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On the Use of Parametric-CAD Systems and Cartesian Methods for Aerodynamic Design

On the Use of Parametric-CAD Systems and Cartesian Methods for Aerodynamic Design
On the Use of Parametric-CAD Systems and Cartesian Methods for Aerodynamic Design

On the Use of Parametric-CAD Systems and Cartesian Methods for Aerodynamic Design Marian Nemec1,Michael J.Aftosmis2,and Thomas H.Pulliam3

1NASA Ames Research Center,Mo?ett Field,CA,USA nemec@https://www.sodocs.net/doc/778826732.html,

2aftosmis@https://www.sodocs.net/doc/778826732.html,

3tpulliam@https://www.sodocs.net/doc/778826732.html,

1Introduction

Automated,high-?delity tools for aerodynamic design face critical issues in attempting to optimize real-life geometry and in permitting radical design changes.Success in these areas promises not only signi?cantly shorter design-cycle times,but also superior and unconventional designs.To address these issues,we investigate the use of a parametric-CAD system in conjunction with an embedded-boundary Cartesian method.Our goal is to combine the mod-eling capabilities of feature-based CAD with the robustness and?exibility of component-based Cartesian volume-mesh generation for complex geometry problems.We present the development of an automated optimization frame-work with a focus on the deployment of such a CAD-based design approach in a heterogeneous parallel computing environment.

2Problem Formulation

The aerodynamic optimization problem consists of determining values of de-sign variables such that a given objective function is minimized,while satis-fying the governing?ow equations and any other side constraints.Examples of objectives and constraints include performance functionals,such as lift and drag,and geometric quantities,such as volumes and thicknesses.The?ow equations are the three-dimensional Euler equations of a perfect gas.

A modular framework is constructed to solve the optimization problem based on two optimizers:1)a genetic algorithm(GA),and2)a BFGS quasi-Newton algorithm,where the objective function gradient is evaluated via central-di?erences.At the core of the framework is the analysis module that consists of a CAD-system interface and the Cart3D?ow-analysis package. The primary components of Cart3D include a Cartesian grid generator[1], and a?ow solver[2].Below,we provide a description of the CAD interface, followed by the optimization framework.See[3]for additional details.

2M.Nemec,M.J.Aftosmis,and T.H.Pulliam

3CAD Interface:CAPRI

The CAD interface controls the regeneration of a CAD model in response to a design change and provides a corresponding watertight surface triangulation.This is accomplished by the use of the Computational Analysis PRogramming Interface (CAPRI)[4,5].CAPRI exposes the master-model feature tree of the CAD model and allows direct modi?cation of parameters within that tree.Most design variables are associated directly with values exposed in the feature tree.Depending on the CAD-face topology of the model,CAPRI triangulates the faces by using either a quality triangulation algorithm [6,4],or by decomposing quadrilaterals generated with an auto-blocking algorithm [7].4Optimization Framework

https://www.sodocs.net/doc/778826732.html,yout of the interface between optimiza-tion processes and geometry server

The synthesis of CAPRI with

the optimization process is

shown in Fig.1.At each it-eration of the optimization,CAD geometry requests are generated for di?erent design-variable values and these are placed in a central reposi-

tory.Independent of the op-timization runs,a distributed

geometry server is initiated

that consists of multiple CAD nodes.The nodes process the

geometry requests by retriev-

ing the required parts and

assemblies,regenerating the CAD models,and providing surface triangulations for the

optimization processes.Since

the geometry requests are independent,the geometry server achieves nearly linear scalability.

The number of CAD nodes is limited by the number of available CAD licenses,as each node consumes one license.An immediate concern is that the CAD nodes may become the bottleneck of the optimization process,idling the processors of the compute engines.To avoid such bottlenecks,we dynamically allocate the processors of the optimization to the number of completed surface triangulations.Figure 2illustrates this on an example with 64processors.At the start of each design iteration,all processors are dedicated to the solution of the ?rst returned surface triangulation from the CAD nodes.This is the base state of the gradient method and the ?rst chromosome of the GA,denoted as

CAD-Based Aerodynamic Design 3

“Geometry 1”in Fig.2.Upon completion of the ?rst geometry analysis,we check the number of completed surface triangulations.These are processed by the CAD nodes while the analysis of the ?rst geometry is performed on the compute engine,denoted as “Geometries 2...K ”in Fig.2.The number of processors is distributed among the completed surface triangulations and multiple analysis modules are executed on subsets of the available processors.This dynamic,coarse-grained parallelism provides not only concurrent execu-tion of serial tasks,but also ensures high parallel e?ciency of the ?ow solver by limiting the number of processors available to each analysis module.

