma floating potential and ion density profiles around the 3D magnetic null.The potential wells near nulls may be related to the energy variations of electrons,so we measured the electron distribution functions(EDFs)at different spatial positions.The axial variation of EDF shows that the electrons deviate from the Maxwell distribution near magnetic nulls.With scanning probes that can directionally measure and theoretically analyze based on curve fitting,the variations of EDFs are linked to the changes of plasma potential under 3D magnetic null topology.The kinetic energy of electrons accelerated by the electric field is 6 eV(v_(e)~7v_(Alfvén-e))and the scale of the region where accelerating electrons exist is in the order of serval electron skin depths.

Innovation leading development:a glimpse into three-dimensional bioprinting in Israel

Three-dimensional(3D)printing has attracted increasing research interest as an emerging manufacturing technology for devel-oping sophisticated and exquisite architecture through hierarchical printing.It has also been employed in various advanced industrial areas.The development of intelligent biomedical engineering has raised the requirements for 3D printing,such as flexible manufacturing processes and technologies,biocompatible constituents,and alternative bioproducts.However,state-of-the-art 3D printing mainly involves inorganics or polymers and generally focuses on traditional industrial fields,thus severely limiting applications demanding biocompatibility and biodegradability.In this regard,peptide architectonics,which are self-assembled by programmed amino acid sequences that can be flexibly functionalized,have shown promising potential as bioinspired inks for 3D printing.Therefore,the combination of 3D printing and peptide self-assembly poten-tially opens up an alternative avenue of 3D bioprinting for diverse advanced applications.Israel,a small but innovative nation,has significantly contributed to 3D bioprinting in terms of scientific studies,marketization,and peptide architectonics,including modulations and applications,and ranks as a leading area in the 3D bioprinting field.This review summarizes the recent progress in 3D bioprinting in Israel,focusing on scientific studies on printable components,soft devices,and tissue engineering.This paper further delves into the manufacture of industrial products,such as artificial meats and bioinspired supramolecular architectures,and the mechanisms,physicochemical properties,and applications of peptide self-assembly.Undoubtedly,Israel contributes significantly to the field of 3D bioprinting and should thus be appropriately recognized.

A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

Numerical three-dimensional modeling of earthen dam piping failure

A physically-based numerical three-dimensional earthen dam piping failure model is developed for homogeneous and zoned soil dams.This model is an erosion model,coupled with force/moment equilibrium analyses.Orifice flow and two-dimensional(2D)shallow water equations(SWE)are solved to simulate dam break flows at different breaching stages.Erosion rates of different soils with different construction compaction efforts are calculated using corresponding erosion formulae.The dam's real shape,soil properties,and surrounding area are programmed.Large outer 2D-SWE grids are used to control upstream and downstream hydraulic conditions and control the boundary conditions of orifice flow,and inner 2D-SWE flow is used to scour soil and perform force/moment equilibrium analyses.This model is validated using the European Commission IMPACT(Investigation of Extreme Flood Processes and Uncertainty)Test#5 in Norway,Teton Dam failure in Idaho,USA,and Quail Creek Dike failure in Utah,USA.All calculated peak outflows are within 10%errors of observed values.Simulation results show that,for a V-shaped dam like Teton Dam,a piping breach location at the abutment tends to result in a smaller peak breach outflow than the piping breach location at the dam's center;and if Teton Dam had broken from its center for internal erosion,a peak outflow of 117851 m'/s,which is 81%larger than the peak outflow of 65120 m3/s released from its right abutment,would have been released from Teton Dam.A lower piping inlet elevation tends to cause a faster/earlier piping breach than a higher piping inlet elevation.

Utility of real-time 3D visualization system in the early stage of phacoemulsification training

●AIM:To determine the teaching effects of a real-time three dimensional(3D)visualization system in the operating room for early-stage phacoemulsification training.●METHODS:A total of 10 ophthalmology residents of the first-year postgraduate were included.All the residents were novices to cataract surgery.Real-time cataract surgical observations were performed using a custom-built 3D visualization system.The training lasted 4wk(32h)in all.A modified International Council of Ophthalmology’s Ophthalmology Surgical Competency Assessment Rubric(ICO-OSCAR)containing 4 specific steps of cataract surgery was applied.The self-assessment(self)and expert-assessment(expert)were performed through the microsurgical attempts in the wet lab for each participant.●RESULTS:Compared with pre-training assessments(self 3.2±0.8,expert 2.5±0.6),the overall mean scores of posttraining(self 5.2±0.4,expert 4.7±0.6)were significantly improved after real-time observation training of 3D visualization system(P<0.05).Scores of 4 surgical items were significantly improved both self and expert assessment after training(P<0.05).●CONCLUSION:The 3D observation training provides novice ophthalmic residents with a better understanding of intraocular microsurgical techniques.It is a useful tool to improve teaching efficiency of surgical education.

