SEARCH · Search NASA

Results for “Generalized Method of Cells”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗

NASA NTRS1991

Application of two-point implicit central-difference methods to hyperbolic systems

This paper presents a general solution algorithm for the set of difference equations that arise when two-point central differences are used to approximate the flux difference terms in systems of hyperbolic differential equations. The general algorithm eliminates the weak points associated with the nonstandard algorithm reported by Wornom and Hafez (1986). The disadvantages of their algorithm relate to its implementation. It consists of separate algorithms for subsonic, supersonic, sonic and shock cells, applied individually, which presents a major bookkeeping problem when multiple sonic and shock cells are present. The general algorithm eliminates this problem and introduces an improved shock treatment which produces shocks with at most one interior shock point.

Wornom, Stephen F.↗

NASA NTRS2018

NASA ACC High Energy Dynamic Impact Methodology and Outcomes

For High Energy Dynamic Impact (HEDI) events, testing to evaluate the structural response of primary aircraft structure for design and certification is both expensive and time consuming. This paper discusses current work seeking to assess, develop, and validate appropriate analytical models that accurately predict physical response, damage, and failure modes for large scale composite structures in HEDI events. Four state-of-the-art Progressive Damage Analysis (PDA) methods were employed for this phased project: LS-DYNA MAT162, LS-DYNA MAT261, Smoothed Particle Galerkin (SPG), and EMU Peridynamics. Multiple material systems were considered, namely T700/5208 textile-infusion triaxial braid, T800/AMD-825 textile-infusion triaxial braid, IM7/8552 uni-directional tape, and SPG 196-PW/8552 plain-weave fabric. Extensive ballistic impact testing was performed to support this activity and measured results were compared to predictive models for assessment using panel delamination, panel displacement, force at the load cells, and threshold velocity as measures. Ultimately, the work under this activity provided significant progress in advancing the state-of-the-art in the use of PDA for HEDI events. Each material model had favorable performance comparing to test in some parameters and needed improvement in others. With the lessons learned from this activity, significant progress was made in the ability to predict panel behavior for a more general case beyond the flat panel in a ballistic impact event. Subsequent Phase II of the NASA ACC HEDI effort will continue to build on the coupon testing, flat panel ballistic impact testing, and analysis performed to-date with application of the PDA methods for intended material selections to test articles with greater complexity of configuration, curvature, and scale. It is not the intention of this paper to present a full set of data, but rather to give an overview of the NASA HEDI effort and show a small representative subset of the test and analysis results.

Hunziker, Kenneth J.↗

NASA NTRS2001

Cancer Detection Using Neural Computing Methodology

This paper describes a novel learning methodology used to analyze bio-materials. The premise of this research is to help pathologists quickly identify anomalous cells in a cost efficient method. Skilled pathologists must methodically, efficiently and carefully analyze manually histopathologic materials for the presence, amount and degree of malignancy and/or other disease states. The prolonged attention required to accomplish this task induces fatigue that may result in a higher rate of diagnostic errors. In addition, automated image analysis systems to date lack a sufficiently intelligent means of identifying even the most general regions of interest in tissue based studies and this shortfall greatly limits their utility. An intelligent data understanding system that could quickly and accurately identify diseased tissues and/or could choose regions of interest would be expected to increase the accuracy of diagnosis and usher in truly automated tissue based image analysis.

liquid crystal tunable filters↗

NASA NTRS1991

Laboratory and theoretical models of planetary-scale instabilities and waves

Meteorologists and planetary astronomers interested in large-scale planetary and solar circulations recognize the importance of rotation and stratification in determining the character of these flows. The two outstanding problems of interest are: (1) the origins and nature of chaos in baroclinically unstable flows; and (2) the physical mechanisms responsible for high speed zonal winds and banding on the giant planets. The methods used to study these problems, and the insights gained, are useful in more general atmospheric and climate dynamic settings. Because the planetary curvature or beta-effect is crucial in the large scale nonlinear dynamics, the motions of rotating convecting liquids in spherical shells were studied using electrohydrodynamic polarization forces to generate radial gravity and centrally directed buoyancy forces in the laboratory. The Geophysical Fluid Flow Cell (GFFC) experiments performed on Spacelab 3 in 1985 were analyzed. The interpretation and extension of these results have led to the construction of efficient numerical models of rotating convection with an aim to understand the possible generation of zonal banding on Jupiter and the fate of banana cells in rapidly rotating convection as the heating is made strongly supercritical. Efforts to pose baroclinic wave experiments for future space missions using a modified version of the 1985 instrument have led us to develop theoretical and numerical models of baroclinic instability. Some surprising properties of both these models were discovered.

