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1

Xu, Taihua, Jie Yang, and Guanglei Gou. "A Force-Directed Algorithm for Drawing Directed Graphs Symmetrically." Mathematical Problems in Engineering 2018 (November 19, 2018): 1–24. http://dx.doi.org/10.1155/2018/6208509.

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Symmetry is one of the most important aesthetic criteria on graph drawing. It is quite necessary to measure the extent to which the drawings can be considered symmetric. For this purpose, a symmetric metric based on vertex coordinate calculation is proposed in this paper. It is proven theoretically and experimentally that the proposed metric is robust to contraction, expansion, and rotation of drawings. This robustness conforms to human perception of symmetry. Star-subgraphs and cycles are two common structures in digraphs. Both of them have inherent symmetry which should be displayed in drawi
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2

Cheong, Se-Hang, and Yain-Whar Si. "Force-directed algorithms for schematic drawings and placement: A survey." Information Visualization 19, no. 1 (2019): 65–91. http://dx.doi.org/10.1177/1473871618821740.

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Force-directed algorithms have been developed over the last 50 years and used in many application fields, including information visualisation, biological network visualisation, sensor networks, routing algorithms, scheduling, and graph drawing. Our survey provides a comprehensive summary of developments and a full roadmap for state-of-the-art force-directed algorithms in schematic drawings and placement. We classified the model of force-directed algorithms into classical and hybrid. The classical force-directed algorithms are further classified as follows: (a) accumulated force models, (b) ene
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3

Kennings, A., and K. P. Vorwerk. "Force-Directed Methods for Generic Placement." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25, no. 10 (2006): 2076–87. http://dx.doi.org/10.1109/tcad.2005.862748.

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4

Giacomin, Giambattista, and Fabio Lucio Toninelli. "Force-induced depinning of directed polymers." Journal of Physics A: Mathematical and Theoretical 40, no. 20 (2007): 5261–75. http://dx.doi.org/10.1088/1751-8113/40/20/003.

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5

Brezani, Alexander, Jozef Kostolny, and Michal Zabovsky. "Force-Directed Immersive 3D Network Visualization." Computers 13, no. 8 (2024): 189. http://dx.doi.org/10.3390/computers13080189.

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Network visualization, in mathematics often referred to as graph visualization, has evolved significantly over time, offering various methods to effectively represent complex data structures. New methods and devices advance the possibilities of visualization both from the point of view of the quality of displayed information and of the possibilities of visualizing a larger amount of data. Immersive visualization includes the user directly in presented visual representation but requires a native 3D environment for direct interaction with visualized information. This article describes an approac
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6

Komáromi, Mátyás, István Bozó, and Melinda Tóth. "Optimising the Force-Directed Layout Generation." Acta Universitatis Sapientiae, Informatica 16, no. 1 (2025): 139–59. https://doi.org/10.47745/ausi-2024-0009.

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A graph visualisation tool can be invaluable in code comprehension. It is a well-known and researched field of graphical informatics. Several good algorithms were developed, but most of the graph drawing tools mainly focus on the generation of static drawing. In this paper, we present an approach to force-directed layout generation that is orders of magnitudes faster than the trivial implementation. This technique is based on the Runge-Kutta methods and is efficient enough to visualise the user-requested parts (views) quickly for relatively large Semantic Program Graphs of Erlang projects in s
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7

Chakraborty, Soham, Souradeep Banerjee, Manasven Raina, and Shubhasis Haldar. "Force-Directed “Mechanointeractome” of Talin–Integrin." Biochemistry 58, no. 47 (2019): 4677–95. http://dx.doi.org/10.1021/acs.biochem.9b00442.

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8

Efrat, Alon, David Forrester, Anand Iyer, Stephen G. Kobourov, Cesim Erten, and Ozan Kilic. "Force-directed approaches to sensor localization." ACM Transactions on Sensor Networks 7, no. 3 (2010): 1–25. http://dx.doi.org/10.1145/1807048.1807057.

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9

Arleo, Alessio, Walter Didimo, Giuseppe Liotta, and Fabrizio Montecchiani. "A Distributed Multilevel Force-Directed Algorithm." IEEE Transactions on Parallel and Distributed Systems 30, no. 4 (2019): 754–65. http://dx.doi.org/10.1109/tpds.2018.2869805.