Fig.2.Dynamic allocation of processors to mask the latency of CAD geometry processing The worst case scenario oc-

curs when the wall-clock time

required for the processing of a geometry request exceeds

the time for completion of

the ?ow solution.If only one CAD node is available,then

this CAD node would not

be

able to feed the compute en-gine with geometries without processor idle time.This sit-

uation is unlikely,since CAD

model regeneration and tes-

sellation tasks have computa-

tional complexity of O (N 2),while volume mesh generation and ?ow solution tasks are

O (N 3).

5Design Example

Fig. 3.CAD model con?guration (before component intersection)We investigate the performance of

the optimization framework for a

design example based on the con-

?guration shown in Fig. 3.This

generic model is a CAD assembly

of ?ve parts,where the wing and

canard are “attached”to the fuse-

lage via two parameters,their hor-

izontal and vertical locations,re-spectively.These parameters are constrained to intersect the projec-

tion of the fuselage on the symme-

try plane within the CAD system.This simple construct avoids non-physical con?gurations,for example wings that detach from the fuselage during the

4M.Nemec,M.J.Aftosmis,and T.H.Pulliam

optimization,even if the fuselage shape and dimensions change.The CAD model is constructed using the Pro/ENGINEER CAD system.

Before presenting optimization results,we characterize the performance of the optimization framework.Table1presents average CPU timing results for the CAD model regeneration and surface triangulation using CAPRI.It is clear from Table1that CAD-model regeneration times are not a signi?cant expense even for problems with many design variables.While the time re-quired for surface triangulation is not prohibitive,it is important to avoid all unnecessary re-triangulations during the optimization.This is accomplished by caching an associated baseline triangulation for each part prior to the optimization.

Table 1.Average CPU time for CAD-model regeneration and

tessellation(600MHz R14000SGI Octane Workstation)

Part CAD-Model Tessellation Number of Tessellation

Regeneration(s)(s)Triangles Algorithm

a

Wing 3.0b16.5≈50,000Right-triangle

a No shape-section change,only global parameter modi?cations

b Shape-section change and planform parameter modi?cations

Table2presents average timing results for individual components within the analysis module.The volume mesh contains roughly1.5million cells for a half-span model of the con?guration.The time for the mesh-solution transfer algorithm used to“warm-start”?nite-di?erence gradient computations is also https://www.sodocs.net/doc/778826732.html,parison of Tables1and2indicates that the time required to Table2.Wallclock times for individual components of the anal-

ysis module(600MHz R14000SGI Origin3000)

Component Time(s)Algorithm

Mesh Generation a132.0Serial

Flow Solution(?owCart1.2)455.0Parallel(64processors)

Mesh Solution Transfer26.0Serial

a Also includes component intersection,domain decomposi-

tion,and multigrid coarse-mesh generation

complete a CAD-model regeneration and surface triangulation is a factor of six smaller than the time required for a?ow solution.This means that by the time the analysis module completes the?ow solution of the?rst chromosome of the

CAD-Based Aerodynamic Design5 GA or the base-state of the gradient method,six new surface triangulations are ready for analysis,ensuring good CPU e?ciency.

We consider the optimization problem of attaining a nearly zero pitching moment coe?cient by optimizing the canard/tail control surface.The design variables are the control surface aspect ratio(AR),twist(tip relative to root section),and axial position along the center line of the fuselage.The problem has two local optima,the tail or canard con?guration,with the canard con?g-uration as the global optimum due to an aft location of the center of gravity. For optimization using the GA,the canard area is also a design variable.This introduces the possibility of a topology change in the design space.We use16 chromosomes for each generation of the GA.For the quasi-Newton algorithm, the control surface area is kept constant(60.0).The freestream Mach number is0.85,and the angle of attack is1.0deg.