Hart, John E.↗

NASA NTRS2007

GRMHD and GRPIC Simulations

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous code. The simulation results show the jet formations from a geometrically thin accretion disk near a nonrotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field configuration including issues for future research. A General Relativistic Particle-in-Cell Code (GRPIC) has been developed using the Kerr-Schild metric. The code includes kinetic effects, and is in accordance with GRMHD code. Since the gravitational force acting on particles is extreme near black holes, there are some difficulties in numerically describing these processes. The preliminary code consists of an accretion disk and free-falling corona. Results indicate that particles are ejected from the black hole. These results are consistent with other GRMHD simulations. The GRPIC simulation results will be presented, along with some remarks and future improvements. The emission is calculated from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by GRMHD simulations considering thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We would like to extend this research using GRPIC simulations and examine a possible new mechanism for certain X-ray quasi-periodic oscillations (QPOs) observed in blackhole X-ray binaries.

Nishikawa, K.-I.↗

NASA NTRS2012

Achieving Accuracy Requirements for Forest Biomass Mapping: A Spaceborne Data Fusion Method for Estimating Forest Biomass and Lidar Sampling Error

The synergistic use of active and passive remote sensing (i.e., data fusion) demonstrates the ability of spaceborne light detection and ranging (LiDAR), synthetic aperture radar (SAR) and multispectral imagery for achieving the accuracy requirements of a global forest biomass mapping mission (+/-20 Mg/ha or 20%, the greater of the two, for at least 80% of grid cells). A data fusion approach also provides a means to extend 3D information from discrete spaceborne LiDAR measurements of forest structure across scales much larger than that of the LiDAR footprint. For estimating biomass, these measurements mix a number of errors including those associated with LiDAR footprint sampling over regional-global extents. A general framework for mapping above ground live forest biomass density (AGB) with a data fusion approach is presented and verified using data from NASA field campaigns near Howland, ME, USA, to assess AGB and LiDAR sampling errors across a regionally representative landscape. We combined SAR and Landsat-derived optical (passive optical) image data to identify contiguous areas (>0.5 ha) that are relatively homogenous in remote sensing metrics (forest patches). We used this image-derived data with simulated spaceborne LiDAR derived from orbit and cloud cover simulations and airborne data from NASA's Laser Vegetation Imaging Sensor (LVIS) to compute AGB and estimate LiDAR sampling error for forest patches and 100 m, 250 m, 500 m, and 1 km grid cells. At both the patch and grid scales, we evaluated differences in AGB estimation and sampling error from the combined use of LiDAR with both SAR and passive optical and with either SAR or passive optical alone. First, this data fusion approach demonstrates that incorporating forest patches into the AGB mapping framework can provide sub-grid forest information for coarser grid-level AGB reporting. Second, a data fusion approach for estimating AGB using simulated spaceborne LiDAR with SAR and passive optical image combinations reduced forest AGB sampling errors 12%-38% from those where LiDAR is used with SAR or passive optical alone. In absolute terms, sampling errors were reduced from 14-40 Mg/ha to 11-28 Mg/ha across all grid scales and prediction methods, where minimum sampling errors were 11, 15, 18, and 22 Mg/ha for 1 km, 500 m, 250 m, and 100 m grid scales, respectively. Third, spaceborne global scale accuracy requirements were achieved whereby at least 80% of the grid cells at 100 m, 250 m, 500 m, and 1 km grid levels met AGB accuracy requirements using a combination of passive optical and SAR along with machine learning methods to predict vegetation structure metrics for forested areas without LiDAR samples. Finally, using either passive optical or SAR, accuracy requirements were met at the 500 m and 250 m grid level, respectively..

LiDAR↗

NASA NTRS2006

Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design.

Nemec, Marian↗

NASA NTRS2011

Clonal Selection Based Artificial Immune System for Generalized Pattern Recognition

The last two decades has seen a rapid increase in the application of AIS (Artificial Immune Systems) modeled after the human immune system to a wide range of areas including network intrusion detection, job shop scheduling, classification, pattern recognition, and robot control. JPL (Jet Propulsion Laboratory) has developed an integrated pattern recognition/classification system called AISLE (Artificial Immune System for Learning and Exploration) based on biologically inspired models of B-cell dynamics in the immune system. When used for unsupervised or supervised classification, the method scales linearly with the number of dimensions, has performance that is relatively independent of the total size of the dataset, and has been shown to perform as well as traditional clustering methods. When used for pattern recognition, the method efficiently isolates the appropriate matches in the data set. The paper presents the underlying structure of AISLE and the results from a number of experimental studies.

pattern recognition↗

NASA NTRS2008

Parallel Anisotropic Tetrahedral Adaptation

An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.