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10

Zielasko, D., B. Weyers, B. Hentschel, and T. W. Kuhlen. "Interactive 3D Force-Directed Edge Bundling." Computer Graphics Forum 35, no. 3 (2016): 51–60. http://dx.doi.org/10.1111/cgf.12881.

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11

Fruchterman, Thomas M. J., and Edward M. Reingold. "Graph drawing by force-directed placement." Software: Practice and Experience 21, no. 11 (1991): 1129–64. http://dx.doi.org/10.1002/spe.4380211102.

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12

Park, Jin-Hoon, and George E. Stelmach. "Force development during target-directed isometric force production in Parkinson's disease." Neuroscience Letters 412, no. 2 (2007): 173–78. http://dx.doi.org/10.1016/j.neulet.2006.11.009.

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13

Mikheyev, V. V., V. N. Kuznetsova, and I. S. Kuznetsov. "MECHANICAL GENERATOR OF STRONGLY DIRECTED PERIODIC FORCE." DYNAMICS OF SYSTEMS, MECHANISMS AND MACHINES 11, no. 1 (2023): 16–22. http://dx.doi.org/10.25206/2310-9793-2023-11-1-16-25.

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The article concerns theoretical basics for generation of highly-directed mechanical oscillations based on the principle of inertial force transformation. The problem of formulation and analysis of the general principle of transformation of mechanical energy in order to generate periodic force directed preferably along chosen axis is considered also from dynamic and kinematic points. As an example of application for described principle the paper represents generator of highly directed periodic force. Detailed kinematic and dynamic analysis of the device is presented in the article. Perspective
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14

Eades, Peter, and Mao Lin Huang. "Navigating Clustered Graphs Using Force-Directed Methods." Journal of Graph Algorithms and Applications 4, no. 3 (2000): 157–81. http://dx.doi.org/10.7155/jgaa.00029.

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15

HARASHIMA, Katsumi, Hiroki TASHIMA, Yusuke HIRAKAWA, and Kunio FUKUNAGA. "An Efficient Approach for Force-Directed Scheduling." Transactions of the Institute of Systems, Control and Information Engineers 10, no. 4 (1997): 191–203. http://dx.doi.org/10.5687/iscie.10.191.

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16

Holten, Danny, and Jarke J. van Wijk. "Force-Directed Edge Bundling for Graph Visualization." Computer Graphics Forum 28, no. 3 (2009): 983–90. http://dx.doi.org/10.1111/j.1467-8659.2009.01450.x.

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17

Micallef, Luana, and Peter Rodgers. "eulerForce: Force-directed layout for Euler diagrams." Journal of Visual Languages & Computing 25, no. 6 (2014): 924–34. http://dx.doi.org/10.1016/j.jvlc.2014.09.002.

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18

Ma, Jiachen, Qiang Liu, and Wei Xie. "An Improved Virtual Force-Directed Particle Swarm." International Journal of Control and Automation 9, no. 5 (2016): 1–10. http://dx.doi.org/10.14257/ijca.2016.9.5.01.

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19

Barry, Chad R., Steven Campbell, and Heiko O. Jacobs. "Nanoxerography: Electrostatic Force Directed Printing of Nanomaterials." NIP & Digital Fabrication Conference 21, no. 2 (2005): 25. http://dx.doi.org/10.2352/issn.2169-4451.2005.21.2.art00010_3.

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20

Walshaw, Chris. "A Multilevel Algorithm for Force-Directed Graph-Drawing." Journal of Graph Algorithms and Applications 7, no. 3 (2003): 253–85. http://dx.doi.org/10.7155/jgaa.00070.

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21

Dubey, Pritish, Ashwini Shingare, and Vrushali Inamdar. "A Force Directed Layout Algorithm for Biological Networks." International Journal of Computer Applications 120, no. 21 (2015): 42–47. http://dx.doi.org/10.5120/21355-4314.

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22

Cruz, António, Joel P. Arrais, and Penousal Machado. "Force-Directed Timelines: Visualizing & Exploring Temporal Patterns." Big Data Research 27 (February 2022): 100291. http://dx.doi.org/10.1016/j.bdr.2021.100291.