Three-dimensional numerical analysis of plant-soil hydraulic interactions on pore water pressure of vegetated slope under different rainfall patterns

Understanding the pore water pressure distribution in unsaturated soil is crucial in predicting shallow landslides triggered by rainfall,mainly when dealing with different temporal patterns of rainfall intensity.However,the hydrological response of vegetated slopes,especially three-dimensional(3D)slopes covered with shrubs,under different rainfall patterns remains unclear and requires further investigation.To address this issue,this study adopts a novel 3D numerical model for simulating hydraulic interactions between the root system of the shrub and the surrounding soil.Three series of numerical parametric studies are conducted to investigate the influences of slope inclination,rainfall pattern and rainfall duration.Four rainfall patterns(advanced,bimodal,delayed,and uniform)and two rainfall durations(4-h intense and 168-h mild rainfall)are considered to study the hydrological response of the slope.The computed results show that 17%higher transpiration-induced suction is found for a steeper slope,which remains even after a short,intense rainfall with a 100-year return period.The extreme rainfalls with advanced(PA),bimodal(PB)and uniform(PU)rainfall patterns need to be considered for the short rainfall duration(4 h),while the delayed(PD)and uniform(PU)rainfall patterns are highly recommended for long rainfall durations(168 h).The presence of plants can improve slope stability markedly under extreme rainfall with a short duration(4 h).For the long duration(168 h),the benefit of the plant in preserving pore-water pressure(PWP)and slope stability may not be sufficient.

Application of three-dimensional MHD equilibrium calculation coupled with plasma response to island divertor experiments on J-TEXT

Three-dimensional(3D) equilibrium calculations, including the plasma rotation shielding effect to resonant magnetic perturbations(RMPs) produced by the island divertor(ID) coils, were carried out using the HINT and MARS-F codes on J-TEXT. Validation of 3D equilibrium calculations with experimental observations demonstrates that the shielding effect will prevent the penetration of the edge m/n = 3/1 mode component when the ID coil current is 4 k A, while change the size of magnetic islands once the current exceeds the penetration threshold. This indicates that equilibrium calculations including the plasma rotation shielding effect to RMPs can lead to better agreements with experimental observations compared to the vacuum approximation method. Additionally, the magnetic topology at the boundary undergoes changes,impacting the interaction between the plasma and the target plate. These results may be important in understanding RMP effects on edge transport and magnetohydrodynamic(MHD)instability control, as well as divertor heat and particle flux distribution control.

Three-dimensional Modeling of Ore-forming Elements and Mineralization Prognosis for the Yechangping Mo Deposit,Henan Province,China

Three-dimensional geochemical modeling of ore-forming elements is crucial for predicting deep mineralization.This approach provides key information for the quantitative prediction of deep mineral localization,three-dimensional fine interpolation,analysis of spatial distribution patterns,and extraction of quantitative mineral-seeking markers.The Yechangping molybdenum(Mo)deposit is a significant and extensive porphyry-skarn deposit in the East Qinling-Dabie Mo polymetallic metallogenic belt at the southern margin of the North China Block.Abundant borehole data on oreforming elements underpin deep geochemical predictions.The methodology includes the following steps:(1)Threedimensional geological modeling of the deposit was established.(2)Correlation,cluster,and factor analyses post delineation of mineralization stages and determination of mineral generation sequence to identify(Cu,Pb,Zn,Ag)and(Mo,W,mfe)assemblages.(3)A three-dimensional geochemical block model was constructed for Mo,W,mfe,Cu,Zn,Pb,and Ag using the ordinary kriging method,and the variational function was developed.(4)Spatial distribution and enrichment characteristics analysis of ore-forming elements are performed to extract geological information,employing the variogram and w(Cu+Pb+Zn+Ag)/w(Mo+W)as predictive indicators.(5)Identifying the western,northwestern,and southwestern areas of the mine with limited mineralization potential,contrasted by the northeastern and southeastern areas favorable for mineral exploration.

Three-dimensional stability calculation method for high and large composite slopes formed by mining stope and inner dump in adjacent open pits

