## What is/are Three Dimensional?

Three Dimensional - We study the properties of slow magneto-acoustic waves that are naturally excited due to turbulent convection and investigate their role in the energy balance of a plage region using three dimensional (3D) radiation-MHD simulations.^{[1]}Herein, PtNi hollow nanoframes (PtNi HNFs) with three dimensional (3D) molecular accessibility were synthesized, EDX results suggested that Ni was evenly distributed inside of the hollow nanoframes, whereas Pt was relatively concentrated at the edges.

^{[2]}MethodsBy using localization markers, we can acquire preoperative CT images of the patients, reconstruct these images into Three Dimensional (3D) virtual graphs using a computer, measure the spatial distance of the tumor from the markers, and in turn calculate the projection location of the tumor on the scalp by the Triangle Pythagorean theorem.

^{[3]}To the best of the authors' knowledge, the present research investigates for the first time modelling of a three dimensional (3D) hollow needle insertion using a multilayer stiffness model of biological tissue using FE based CEL method and presents a comparison of simulation results with experimental data.

^{[4]}Recent studies are being conducted on the development of three dimensional (3D) PTM which have demonstrated excellent performances as compared to their two dimensional counterparts.

^{[5]}To begin with the construction of two high-resolution discretization schemes for convection terms, a three dimensional algorithm for liquid jet buckling phenomenon is established based on two phase flow model and discretization via finite volume method.

^{[6]}Three dimensional (3D) DenseNet was used to model and predict GGN invasiveness, and five-fold cross validation was performed.

^{[7]}On the other hand, signs of three dimensionalities are observed on the free surface structure for higher Fn, even the predicted wave elevations are very close to 2D calculations in the midsection.

^{[8]}In this electrode configuration, carbon cloth is the three dimensional and conductive skeleton; NiCo-LDH nanosheets, as the template, ensure the oriented growth of MoS2 nanosheet arrays.

^{[9]}Three dimensional trajectories of 39 reflective markers were recorded.

^{[10]}Liquid sloshing in square or nearly square-base tanks becomes more complex due to the emergence of three dimensional waves around resonance.

^{[11]}More precisely, we show that, if the initial data of the three dimensional Keller–Segel–Navier–Stokes system is close to the smooth initial function ( 0 , 0 , u s ( 0 , x ) ) T $(0,0,\textbf{u}_{s}(0,x) )^{T}$ , then there exists a blowup solution of the three dimensional linear Keller–Segel–Navier–Stokes system satisfying the decomposition ( n ( t , x ) , c ( t , x ) , u ( t , x ) ) T = ( 0 , 0 , u s ( t , x ) ) T + O ( ε ) , ∀ ( t , x ) ∈ ( 0 , T ∗ ) × R 3 , $$ \bigl(n(t,x),c(t,x),\textbf{u}(t,x) \bigr)^{T}= \bigl(0,0, \textbf{u}_{s}(t,x) \bigr)^{T}+\mathcal{O}(\varepsilon ), \quad \forall (t,x)\in \bigl(0,T^{*}\bigr) \times \mathbb{R}^{3}, $$ in Sobolev space H s ( R 3 ) $H^{s}(\mathbb{R}^{3})$ with s = 3 2 − 5 a $s=\frac{3}{2}-5a$ and constant 0 < a ≪ 1 $0< a\ll 1$ , where T ∗ $T^{*}$ is the maximal existence time, and u s ( t , x ) $\textbf{u}_{s}(t,x)$ given in (Yan 2018 ) is the explicit blowup solution admitted smooth initial data for three dimensional incompressible Navier–Stokes equations.

^{[12]}The fact that detailed data are required for good results and that three dimensional examples cannot always be simplified leads to a high computation time and memory demand.

^{[13]}This research paper emphasizes on three dimensional hydrodynamics and temperature distribution during photo biohydrogen generation by Rhodobacter sphaeroides strain O.

^{[14]}The performance of a three dimensional integrated circuit primarily depends on the filler material used in through silicon via (TSV).