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23

Rahman, Md Khaledur, Majedul Haque Sujon, and Ariful Azad. "Scalable force-directed graph representation learning and visualization." Knowledge and Information Systems 64, no. 1 (2022): 207–33. http://dx.doi.org/10.1007/s10115-021-01634-9.

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24

Jenny, Bernhard, Daniel M. Stephen, Ian Muehlenhaus, et al. "Force-directed layout of origin-destination flow maps." International Journal of Geographical Information Science 31, no. 8 (2017): 1521–40. http://dx.doi.org/10.1080/13658816.2017.1307378.

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25

Strip, David R. "Primitives for robotic mechanical assembly: Force directed insertions." Robotics and Computer-Integrated Manufacturing 6, no. 4 (1989): 283–86. http://dx.doi.org/10.1016/0736-5845(89)90117-8.

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26

Strip, David R. "Technology for Robotic Mechanical Assembly: Force-Directed Insertions." AT&T Technical Journal 67, no. 2 (1988): 23–34. http://dx.doi.org/10.1002/j.1538-7305.1988.tb00242.x.

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27

ZHAO, TONG-JUN, YI-ZHONG ZHUO, YONG ZHAN, QING JI, and TIAN-GUANG CAO. "TWO-DIMENSIONAL RATCHETS WITH NON-CONSERVATIVE IMPULSIVE FORCE." Modern Physics Letters B 16, no. 26 (2002): 999–1006. http://dx.doi.org/10.1142/s0217984902004706.

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We discuss the directed motion of overdamped Brownian particles based on a two-dimensional ratchet model with a non-conservative impulsive force field. We consider the combined effects on the stationary current due to local spatial asymmetry in the longitudinal direction as well as the constrained harmonic force in the transverse direction. We notice that the current reversal is induced by the change of colored noise strength and the dynamics in the transverse direction influences the directed motion in the longitudinal direction significantly. The non-conservative impulsive force that represe
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28

Wu, Jie, and Qiu Quan Wang. "Research of Automatic Drawing Scheduling Network Method Based on Force-Directed." Applied Mechanics and Materials 722 (December 2014): 338–43. http://dx.doi.org/10.4028/www.scientific.net/amm.722.338.

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Automatic drawing algorithm has been one of the hotspot in research of drawing. So far there is no completely effective method. Force-directed graph drawing algorithm is based on physics model, makes the drawing problem into force for solving the problem in physics, then into unconstrained optimization for solving the problem in mathematics. Its advantage is based on people familiar with the physical model, and the principle is easy to understand. We can draw large-scale graphics with symmetrical and beautiful appearance through certain set and the improvement. At the advantages of Force-direc
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29

Lee, Jing, and Ching-Hsing Pei. "Force-Directed Method in Mirror Frames for Graph Drawing." International Journal of Intelligent Systems and Applications 2, no. 1 (2010): 8–14. http://dx.doi.org/10.5815/ijisa.2010.01.02.

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30

Alupoaei, S., and S. Katkoori. "Net-based force-directed macrocell placement for wirelength optimization." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 10, no. 6 (2002): 824–35. http://dx.doi.org/10.1109/tvlsi.2002.808453.

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31

Paulin, P. G., and J. P. Knight. "Force-directed scheduling for the behavioral synthesis of ASICs." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 8, no. 6 (1989): 661–79. http://dx.doi.org/10.1109/43.31522.

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32

CHRZANOWSKA-JESKE, MALGORZATA, and SHYANG-KUEN HER. "I/O pad assignment for force-directed placement algorithms." International Journal of Electronics 77, no. 4 (1994): 467–79. http://dx.doi.org/10.1080/00207219408926079.

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33

Bertault, François. "A force-directed algorithm that preserves edge-crossing properties." Information Processing Letters 74, no. 1-2 (2000): 7–13. http://dx.doi.org/10.1016/s0020-0190(00)00042-9.

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34

Gutkin, Eugene. "Asymptotics of trajectories for Newtonian dynamics with directed force." Physica D: Nonlinear Phenomena 26, no. 1-3 (1987): 156–64. http://dx.doi.org/10.1016/0167-2789(87)90219-3.