The objective function uses a quadratic-penalty formulation,with a target lift coe?cient of0.222and a target pitching moment coe?cient of0.001.The initial pitching moment is?0.0714.Figure4(a)shows the convergence history of the objective function.The label“Design Iteration”refers to the number of generations evaluated by the GA,and the number of objective function and gradient evaluations by the quasi-Newton algorithm.The GA converges within 5design iterations,requiring only80function evaluations.The quasi-Newton algorithm requires56function evaluations to trim the con?guration.

Figures4(b)and4(c)show the initial and?nal designs for the quasi-Newton algorithm.The control surface converged to the minimum allowable forward location on the fuselage(8%of fuselage length),a twist angle of2.98 deg.,and AR of6.03.Figure4(d)shows the?nal design using the GA.For this case,the optimization converged to the upper bound of the control surface area,which is60.0,a forward location of8.2%of fuselage length,a twist angle of3.41deg.,and AR of4.36.The small di?erences in the two designs indicate that there may be many control surfaces that trim this con?guration and further constraints are required to de?ne a unique problem.

6Conclusions

A modular framework for the aerodynamic optimization of complex geome-tries has been developed.The framework includes a direct interface to a parametric-CAD system that allowed an e?cient manipulation and surface tessellation of generic-CAD models.Furthermore,the use of a component-based Cartesian method reduced the demands on the CAD system by reusing cached component triangulations,and improved the robustness of the frame-work due to the decoupling of the surface mesh form the volume mesh.Par-allel e?ciency of the framework was maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the?ow solver, thereby using the scalability of the solver to mask the latency of the geometry server.

6M.Nemec,M.J.Aftosmis,and T.H.Pulliam

(a)Convergence history(b)Initial con?guration,Gradient

(c)Final con?guration,Gradient(d)Final con?guration,GA

Fig.4.Design example summary(Contour plots denote surface Mach number) 7Acknowledgments

The authors gratefully acknowledge Robert Haimes(MIT).This work was performed while the?rst author held an NRC Research Associateship Award.

References

1.Aftosmis,M.J.,Berger,M.J.,and Melton,J.E.,“Robust and E?cient Cartesian

Mesh Generation for Componenet-Based Geometry,”AIAA J.,Vol.36-6,1998.

2.Aftosmis,M.J.,Berger,M.J.,and Adomavicius,G.,“A Parallel Multilevel

Method for Adaptively Re?ned Cartesian Grids with Embedded Boundaries,”

AIAA Paper2000–0808,Reno,NV,Jan.2000.

3.Nemec,M.,Aftosmis,M.J.,and Pulliam,T.H.,“CAD-Based Aerodynamic

Design of Complex Con?gurations Using a Cartesian Method,”AIAA Paper 2004–0113,Reno,NV,Jan.2004.

4.Haimes,R.and Aftosmis,M.J.,“On Generating High Quality”Water-tight”

Triangulations Directly from CAD,”ISGG,June2002.

5.Haimes,R.and Crawford,C.,“Uni?ed Geometry Access for Analysis and De-

sign,”12th International Meshing Roundtable,Sept.2003.

6.Aftosmis,M.J.,“On the Use of CAD-Native Predicates and Geometry in Surface

Meshing,”NASA TM1999–208782,Aug.1999.

7.Haimes,R.and Aftosmis,M.J.,“Watertight Anisotropic Surface Meshing Using

Quadrilateral Patches,”13th International Meshing Roundtable,Sept.2004.

The use of force

孩子。 Does your throat hurt you? Added the mother to the child. 女孩的表情没有任何变化,而她的目光却一直没有从我的脸上移开。 But the little girl’s expression didn’t change nor did she move her eyes from my face. 你看过她的嗓子了吗? Have you looked? 我想看,孩子的母亲说,但看不见。 I tried to, said the mother but II couldn’t see. 这个月碰巧她上学的那个学校已经有好几例白喉病。虽然到目前为止没有人说出这件事,但很显然,我们心里都想到了。 As it happens we had been having a number of cases of diphtheria in the school to which this child went during that month and we were all, quite apparently, thinking of that, though no one had as yet spoken of the thing. 好了,我说,我们先看看嗓子吧。 Well, I said, suppose we take a look at the throat first. 我以医生特有的职业方式微笑着,叫着孩子的名字。我说,来吧,玛蒂尔达,张开嘴,让我看一下你的嗓子。 I smiled in my best professional manner and asking for the child’s first name I said, come on, Mathilda, open your mouth and let’s take a look at your throat.没有任何反应。 Nothing doing. 哦,来吧,我劝道,张大你的嘴,让我看看。看,我说着把两只手伸开,我的手里没有东西,张大嘴,让我看看。 Aw, come on, I coaxed, just open your mouth wide and let me take a look. Look, I said opening both hands wide, I haven’t anything in my hands. Just open up and let me see.