The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of significant importance to develop an effective 3D stability calculation method for composite slopes to enhance the design and stability control of open-pit slope engineering.Using the composite slope formed by the mining stope and inner dump in Baiyinhua No.1 and No.2 open-pit coal mine as a case study,this research investigates the failure mode of composite slopes and establishes spatial shape equations for the sliding mass.By integrating the shear resistance and sliding force of each row of microstrip columns onto the bottom surface of the strip corresponding to the main sliding surface,a novel 2D equivalent physical and mechanical parameters analysis method for the strips on the main sliding surface of 3D sliding masses is proposed.Subsequently,a comprehensive 3D stability calculation method for composite slopes is developed,and the quantitative relationship between the coordinated development distance and its 3D stability coefficients is examined.The analysis reveals that the failure mode of the composite slope is characterized by cutting-bedding sliding,with the arc serving as the side interface and the weak layer as the bottom interface,while the destabilization mechanism primarily involves shear failure.The spatial form equation of the sliding mass comprises an ellipsoid and weak plane equation.The analysis revealed that when the coordinated development distance is 1500 m,the error rate between the 3D stability calculation result and the 2D stability calculation result of the composite slope is less than 8%,thereby verifying the proposed analytical method of equivalent physical and mechanical parameters and the 3D stability calculation method for composite slopes.Furthermore,the3D stability coefficient of the composite slope exhibits an exponential correlation with the coordinated development distance,with the coefficient gradually decreasing as the coordinated development distance increases.These findings provide a theoretical guideline for designing similar slope shape parameters and conducting stability analysis.

Three-dimensional constrained gravity inversion of Moho depth and crustal structural characteristics at Mozambique continental margin

Mozambique's continental margin in East Africa was formed during the break-off stage of the east and west Gondwana lands. Studying the geological structure and division of continent-ocean boundary(COB) in Mozambique's continental margin is considered of great significance to rebuild Gondwana land and understand its movement mode. Along these lines, in this work, the initial Moho was fit using the known Moho depth from reflection seismic profiles, and a 3D multi-point constrained gravity inversion was carried out. Thus, highaccuracy Moho depth and crustal thickness in the study area were acquired. According to the crustal structure distribution based on the inversion results, the continental crust at the narrowest position of the Mozambique Channel was detected. According to the analysis of the crustal thickness, the Mozambique ridge is generally oceanic crust and the COB of the whole Mozambique continental margin is divided.

Multi-Branch High-Dimensional Guided Transformer-Based 3D Human Posture Estimation

The human pose paradigm is estimated using a transformer-based multi-branch multidimensional directed the three-dimensional(3D)method that takes into account self-occlusion,badly posedness,and a lack of depth data in the per-frame 3D posture estimation from two-dimensional(2D)mapping to 3D mapping.Firstly,by examining the relationship between the movements of different bones in the human body,four virtual skeletons are proposed to enhance the cyclic constraints of limb joints.Then,multiple parameters describing the skeleton are fused and projected into a high-dimensional space.Utilizing a multi-branch network,motion features between bones and overall motion features are extracted to mitigate the drift error in the estimation results.Furthermore,the estimated relative depth is projected into 3D space,and the error is calculated against real 3D data,forming a loss function along with the relative depth error.This article adopts the average joint pixel error as the primary performance metric.Compared to the benchmark approach,the estimation findings indicate an increase in average precision of 1.8 mm within the Human3.6M sample.

Mass Transfer-Promoted Fe^(2+)/Fe^(3+)Circulation Steered by 3D Flow-Through Co-Catalyst System Toward Sustainable Advanced Oxidation Processes

Realizing fast and continuous generation of reactive oxygen species(ROSs)via iron-based advanced oxidation processes(AOPs)is significant in the environmental and biological fields.However,current AOPs assisted by co-catalysts still suffer from the poor mass/electron transfer and non-durable promotion effect,giving rise to the sluggish Fe^(2+)/Fe^(3+)cycle and low dynamic concentration of Fe^(2+)for ROS production.Herein,we present a three-dimensional(3D)macroscale co-catalyst functionalized with molybdenum disulfide(MoS_(2))to achieve ultra-efficient Fe^(2+)regeneration(equilibrium Fe^(2+)ratio of 82.4%)and remarkable stability(more than 20 cycles)via a circulating flow-through process.Unlike the conventional batch-type reactor,experiments and computational fluid dynamics simulations demonstrate that the optimal utilization of the 3D active area under the flow-through mode,initiated by the convectionenhanced mass/charge transfer for Fe^(2+)reduction and then strengthened by MoS_(2)-induced flow rotation for sufficient reactant mixing,is crucial for oxidant activation and subsequent ROS generation.Strikingly,the flow-through co-catalytic system with superwetting capabilities can even tackle the intricate oily wastewater stabilized by different surfactants without the loss of pollutant degradation efficiency.Our findings highlight an innovative co-catalyst system design to expand the applicability of AOPs based technology,especially in large-scale complex wastewater treatment.