Park, Michael A.↗

NASA NTRS1993

FAS multigrid calculations of three dimensional flow using non-staggered grids

Grid staggering is a well known remedy for the problem of velocity/pressure coupling in incompressible flow calculations. Numerous inconveniences occur, however, when staggered grids are implemented, particularly when a general-purpose code, capable of handling irregular three-dimensional domains, is sought. In several non-staggered grid numerical procedures proposed in the literature, the velocity/pressure coupling is achieved by either pressure or velocity (momentum) averaging. This approach is not convenient for simultaneous (block) solvers that are preferred when using multigrid methods. A new method is introduced in this paper that is based upon non-staggered grid formulation with a set of virtual cell face velocities used for pressure/velocity coupling. Instead of pressure or velocity averaging, a momentum balance at the cell face is used as a link between the momentum and mass balance constraints. The numerical stencil is limited to 9 nodes (in 2D) or 27 nodes (in 3D), both during the smoothing and inter-grid transfer, which is a convenient feature when a block point solver is applied. The results for a lid-driven cavity and a cube in a lid-driven cavity are presented and compared to staggered grid calculations using the same multigrid algorithm. The method is shown to be stable and produce a smooth (wiggle-free) pressure field.

Matovic, D.↗

NASA NTRS1994

Computational Approaches to Vestibular Research

The Biocomputation Center at NASA Ames Research Center is dedicated to a union between computational, experimental and theoretical approaches to the study of neuroscience and of life sciences in general. The current emphasis is on computer reconstruction and visualization of vestibular macular architecture in three-dimensions (3-D), and on mathematical modeling and computer simulation of neural activity in the functioning system. Our methods are being used to interpret the influence of spaceflight on mammalian vestibular maculas in a model system, that of the adult Sprague-Dawley rat. More than twenty 3-D reconstructions of type I and type II hair cells and their afferents have been completed by digitization of contours traced from serial sections photographed in a transmission electron microscope. This labor-intensive method has now been replace d by a semiautomated method developed in the Biocomputation Center in which conventional photography is eliminated. All viewing, storage and manipulation of original data is done using Silicon Graphics workstations. Recent improvements to the software include a new mesh generation method for connecting contours. This method will permit the investigator to describe any surface, regardless of complexity, including highly branched structures such as are routinely found in neurons. This same mesh can be used for 3-D, finite volume simulation of synapse activation and voltage spread on neuronal surfaces visualized via the reconstruction process. These simulations help the investigator interpret the relationship between neuroarchitecture and physiology, and are of assistance in determining which experiments will best test theoretical interpretations. Data are also used to develop abstract, 3-D models that dynamically display neuronal activity ongoing in the system. Finally, the same data can be used to visualize the neural tissue in a virtual environment. Our exhibit will depict capabilities of our computational approaches and some of our findings from their application. For example, our research has demonstrated that maculas of adult mammals retain the property of synaptic plasticity. Ribbon synapses increase numerically and undergo changes in type and distribution (p<0.0001) in type II hair cells after exposure to microgravity for as few as nine days. The finding of macular synaptic plasticity is pertinent to the clinic, and may help explain some. balance disorders in humans. The software used in our investigations will be demonstrated for those interested in applying it in their own research.

Ross, Muriel D.↗

NASA NTRS1996

Hierarchical and Parallelizable Direct Volume Rendering for Irregular and Multiple Grids

A general volume rendering technique is described that efficiently produces images of excellent quality from data defined over irregular grids having a wide variety of formats. Rendering is done in software, eliminating the need for special graphics hardware, as well as any artifacts associated with graphics hardware. Images of volumes with about one million cells can be produced in one to several minutes on a workstation with a 150 MHz processor. A significant advantage of this method for applications such as computational fluid dynamics is that it can process multiple intersecting grids. Such grids present problems for most current volume rendering techniques. Also, the wide range of cell sizes (by a factor of 10,000 or more), which is typical of such applications, does not present difficulties, as it does for many techniques. A spatial hierarchical organization makes it possible to access data from a restricted region efficiently. The tree has greater depth in regions of greater detail, determined by the number of cells in the region. It also makes it possible to render useful 'preview' images very quickly (about one second for one-million-cell grids) by displaying each region associated with a tree node as one cell. Previews show enough detail to navigate effectively in very large data sets. The algorithmic techniques include use of a kappa-d tree, with prefix-order partitioning of triangles, to reduce the number of primitives that must be processed for one rendering, coarse-grain parallelism for a shared-memory MIMD architecture, a new perspective transformation that achieves greater numerical accuracy, and a scanline algorithm with depth sorting and a new clipping technique.