^{[15]}To overcome these drawbacks with improved PLQY and EQE, we summarize and analyze the recent advances towards the development of three dimensional (3D), two dimensional (2D) and quasi-2D perovskites film employing composition and/or dimensional engineering.

^{[16]}The delivery form comprised of bicontinuous lipid bilayers arranged in three dimensional honeycombs like structure provided with two internal aqueous channels for incorporation of number of biologically active ingredients.

^{[17]}We study the partial regularity problem for a three dimensional simplified Ericksen–Leslie system, which consists of the Navier–Stokes equations for the fluid velocity coupled with a convective Ginzburg-Landau type equations for the molecule orientation, modelling the incompressible nematic liquid crystal flows.

^{[18]}A three dimensional Monte Carlo simulation was developed to obtain the electron energy distribution function, a necessary parameter in the extended corona model, and we discuss its dependence on oxygen percentage and discharge pressure.

^{[19]}Three dimensional bioprinter technologies created an availability to use alive cells and molecules to replace or repair a damaged part of the body.

^{[20]}There are a number of approaches to this problem, such as evaluations based on seismic field observations, the microtremor method, the method using the weak motion data, the method using the strong motion data, the one-dimensional wave propagation method or the three dimensional wave propagation method with simulation etc.

^{[21]}Conclusion: The IS is three dimensional in the pharmaceutical manager sample.

^{[22]}Furthermore, by artificially remodelling the microenvironment, we showed that the directionality of collective cell migration, as well as the three dimensional branch pattern formation of lung epithelial cells, can be controlled.

^{[23]}Four new two and three dimensional coordination polymers, namely, [Co2(µ4-L)(µ-obix)2]n (1), [Zn2(µ4-L)(µ-obix)2]n (2), {[Zn2(µ4-L)(µ-obix)2]·2CH3CN}n (3), and {[Cd2(µ4-L)(H2O)4(µ-obix)]n·2H2O}n (4), where H4L = 5,5′-(but-2-ene-1,4-diylbis(oxy))diisophthalic acid and obix = 1,2-bis((1H-imidazol-1-yl)methyl)benzene), were synthesized under solvothermal conditions.

^{[24]}Number of researches have been introduced for stope boundary optimization but true optimal solution in three dimensional spaces is still out of reach.

^{[25]}Three dimensional (3D) printed models are increasingly used for training and reconstruction.

^{[26]}On the other hand, ammonium undergoes a facile rotation in three dimensional space, leading to frequent changes in the NH bonds involved in the coordination with the crown ether.

^{[27]}Due to the highly oriented MXene-based three dimensional conductive networks, the hydrogel sensor achieved extremely high tensile sensitivity (18.

^{[28]}In this review, the three dimensional approaches, their underlying models, and common instruments are introduced, and empirical studies on similarities and differences between the concepts and the categorical classification are summarized.

^{[29]}Three dimensional (3D) electroanatomical maps (EAMs) created during electrophysiology procedures are traditionally displayed on 2D monitors connected to mapping systems.

^{[30]}After the aptasensor incubation in MCF-7 cancer cells, the cell membrane proteins interacted specifically with the three dimensional-structure of the AS1411 aptamer, resulting in the cell capture on the aptasensor.

^{[31]}Three dimensional attenuation images of Mt.

^{[32]}Three dimensional (3D) hand pose estimation is the task of estimating the 3D location of hand keypoints.

^{[33]}This paper investigates a novel distributed fusion system for target tracking in three dimensional surveillance using multiple asynchronous BO sensors by simultaneously addressing the problems of target mis-detection and clutter disturbance as well as the out-of-sequence (OOS) information fusion.

^{[34]}The three dimensional analysis shows that this latter remains the optimal performing airfoil reaching a power density of 2.

^{[35]}Here we present a three dimensional radially anisotropic model of NCC derived from wave-equation traveltime tomography to address this issue.