The use of force

The use of force 大意: Mathilda had been ill for three days. Her mother had given her some medicine, but it didn’t do any good. So they had to ask the doctor to come. There had been a number of cases of diphtheria in Mathilda School and two of them had been dead. When the doctor arrived at Olson’s home, he wanted to examine Mathilda throat first. But no matter how he coaxed, She wouldn’t open her mouth. So the doctor had to get the tongue depressor into her mouth. But Mathilda reduced it to splinters. In orde r to protect Mathilda herself and other children, the doctor had to make sure whether she had diphtheria or not, so that he could treat her in time. Letting Mathilda‘s father hold her wrists he tried his best to open her mouth and found she really had diphtheria. This story made us can think such a question that something in life can’t only depend on self-willingness. Under some circumstances, certain force seems necessary. 对医生的评价:After the doctor arrived at the girl’s home, he wanted to see her throat. As there had been a number of cases of diphtheria in the school to which the girl went during that month, the doctor also thought that of the girl. So he smiled to the girl and asked her to open her mouth and let him have a look at her throat. No matter how the doctor coaxed, the girl shut her mouth firmly. Thinking that the girl might have diphtheria and possibly die of it, the doctor decided to use force to open her mouth. He had seen at least two children lying dead in bed of neglect in such cases. He felt that he must get a diagnosis now. So he grasped the girl’s head with his left hand and tried to get the wooden tongue depressor between her teeth. But when the doctor got the wooden spatula behind her last teeth. She gripped the blade between her molars and reduced it to splinters. In the final unreasoning assault the doctor outer powered the girl. He forced the heavy silver spoon back of her teeth and down her throat till she gagged. Her both tonsils were covered with membrane. From that the doctor had done, I thought he was a responsible person. In order to save the lives of the patients, especially those children who did not know how to co-operate with the doctor, he had to take some measure. Otherwise a good or suitable time of treatment would be missed. The doctor appears to be compassionate and keen to human behavior, characteristic of a good doctor, though he is also undeniably blunt and slightly prejudiced. 思想: Though there are reasons often justifiable, what compels the use of force against others isn't simply altruism alone. The overall theme of the story revolves around power and submission and the doctor's unnerved feeling following the forceful encounter. 作者如何写的: The story is narrated in first person by a doctor, who is answering a house visit to see a sick girl. Williams uses interior monologue as a "stream-of-consciousness" tool reflects the narrator's experience of dialogue and gives insight into the character and his appraisal of the situations he encounters. The story is written without the use of quotation marks, and the dialogue is not distinguished from the narrator's comments. The story is rendered from the subjective point of view of the doctor, and explores his subdued enjoyment of forcefully subduing the stubborn child in an attempt to acquire the throat sample.