A three-dimensional co-continuous network structure polymer electrolyte with efficient ion transport channels enabling ultralong-life all solid-state lithium metal batteries

Solid polymer electrolytes(SPEs)have emerged as one of the most promising candidates for the construction of solid-state lithium batteries due to their excellent flexibility,scalability,and interface compatibility with electrodes.Herein,a novel all-solid polymer electrolyte(PPLCE)was fabricated by the copolymer network of liquid crystalline monomers and poly(ethylene glycol)dimethacrylate(PEGDMA)acts as a structural frame,combined with poly(ethylene glycol)diglycidyl ether short chain interspersed serving as mobile ion transport entities.The preparaed PPLCEs exhibit excellent mechanical property and out-standing electrochemical performances,which is attributed to their unique three-dimensional cocontinuous structure,characterized by a cross-linked semi-interpenetrating network and an ionic liquid phase,resulting in a distinctive nanostructure with short-range order and long-range disorder.Remarkably,the addition of PEGDMA is proved to be critical to the comprehensive performance of the PPLCEs,which effectively modulates the microscopic morphology of polymer networks and improves the mechanical properties as well as cycling stability of the solid electrolyte.When used in a lithiumion symmetrical battery configuration,the 6 wt%-PPLCE exhibites super stability,sustaining operation for over 2000 h at 30 C,with minimal and consistent overpotential of 50 mV.The resulting Li|PPLCE|LFP solid-state battery demonstrates high discharge specific capacities of 160.9 and 120.1 mA h g^(-1)at current densities of 0.2 and 1 C,respectively.Even after more than 300 cycles at a current density of 0.2 C,it retaines an impressive 73.5%capacity.Moreover,it displayes stable cycling for over 180 cycles at a high current density of 0.5C.The super cycle stability may promote the application for ultralong-life all solid-state lithium metal batteries.

3D image system improves the learning curve and contributes to medical education of rhinoplasty

Background: Rhinoplasty is a complex surgical procedure that requires critical analysis and precise design before surgery, making it a challenging operation for both the surgical team and medical educators. This study aimed to evaluate the impact of 3D design involvement on learning curves and to establish a more effective method for rhinoplasty education.Methods: Surgeons who participated in an educational program were divided into two groups. The experimental group was involved in the 3D design before the operation, and the control group was asked to review the rhinoplasty atlas. A self-assessment questionnaire was used to evaluate the learning curve of the eight rhinoplasty procedures for each surgeon, and the overall satisfaction rate data were also collected.Results: The self-assessment scores in both groups showed an increasing trend from the first to the eighth operation. The mean scores of the experimental group were significantly higher than those of the control group at the fifth operation(P=0.01). The satisfaction rate of the experimental group(91.7%) was higher than that of the control group(54.5%).Conclusion: The 3D imaging system can improve the learning curve and satisfaction rate of rhinoplasty education,proving that it is an easy and effective tool for medical education.

Three-Dimensional Density Distribution and Seismic Activity along the Guxiang–Tongmai Segment of the Jiali Fault,Tibet

The Guxiang-Tongmai segment of the Jiali fault is situated northeast of the Namche Barwa Syntaxis in northeastern Tibet.It is one of the most active strike-slip faults near the syntaxis and plays a pivotal role in the examination of seismic activity within the eastern Himalayan Syntaxis.New study in the research region has yielded a 1:200000 gravity dataset covering an area 1500 km^(2).Using wavelet transform multiscale decomposition,scratch analysis techniques,and 3D gravity inversion methods,gravity anomalies,fault distributions,and density structures were determined across various scales.Through the integration of our new gravity data with other geophysical and geological information,our findings demonstrate substantial variations in the overall crustal density within the region,with the fault distribution closely linked to these density fluctuations.Disparities in stratigraphic density are important causes of variations in the capacity of geological formations to endure regional tectonic stress.Earthquakes are predominantly concentrated within the density transition zone and are primarily situated in regions of elevated density.The hanging wall stress within the Guxiang-Tongmai segment of the Jiali fault exhibits a notable concentration,marked by pronounced anisotropy,and is positioned within the density differential zone,which is prone to earthquakes.

Intelligent 3D garment system of the human body based on deep spiking neural network

Background Intelligent garments,a burgeoning class of wearable devices,have extensive applications in domains such as sports training and medical rehabilitation.Nonetheless,existing research in the smart wearables domain predominantly emphasizes sensor functionality and quantity,often skipping crucial aspects related to user experience and interaction.Methods To address this gap,this study introduces a novel real-time 3D interactive system based on intelligent garments.The system utilizes lightweight sensor modules to collect human motion data and introduces a dual-stream fusion network based on pulsed neural units to classify and recognize human movements,thereby achieving real-time interaction between users and sensors.Additionally,the system incorporates 3D human visualization functionality,which visualizes sensor data and recognizes human actions as 3D models in real time,providing accurate and comprehensive visual feedback to help users better understand and analyze the details and features of human motion.This system has significant potential for applications in motion detection,medical monitoring,virtual reality,and other fields.The accurate classification of human actions contributes to the development of personalized training plans and injury prevention strategies.Conclusions This study has substantial implications in the domains of intelligent garments,human motion monitoring,and digital twin visualization.The advancement of this system is expected to propel the progress of wearable technology and foster a deeper comprehension of human motion.

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.