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35

Lu, Jiawei, and Yain-Whar Si. "Clustering-based force-directed algorithms for 3D graph visualization." Journal of Supercomputing 76, no. 12 (2020): 9654–715. http://dx.doi.org/10.1007/s11227-020-03226-w.

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36

Sciegaj, Mark, and Nancy Hooyeman. "WORK FORCE COMPETENCIES AND TRAINING FOR SELF-DIRECTED SERVICE PROGRAMS." Innovation in Aging 3, Supplement_1 (2019): S232. http://dx.doi.org/10.1093/geroni/igz038.861.

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Abstract In 2017 over one million individuals of all ages were enrolled in approximately 260 self-directed long-term services and support programs nationwide. Research conducted by the National Resource Center for Participant-Directed Care (NRCPDS) and the Council for Social Work Education identified training gaps among current aging and disability network professionals and within social work education. Believing that both self-directing individuals and their family caregivers would benefit from a workforce that has the knowledge and skills to implement the principles of self-directed care, NR
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37

Xu, Zhuang, Tingyun Mao, Guangluan Xu, Yang Wang, and Daoyu Lin. "Multivariate Network Layout Using Force-Directed Method with Attribute Constraints." Applied Sciences 12, no. 9 (2022): 4561. http://dx.doi.org/10.3390/app12094561.

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Graph visualization with proper layout is widely applied to understand the relationship between entities in a complex system and the topological structure information is mainly used. Real-world graphs often have the community structures property which is ignored in many existing graph layout methods. Thus, we propose a multivariate network layout method using the force-directed method with attribute constraints. This method can effectively take into account the hierarchical structure, connection strength, and quantitative comparison between communities. First, the layout of community centers i
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38

Dmytriv, Vasyl, Ihor Dmytriv, Roman Gorodnyak, and Oleh Sahan. "Simulation of bulk material descent from centrifugal cone disc dispenser." Avtomatizacìâ virobničih procesìv u mašinobuduvannì ta priladobuduvannì 55 (2021): 43–51. http://dx.doi.org/10.23939/istcipa2021.55.043.

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Aim. Development of an analytical model and study of particle movement on the surface of a conical disk rotary dispenser-mixer of bulk material. Method. The particle, which is placed on the conical disk, is subjected to gravity directed vertically downwards, the pressure force of the vertical component of the bulk component. The force of the normal reaction of the surface of the conical disk is directed perpendicular to the cone generating line of the dispenser disk at a given point where the material particle is located. Cartesian coordinate system. The x-axis is directed along the generator
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39

FLORIO, C. S. "MUSCLE FORCE MAGNITUDES IN THE HUMAN LEG FOR ISOMETRIC EXERCISES WITH VARIOUS RESULTANT FORCE DIRECTIONS AND JOINT ANGLES." Journal of Mechanics in Medicine and Biology 16, no. 06 (2016): 1650083. http://dx.doi.org/10.1142/s0219519416500834.

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Using a gradient-based numerical optimization routine, the force magnitudes required of 10 major sagittal plane leg muscles to create a constant magnitude isometric resultant force against a fixed surface at the toe directed anteriorly, posteriorly, superiorly, and inferiorly were quantitatively predicted for three sets of joint angles: a straight leg configuration, with the knee flexed, and with both the hip and knee flexed. Comparisons over the conditions studied for each individual system muscle found that the maximum variation occurred in knee and hip extensor forces (up to two orders of m
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40

Raoof, M., and R. E. Hobbs. "Tangential Compliance of Rough Elastic Bodies in Contact." Journal of Tribology 111, no. 4 (1989): 726–29. http://dx.doi.org/10.1115/1.3262002.

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A simple method is presented for determining the tangential force-displacement relationship between two elastically identical generally curved bodies when the tangential force is not directed along either of the principal axes of the contact patch. It is shown that with one suitable assumption the desired solution of the general problem can be derived using the available closed form solutions for the particular cases where the tangential force is directed along one or other of the principal axes of contact. The analysis was motivated by a study of wire rope behavior, but has potential applicat
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41

Huang, Yu-Jung, and Shen-Li Fu. "Thermal Placement Design for MCM Applications." Journal of Electronic Packaging 122, no. 2 (1999): 115–20. http://dx.doi.org/10.1115/1.483142.