Wilhelms, Jane↗

NASA NTRS1993

Time-dependent grid adaptation for meshes of triangles and tetrahedra

This paper presents in viewgraph form a method of optimizing grid generation for unsteady CFD flow calculations that distributes the numerical error evenly throughout the mesh. Adaptive meshing is used to locally enrich in regions of relatively large errors and to locally coarsen in regions of relatively small errors. The enrichment/coarsening procedures are robust for isotropic cells; however, enrichment of high aspect ratio cells may fail near boundary surfaces with relatively large curvature. The enrichment indicator worked well for the cases shown, but in general requires user supervision for a more efficient solution.

Russ D Rausch↗

NASA NTRS1994

Heavy ion induced DNA-DSB in yeast and mammalian cells

Molecular changes at the DNA are assumed to be the main cause for radiation effects in a number of organisms. During the course of the last decades techniques have been developed for measuring DNA double-strand breaks (dsb), generally assumed to be the most critical DNA lesions. The outcome of all those different approaches portrays a collection of data useful for a theoretical description of radiation action mechanisms. However, in the case of heavy ion induced DNA dsb the picture is not quite clear yet and further projects and strategies have to be developed. The biological systems studied in our group are yeast and mammalian cells. While in the case of yeast cells technical and methodical reasons highlight these organisms mammalian cells reach greater importance when dsb repair studies are performed. In both types of organisms the technique of pulsed-field gel electrophoresis (PFGE) is applied, although with different modifications and evaluation procedures mainly due to the different genome sizes.

Loebrich, M.↗

NASA NTRS2004

Modeling and Analysis of Large Amplitude Flight Maneuvers

Analytical methods for stability analysis of large amplitude aircraft motion have been slow to develop because many nonlinear system stability assessment methods are restricted to a state-space dimension of less than three. The proffered approach is to create regional cell-to-cell maps for strategically located two-dimensional subspaces within the higher-dimensional model statespace. These regional solutions capture nonlinear behavior better than linearized point solutions. They also avoid the computational difficulties that emerge when attempting to create a cell map for the entire state-space. Example stability results are presented for a general aviation aircraft and a micro-aerial vehicle configuration. The analytical results are consistent with characteristics that were discovered during previous flight-testing.

Anderson, Mark R.↗

NASA NTRSDate not supplied

Preliminary Testing of Electrolytic Silver Ion Generation for Spacecraft Potable Water Systems

Anodic dissolution of silver electrodes, or “silver electrolysis,” is being investigated as a means of imparting biocidal silver into potable water on exploration spacecraft. This method of water disinfection is used commercially in hospitals and marine vessels, but the spacecraft application poses unique challenges such as low water conductivity, increased importance of electrode longevity, and an interface with other systems that may be sensitive to any particles released in the electrolysis process. Testing has shown that due to the low conductivity of the water, the electroactive area of the cell can be scaled linearly to achieve a target electrolysis current despite the general non-linearity of electrochemical systems. More importantly, however, the low conductivity dictates that a large electroactive area and minimal electrode gap be employed in the design. Furthermore, thermodynamic considerations suggest that a low applied voltage is necessary to avoid undesired electrode reactions that could negatively impact long-term performance. Preliminary testing of long-term electrode health suggests that anodic oxide formation may not present as significant a challenge as anticipated; however, further testing in a system closed to the atmosphere is required to rule out the influence of atmospheric CO2 on the pH of the process water. Comparison of filtered and unfiltered silver concentration measurements indicates that release of particles larger than 0.2 μm was negligible in this preliminary test. A test article has been developed to facilitate further testing of silver electrolysis, which continues to be a candidate technology for spacecraft potable water disinfection.

silver↗

NASA NTRS2001

Computational Aeroacoustics by the Space-time CE/SE Method

In recent years, a new numerical methodology for conservation laws-the Space-Time Conservation Element and Solution Element Method (CE/SE), was developed by Dr. Chang of NASA Glenn Research Center and collaborators. In nature, the new method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its rigorous treatment of the fluxes and geometry, it is different from the existing schemes. The CE/SE scheme features: (1) space and time treated on the same footing, the integral equations of conservation laws are solve( for with second order accuracy, (2) high resolution, low dispersion and low dissipation, (3) novel, truly multi-dimensional, simple but effective non-reflecting boundary condition, (4) effortless implementation of computation, no numerical fix or parameter choice is needed, an( (5) robust enough to cover a wide spectrum of compressible flow: from weak linear acoustic waves to strong, discontinuous waves (shocks) appropriate for linear and nonlinear aeroacoustics. Currently, the CE/SE scheme has been developed to such a stage that a 3-13 unstructured CE/SE Navier-Stokes solver is already available. However, in the present paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen as a prototype and is sketched in Section 2. Then applications of the CE/SE scheme to linear, nonlinear aeroacoustics and airframe noise are depicted in Sections 3, 4, and 5 respectively to demonstrate its robustness and capability.

Loh, Ching Y.↗