^{[36]}How to establish the real three-dimensional (3D) rough surface, using inter-polation surface reconstruction based on real data, especially in the three dimensional precision measurement data processing, etc, also the lack of research and practice, so in this paper, fractal interpolation and spline interpolation, Fourier interpolation surface modeling interpolation algorithm of three methods for modeling, a detailed analysis and expounds the advantages and disadvantages of the three ways of modeling with surface, and finally to the surface of the atomic force microscope to measure the actual extraction of a small number of sampling points are simulated.

^{[37]}Deep learning for three dimensional (3D) abdominal organ segmentation on high-resolution computed tomography (CT) is a challenging topic, in part due to the limited memory provide by graphics processing units (GPU) and large number of parameters and in 3D fully convolutional networks (FCN).

^{[38]}By using multiple radars, three dimensional wind field is estimated by using the dualDoppler analysis technique.

^{[39]}The successful outcome of endodontic treatment is dependent on complete cleaning, shaping as well as three dimensional obturation of the root canal system.

^{[40]}Here, we achieve the selective control of the geometry of colloidal quasi-spherical PbS QDs in highly-ordered two and three dimensional superlattices: Disordered, simple cubic (sc), and face-centered cubic (fcc).

^{[41]}Three dimensional printing (3DP) enables the development of diverse geometries through computer aided design using different techniques and materials for desired applications such as pharmaceutical drug delivery system.

^{[42]}In two and three dimensional Lipschitz, but not necessarily convex, polytopal domains, we devise and analyze a reliable and efficient a posteriori error estimator for a semilinear optimal control problem; control constraints are also considered.

^{[43]}As a new type of molding technology, three dimensional (3D) printing can realize the manufacturing of devices with complex shapes.

^{[44]}Three dimensional images can replace or supplement classroom activities, such as the identification of rocks and minerals from hand samples or the identification of geologic structures from 2-D photographs and limited field observations.

^{[45]}The SIMPLE algorithm together with the finite volume method are extended to the three dimensional case and applied to treat the governing equations.

^{[46]}These sufficient conditions always hold for two and three dimensional systems.

^{[47]}The aim of the study is to investigate the craniometric patterns in the Nigerian population based on three dimensional computed tomographic data, with the objectives of determining the age of individuals in the eastern part of Nigeria as well as determining if the skull of individual varies with age using computed tomography.

^{[48]}Three dimensional simulation was conducted for improved observation of the physical model.

^{[49]}Three dimensional (3D) printing is the favoured technique in contemporary manufacturing firms, that facilitates the solid 3D model from any modelling software to the real-time application in aerospace, automobile, construction, and lately, tissue engineering and medical implants that have gained traction with ongoing research studies.

^{[50]}

## finite element model

A three dimensional finite element model of the slewing bearing is established and analyzed.^{[1]}To establish a joint dowel bar and dowel bar set of cement concrete pavement structure in three dimensional finite element model, using the method of numerical analysis, analysis of the joint of cement concrete road surface of the load stress, deflection and deflection difference, to study the foundation modulus, dowel bar diameter on the load stress and the influence law of deflection is poor, and the condition of the same calculation results are analyzed in comparison.

^{[2]}A three dimensional (3D) finite element model of the femur from 55-year-old male donor was developed, and then a stability analysis was performed for the fixation provided by the retrograde nail at a distal fracture with different fracture gaps: 0.

^{[3]}The temperature gradient over the glass fiber reinforced polymer specimen has been analyzed and validated with a commercially available three dimensional mathematical finite element model to retrieve the quantitative information regarding the subsurface defects.

^{[4]}Three dimensional finite element models of composite joints were established to investigate the load-displacement behavior, failure mode of multi-axial tubular joints under bending load, and stress-strain relationship in some key positions.

^{[5]}This paper presents development of a three dimensional finite element model for simulations of a conformable piezoelectric sensor utilizing COMSOL Multiphysics.

^{[6]}Two types of three dimensional finite element models of transmission towers are developed in the OpenSees platform.