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This paper introduces an algorithm that focuses on the placement of the power dissipating chips for multichip module applications. The main design issue is addressed on the chip placement to achieve uniform thermal distribution. Our approach to the placement problem is based on the modified force-directed placement method. The proposed thermal force-directed placement method is to relate the force equations to the power dissipation values of the individual bare chip. Examples of multichip placement are presented. The finite element simulation results are also investigated and compared with qua
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42

Ma, Xin Min, Xu Qian, and Wen Chao Gao. "An Effective Cell Spreading Method for Force-Directed Global Placement." Applied Mechanics and Materials 519-520 (February 2014): 911–18. http://dx.doi.org/10.4028/www.scientific.net/amm.519-520.911.

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Force-directed placement method for large scale integration physical design is a very effective and fast method to spread the cell uniformly in the placement region. But this kind of method also create large amount of cell overlap in initial placement. In this paper, we present an effective method to cope with cell spreading and add additional force without damaging the wire length. It mainly takes the following method: Firstly, in the prior period of iteration n we keep limit the cell moving distance using a rectangle structure .Because the prior iteration play a decisive role in the final pl
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43

Bhimani, Rohan, Bart Lubberts, Noortje Hagemeijer, et al. "Arthroscopic Evaluation of Subtle Syndesmotic Instability: Are We Pulling Correctly in the Coronal Plane?" Foot & Ankle Orthopaedics 7, no. 4 (2022): 2473011421S0058. http://dx.doi.org/10.1177/2473011421s00588.

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Category: Ankle; Sports; Trauma Introduction/Purpose: While the lateral hook test (LHT) has been widely used to arthroscopically evaluate syndesmotic instability in the coronal plane, it is unclear whether the angulation of the applied force has any impact on the degree of instability. The aim of this study was to determine if changing the direction of the force applied while performing the LHT impacts the amount of coronal diastasis observed in purely ligamentous syndesmotic injuries. Methods: In 10 cadaveric specimens, arthroscopic evaluation of the distal tibiofibular joint in the coronal p
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44

Artis, Andrew B., and Eric G. Harris. "Self-Directed Learning and Sales Force Performance: An Integrated Framework." Journal of Personal Selling & Sales Management 27, no. 1 (2007): 9–24. http://dx.doi.org/10.2753/pss0885-3134270101.

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45

Yakushev, A. G., and T. Yu Bokov. "Study of Rapid Goal-Directed Force of Upper Limb Movement." Journal of Mathematical Sciences 253, no. 6 (2021): 920–28. http://dx.doi.org/10.1007/s10958-021-05282-w.

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46

Sinha, Arun Kumar, Mrinmoyee Basu, Sougata Sarkar, Mukul Pradhan, and Tarasankar Pal. "Electrostatic Field Force Directed Gold Nanowires from Anion Exchange Resin." Langmuir 26, no. 22 (2010): 17419–26. http://dx.doi.org/10.1021/la102387x.

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47

Verhaegh, W. F. J., P. E. R. Lippens, E. H. L. Aarts, J. H. M. Korst, J. L. van Meerbergen, and A. van der Werf. "Improved force-directed scheduling in high-throughput digital signal processing." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 14, no. 8 (1995): 945–60. http://dx.doi.org/10.1109/43.402495.

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48

Cheng *, Feng, and Junfa Mao. "An efficient heuristic force directed placement algorithm based on partitioning." International Journal of Electronics 92, no. 7 (2005): 427–36. http://dx.doi.org/10.1080/08827510410001694996.

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49

Zhang, Xitao, Lingda Wu, Shaobo Yu, and Zhonghua Yao. "A Multi-Force Directed Layout Algorithm for Multilayer Networks Visualization." Journal of Computer-Aided Design & Computer Graphics 31, no. 4 (2019): 639. http://dx.doi.org/10.3724/sp.j.1089.2019.17365.

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50

Brak, R., P. Dyke, J. Lee, et al. "A self-interacting partially directed walk subject to a force." Journal of Physics A: Mathematical and Theoretical 42, no. 8 (2009): 085001. http://dx.doi.org/10.1088/1751-8113/42/8/085001.

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