Unit 1 Text A The Use of Force翻译

‘Unit 1 Text A The Use of Force 他们是我的新病人,我所知道的只有名字,奥尔逊。 They were new patients to me, all I had was the name, Olson. 请您尽快赶来,我女儿病得很重。 “Please come down as soon as you can, my daughter is very sick.” 当我到达时,孩子的母亲迎接了我,这是一位看上去惊恐不安的妇人,衣着整洁却一脸忧伤的神色她只是说,这位就是医生吗? When I arrived I was met by the mother, a big startled looking woman, very clean and apologetic who merely said, Is this the doctor? 然后带我进了屋。 And let me in. 在后面,她又说到,请你一定要原谅我们,医生,我们让她呆在厨房里,那儿暖和,这里有时很潮湿。 In the back, she added. Y ou must excuse us, doctor, we have her in the kitchen where it is warm. It is very damp here sometimes. 在厨房的桌子旁边,这个孩子穿得严严实实的,坐在她父亲的腿上。 The child was fully dressed and sitting on here father’s lap near the kitchen table. 他父亲试图站起来,但我向他示意不用麻烦,然后我脱下外套开始检查。 He tried to get up, but I motioned for him not to bother, took off my overcoat and started to look things over. 我能够觉察出他们都很紧张,而且用怀疑的眼光上下打量着我。 I could see that they were all very nervous, eyeing me up and down distrustfully. 在这种情形下,他们通常不会提供太多的情况,而是等着我告诉他们病情,这就是为什么他们会在我身上花3美元。 As often, in such cases, they weren’t telling me more than they had to, it was up to me to tell them; that’s why they were spending three dollars on me. 这个孩子用她那冷漠而镇定的目光目不转睛地盯着我,脸上没有任何表情。 The child was fairly eating me up with her cold, steady eyes, and no expression on her face whatever. 她纹丝不动,内心似乎很平静。这是一个非常惹人喜爱的小东西,外表长得象小牛一样结实。 She did not move and seemed, inwardly, quiet; an unusually attractive little thing, and as strong as a heifer in appearance. 但是她的脸发红,而且呼吸急促,我知道她在发着高烧。 But her face was flushed, she was breathing rapidly, and I realized that she had a high fever. 她长着一头漂亮浓密的金发,就像刊登在广告插页上和周日报纸图片版上的那些孩子一样。 She had magnificent blonde hair, in profusion. One of those picture children often reproduced in advertising leaflets and the photogravure sections of the Sunday papers.

新视野读写教程第三版大学英语4翻译

第一单元 一、英译汉 Aristotle was an ancient Greek philosopher and scientist. 亚里士多德是古希腊的哲学家和科学家。 His writings cover many subjects, including physics, biology, zoology, logic, ethics, poetry, theater, music, linguistics, politics and government, and constitute the first comprehensive system of Western philosophy. 他的作品涵盖了许多学科,包括物理学、生物学、动物学、逻辑学、伦理学、诗歌、戏剧、音乐、语言学、政治和政府,构成了第一个综合的西方哲学体系。 Aristotle was the first to classify areas of human knowledge into distinct disciplines such as mathematics, biology, and ethics. 亚里士多德是第一个将人类的知识领域划分为不同学科的人,如数学,生物学和伦理学。 He believed all people's concepts and all their knowledge were ultimately based on perception. 他相信人所有的观念和所有的知识在根本上都是基于感知能力。 His views on natural sciences laid the groundwork for many of his works. 他对自然科学的看法构成了他许多作品的基础。 He contributed to almost every field of human knowledge in his era. 他几乎对他所处时期的每一个人类知识领域都作出了贡献。 His works contain the earliest known formal study of logic, and even today all aspects of Aristotle's philosophy continue to be the important subject of academic study. His philosophy had a long-lasting influence on the development of all Western philosophical theories.

The Pragmatics of Translation一书介绍

Leo, Hickey (ed.) The Pragmatics of Translation. Clevedon/ P h i l a d e l p h i a:M u l t i l i n g u a l Matters, 1998, 242 pp. The Pragmatics of Translation is a collection of thirteen articles compiled by author and editor Leo Hickey. Each individual author represents in his or her article a different approach to translation through the use of various translation theories and practices. The intention of these articles, according to Hickey, is to present the ways in which pragmatics rela-tes to translation and how one may achieve what he calls “pragmatic equivalence”. The authors attempt to answer various questions concerning the relationship between original texts and their translations, and what exactly these translations intend to achieve. Hickey claims in