^{[7]}For the purpose of this research, a three dimensional finite element model has been developed and applied.

^{[8]}Experimental transmission losses compare well with three dimensional finite element model obtained either on the whole silencer, either on a periodic cell.

^{[9]}Firstly three dimensional finite element model of the ordinary long-span suspension bridge is established based on the powerful and attractive finite element software ANSYS.

^{[10]}In this paper, the interface damage evolution and fracture behavior between ceramic films and metallic substrates were simulated by developing a three dimensional finite element model of alumina films on Ni substrates with cohesive elements in the interfaces.

^{[11]}A three dimensional finite element model was established to study the residual stresses in the ZTA composite/Ti6Al4V alloy joints.

^{[12]}A three dimensional Finite Element Model was developed to identify the main parameters involved in this response for three different fullness ratio (0.

^{[13]}

## computational fluid dynamic

This paper proposes a framework of computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling approach that can deal with the three dimensional aeroelastic problems with both the free-play nonlinearity and the aerodynamic nonlinearity.^{[1]}Three dimensional simulation using Computational Fluid Dynamics was used in the numerical analysis of the temperature characteristics on solar PV arrays.

^{[2]}Firstly, a three dimensional (3D) PEM fuel cell model was developed, and simulations were conducted using commercial computational fluid dynamics (CFD) ANSYS FLUENT to examine the effect of each bipolar plate materials on cell performance.

^{[3]}In this paper, the three dimensional (3D) computational fluid dynamics analysis of a large-scale 5 MW VAWT is conducted.

^{[4]}The Computational Fluid Dynamics solution are done for a three dimensional model (3DCFD) using ANSYS/ Fluent R19.

^{[5]}In this work, a three dimensional (3D) Euler–Lagrangian computational fluid dynamic model is used to understand the transmission and evaporation of micrometer-size droplets generated due to a coughing event in this setting.

^{[6]}This paper is primarily concerned with the development of three dimensional (3-D) multiphase computational fluid dynamics models for use in Pressurized Water Nuclear Reactor (PWR) design and analysis.

^{[7]}To evaluate the effect of humidity and condensation on thermal performance, a three dimensional computational fluid dynamic (3D-CFD) model was developed.

^{[8]}A three dimensional computational fluid dynamics (CFD) model has been developed to study the effect of tool pin profile on the material flow and temperature development in friction stir welding (FSW) of high specific strength AA 7068 alloy.

^{[9]}The three dimensional unsteady computational fluid dynamic analysis of a VCRT at the engine conditions are performed, and the seal flow ejected downstream of the high pressure rotor row at six sealing flow rate are modeled.

^{[10]}In this paper, the three dimensional (3D) computational fluid dynamics analysis of a large-scale 5 MW VAWT is conducted.

^{[11]}Three dimensional models have been created in solid works and computational fluid dynamic simulations have been carried out on all the three types of electrolysers in ANSYS Fluent.

^{[12]}A three dimensional Computational Fluid Dynamics (CFD) model to study the dispersion of virus laden aerosols in a car moving with its windows open is reported.

^{[13]}

## convolutional neural network

To do so, a convolutional neural network architecture is proposed for the generator and trained on a synthetic climate database, computed using a simple three dimensional climate model: PLASIM.^{[1]}Third, a deep learning-based predictor, which uses three dimensional convolutional neural network and bidirectional long short-term memory neural network, is applied to predict decomposition components of each cluster.

^{[2]}To address these issues, we propose a Three Dimensional Tensor Convolutional Neural Network (3DTCNN) for spectral-spatial low-rank feature representation and a Semisupervised Classifier based on 3DTCNN (S-TCNN) for classification with limited labeled samples.

^{[3]}Our results show that two and three dimensional convolutional neural networks can be trained to stage developing zebrafish tail buds based on both morphological and gene expression confocal microscopy images, achieving in each case up to 100% test accuracy scores.

^{[4]}To solve these problems, we propose an automatic liver segmentation framework based on three dimensional (3D) convolutional neural networks with a hybrid loss function.

^{[5]}The accuracy performance of our three dimensional convolutional neural network is able to converge to 100 % during classification.

^{[6]}The computer numerical simulation results show that the overall classification accuracy based on our proposed method is higher than the two dimensional real valued singular spectrum analysis based method, the three dimensional singular spectrum analysis based method, the multivariate two dimensional singular spectrum analysis based method, the median filtering based method, the principal component analysis based method, the Tucker decomposition based method and the hybrid spectral convolutional neural network (hybrid SN) based method.

^{[7]}This letter proposes a deep learning based solution to predict the downlink CSI in frequency division duplex (FDD) systems, which is termed as complex-valued three dimensional convolutional neural network (CV-3DCNN).

^{[8]}In this work we implement an automatic emitter identification system using three dimensional convolutional neural networks (3D-CNN).

^{[9]}

## finite element method

Three dimensional finite element method of electromagnetic field and structure are used to calculate the magnetic flux density, radial force and vibration for the motors of PVPW and SEP.^{[1]}Second, the performance of the proposed motor is analyzed by means of three dimensional finite element method, and compared with the traditional motor.

^{[2]}Earlier, in 2019 by using a three dimensional (3D) finite element method (FEM) the possibility of the excitation and registration of such waves in the piezoelectric plates was theoretically shown.

^{[3]}Then, three dimensional continuum method (finite element method) is used and the general equation of API are updated to provide compatibility.

^{[4]}In this paper, we present a three dimensional analysis of 106 W multi-chip LEDs lamp using finite element method.

^{[5]}A fully electromechanically coupled, three dimensional phenomenological constitutive model for relaxor ferroelectric materials was developed for the use in a finite-element-method (FEM) solution procedure.

^{[6]}Precisely, for general quadratic cost function, in two or three dimensional cases, a semi discrete (time continuous, spatial discrete) algorithm consisting of finite element method and conjugate gradient method, would be utilized for solving a numerical solution of state system, and obtaining quantum optimal control from a initial guess of control input.

^{[7]}

## reduced graphene oxide

Herein, a novel three dimensional (3D) flower-like Ni-V-Se composite was established by the hydrothermal method and vertically grew on reduced graphene oxide/Ni foam (rGO/NF) with tunable composition and morphologies.^{[1]}For this intention, three dimensional (3D) heterostructure of Co3O4 and Co3S4 on nickel foam (NF) that covered by reduced graphene oxide (rGO) is prepared by the following of a facile multi- stage method.

^{[2]}Here, three-dimensional inverse opal (3D-IO) mesostructured Ni@TiO2@RGO electrodes were fabricated by templating nickel electrodeposition with self-assembled, three dimensionally ordered polystyrene (PS) opals, followed by atomic layer deposition (ALD) of TiO2 and spray coating of reduced graphene oxide (RGO).

^{[3]}The present work describes the deposition of coppersulfide (Cu2S) nanoflakes onto reduced graphene oxide (rGO) on three dimensional (3D) nickel foam byinexpensive chemical methods.

^{[4]}Two layers make up the sulfur cathode, active layer (sulfur-acethlene black (SC) spheres) and barrier layer (three dimensional MnO2-graphene oxide-multi-walled carbon nanotubes (MnO2-GO-CNTs) composites), which are integrated together by reduced graphene oxide (rGO) through self-binding.

^{[5]}

## quantitative structure activity

In the constructed three dimensional quantitative structure-activity relationship model (3D-QSAR) model, the regression coefficient (R2) for the degree of dispersion between the predicted molecular and the experimental values of the six peptides was 0.^{[1]}Therefore, three dimensional quantitative structure-activity relationship (3D-QSAR), molecular docking and molecular dynamics (MD) simulations, to the best of our knowledge, for the first time were performed to explore the correlation between the structures and activities.