The use of force 使用暴力

The use of force 使用暴力 -- by William Carlos Williams Text They will new patients to me, all I had was the name, Olson. Please come down as soon as you can, my daughter is very sick. 他们是我的新病人,我所知道的只有名字,奥尔逊。请您尽快赶来,我女儿病得很重。 When I arrived I was met by the mother, a big startled looking woman, very clean and apologetic who merely said, Is this the doctor? And let me in. In the back, she added. You must excuse us, doctor, we have her in the kitchen where it is warm. It is very damp here sometimes. 当我到达时,孩子的母亲迎接了我,她身材高大,一脸惊慌,衣着整洁,带着歉意,只问,您是医生吧?就让我进了屋。在后面,她又说,请你一定要原谅我们,医生,我们让她呆在厨房里,那儿暖和。这里有时很潮湿。 The child was fully dressed and sitting on her father’s lap near the kitchen table. He tried to get up, but I motioned for him not to bother took of my overcoat and started to look things over. I could see that they were all very nervous, eyeing me up and down distrustfully. As often, in such cases, they weren ’t telling me more than they had to, it was up to me to tell them; that ’s why were spending three dollars on me. 在厨房的桌子旁,这个孩子穿得严严实实的,坐在她父亲的腿上。他试图站 起来,但我示意不必了,然后我脱下外套并开始检查。我能够觉察出他们都很紧张,怀疑地上下打量着我。通常在这样的情况下,除非必要,他们不会对我讲得太多,而是要我告诉他们,这就是他们为什么会在我身上花3美元。 The child was fairly eating me up with her cold, steady eyes, and no expression on her face whatever. She did not move and seemed, inwardly, quiet; an unusually attractive little thing, and as strong as a heifer in appearance. But her face was flushed, she was breathing rapidly, and I realized that she had a high fever. She had magnificent blonde hair, in profusion. One of those picture children often reproduced in advertising leaflets and the photogravure sections of the Sunday papers. 这个孩子用她那冷漠而平静的目光小心仔细地打量着我,脸上没有任何表情。她没有动好像内心很平静,这是一位非常具有魅力的小东西,外表像小母牛一样结实。但她的脸很红,而且呼吸急促,我知道她在发高烧。她长了一头漂亮的金发,非常浓密,和经常出现在广告插页或周日报纸图片上的孩子一样。 She ’s had a fever for three days, began the father and we don ’t know what it comes from. My wife has given her things, you know, like people do, but it don ’t do no good. And there ’s been a lot of sickness around. So we tho ’t you ’ d

A3 The Use of Force

Lesson Three The Use of Force by William Carlos Williams 使用暴力 威廉·卡洛斯·威廉斯 ○课文逐句翻译 他们是我的新病人,我所知道的只有名字,奥尔逊。 They were new patients to me, all I had was the name, Olson. 请您尽快赶来,我女儿病得很重。 “Please come down as soon as you can, my daughter is very sick.” 当我到达时,孩子的母亲迎接了我,这是一位看上去惊恐不安的妇人,衣着整洁却一脸忧伤的神色她只是说,这位就是医生吗? When I arrived I was met by the mother, a big startled looking woman, very clean and apologetic who merely said, Is this the doctor? 然后带我进了屋。 And let me in. 在后面,她又说到,请你一定要原谅我们,医生,我们让她呆在厨房里,那儿暖和,这里有时很潮湿。 In the back, she added. Y ou must excuse us, doctor, we have her in the kitchen where it is warm. It is very damp here sometimes. 在厨房的桌子旁边,这个孩子穿得严严实实的,坐在她父亲的腿上。 The child was fully dressed and sitting on here father?s lap near the kitchen table. 他父亲试图站起来,但我向他示意不用麻烦,然后我脱下外套开始检查。 He tried to get up, but I motioned for him not to bother, took off my overcoat and started to look things over. 我能够觉察出他们都很紧张,而且用怀疑的眼光上下打量着我。 I could see that they were all very nervous, eyeing me up and down distrustfully. 在这种情形下,他们通常不会提供太多的情况,而是等着我告诉他们病情,这就是为什么他们会在我身上花3美元。 As often, in such cases, they weren?t telling me more than they had to, it was up to me to tell them; that?s why they were spending three dollars on me. 这个孩子用她那冷漠而镇定的目光目不转睛地盯着我,脸上没有任何表情。 The child was fairly eating me up with her cold, steady eyes, and no expression on her face whatever. 她纹丝不动,内心似乎很平静。这是一个非常惹人喜爱的小东西,外表长得象小牛一样结实。 She did not move and seemed, inwardly, quiet; an unusually attractive little thing, and as strong as a heifer in appearance. 但是她的脸发红,而且呼吸急促,我知道她在发着高烧。 But her face was flushed, she was breathing rapidly, and I realized that she had a high fever. 她长着一头漂亮浓密的金发,就像刊登在广告插页上和周日报纸图片版上的那些孩子一样。 She had magnificent blonde hair, in profusion. One of those picture children often reproduced in advertising leaflets and the photogravure sections of the Sunday papers.

新视野大学英语-第三版-读写教程3-选词填空

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