^{[2]}Three dimensional quantitative structure activity relationship (3D QSAR) pharmacophore, and absorption, distribution, metabolism, excretion, and toxicity (ADMET) studies were also carried out showing proper pharmacokinetic and drug-likeness which aided in the prediction of the structure requirements responsible for the observed antitumor activity.

^{[3]}A three dimensional quantitative structure-activity relationship (QSAR) study using the comparative molecular field analysis (CoMFA) method was performed on 32 Des C analogues.

^{[4]}

## finite difference method

We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property.^{[1]}In this paper we derive the discretization of the nonlinear Monge-Ampere equation by means of the explicit formulae of the meshless Generalized Finite Difference Method (GFDM) in both two and three dimensional settings (2D and 3D).

^{[2]}To achieve the goal, a three dimensional mathematical thermal model is developed and solved numerically using implicit finite difference method.

^{[3]}To solve the three dimensional Schrodinger equation, we have used a theoretical method which is combined the coordinate transformation and the finite difference method (FDM).

^{[4]}

## ray computed tomography

For this work, the structure was scanned with X-ray computed tomography (CT) to capture the three dimensional density of the structure including both the solid ceramic elements as well as the interstitial space.^{[1]}Three dimensional (3D) X-ray microscopy, also referred to as X-ray computed tomography, is a data-rich characterization technique that can provide surface and subsurface spatial information in a non-destructive manner.

^{[2]}In this work, epoxy nanocomposites reinforced by graphite nanoplatelet (GNP) were prepared and nano-scale X-ray computed tomography was used to visualize the geometry, morphology and defects of the flakes, as well as the three dimensional agglomerates that are normally difficult to characterise by other techniques.

^{[3]}

## magnetic resonance angiography

To prospectively compare image-quality, reliability and graft sizing of a prototype self-navigated and a navigator-gated non-contrast three dimensional (3D) whole-heart magnetic-resonance-angiography (MRA) sequence with computed-tomography-angiography (CTA) for planning transcatheter-aortic-valve-intervention (TAVI).^{[1]}OBJECTIVES To prospectively compare image-quality, reliability and graft sizing of a prototype self-navigated and a navigator-gated non-contrast three dimensional (3D) whole-heart magnetic-resonance-angiography (MRA) sequence with computed-tomography-angiography (CTA) for planning transcatheter-aortic-valve-implantation (TAVI).

^{[2]}Methods A total of 57 symptomatic patients with MCA atherosclerotic plaques recruited in the Affiliated Hospital of Yangzhou University from January 2014 to January 2016 were imaged with diffusion weighted imaging (DWI), three dimensional time of flight magnetic resonance angiography (3D TOF-MRA) and HR-MRI scanning for plaque on a 3.

^{[3]}

## specific surface area

Synthesis of three dimensional nanostructures with high specific surface area is very much essential to enhance the capacitance of supercapacitors.^{[1]}The results show that the three dimensional (3D) BSFC-F800 prepared by the low-temperature calcination method (800 °C) has a well-organized porous structure and larger specific surface area and porosity.

^{[2]}According to analysis results, the MLPC with three dimensional (3D) interconnected networks possesses high specific surface area (671.

^{[3]}

## fourth order linearized

We study the realized power variations for the fourth order linearized Kuramoto–Sivashinsky (LKS) SPDEs and their gradient, driven by the space–time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions.^{[1]}We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces.

^{[2]}Let U=U(t,x) for (t,x)∈R+×Rd and ∂xU=∂xU(t,x) for (t,x)∈R+×R be the solution and gradient solution of the fourth order linearized Kuramoto–Sivashinsky (L-KS) SPDE driven by the space-time white noise in one-to-three dimensional spaces, respectively.

^{[3]}

## co glycolic acid

Methods: The Poly-lactic-co-glycolic acid-Methoxypolyethylene glycols (PLGA-mPEG) microspheres were prepared by encapsulating the doxycycline, and they were incorporated into three dimensional BCP scaﬀold to build a doxycycline sustained release system of BCP scaﬀold.^{[1]}In this study, we introduced