V. Egor, K. A. Yakovlev, K. I. Komarov, N. P. Zaytsev, K. I. Kryuchkov et al., Tunable two-dimensional assembly of colloidal particles in rotating electric fields

, Creative Commons Attribution 4.0 International License, Scientific Reports, vol.7, issue.1, p.13727, 2017.

G. M. Whitesides, Self-Assembly at All Scales. Science, vol.295, issue.5564, pp.2418-2421, 2002.

A. Bartosz, C. E. Grzybowski, J. Wilmer, K. P. Kim, K. J. Browne et al., Self-assembly: from crystals to cells, Soft Matter, vol.5, issue.6, p.1110, 2009.

R. Gross and M. Dorigo, Self-Assembly at the Macroscopic Scale, Proceedings of the IEEE, vol.96, pp.1490-1508, 2008.

M. Wang, L. He, and Y. Yin, Magnetic field guided colloidal assembly, Materials Today, vol.16, issue.4, pp.110-116, 2013.

O. Carvente, G. G. Peraza-mues, J. M. Salazar, and J. C. Ruiz-suárez, Selfassembling of non-Brownian magnetized spheres, Granular Matter, vol.14, issue.3, pp.303-308, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00761192

R. Messina, S. Aljawhari, L. Bécu, J. Schockmel, G. Lumay et al., Quantitatively mimicking wet colloidal suspensions with dry granular media, Sci. Rep, vol.5, p.10348, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01515840

X. N. Hou, Y. H. Liu, O. V. Kravchenko, T. A. Lapushkina, O. A. Azarova et al., Structures and dynamics in a two-dimensional dipolar dust particle system, Physics of Plasmas, vol.25, issue.5, p.53701, 2018.

A. Darras, J. Fiscina, M. Pakpour, N. Vandewalle, and G. Lumay, Ribbons of superparamagnetic colloids in magnetic field, Eur. Phys. J. E, vol.39, issue.4, p.47, 2016.

A. Pal, V. Malik, L. He, H. Ben, Y. Erné et al., Tuning the Colloidal Crystal Structure of Magnetic Particles by External Field, Angew. Chem. Int. Ed, vol.54, issue.6, p.105, 2014.

U. Gasser, Crystallization in three-and two-dimensional colloidal suspensions, Journal of Physics: Condensed Matter, vol.21, issue.20, p.203101, 2009.

A. Yethiraj and A. Van-blaaderen, A colloidal model system with an interaction tunable from hard sphere to soft and dipolar, Nature, vol.421, pp.513-517, 2003.

C. N. Sven-van-teeffelen, H. Likos, and . Löwen, Colloidal Crystal Growth at Externally Imposed Nucleation Clusters, Physical Review Letters, vol.100, issue.10, p.108302, 2008.

C. Holm and J. Weis, The structure of ferrofluids: A status report, Current Opinion in Colloid & Interface Science, vol.10, issue.3-4, pp.133-140, 2005.

S. Valentin, A. O. Mendelev, and . Ivanov, Ferrofluid aggregation in chains under the influence of a magnetic field, Phys. Rev. E, vol.70, p.51502, 2004.

D. J. Juan-de-vicente, R. Klingenberg, and . Hidalgo-alvarez, Magnetorheological fluids: a review, Soft Matter, vol.7, issue.8, p.3701, 2011.

F. Smallenburg, A. Hanumantha-rao-vutukuri, and . Imhof, Self-assembly of colloidal particles into strings in a homogeneous external electric or magnetic field, Journal of Physics: Condensed Matter, vol.24, issue.46, p.464113, 2012.

D. Samsonov, G. Zhdanov, V. Morfill, and . Steinberg, Levitation and agglomeration of magnetic grains in a complex (dusty) plasma with magnetic field, New Journal of Physics, vol.5, pp.24-24, 2003.

Y. Lu, L. Dong, L. Zhang, Y. Su, and S. Yu, Biogenic and biomimetic magnetic nanosized assemblies, Nano Today, vol.7, issue.4, p.36, 2012.

R. Tao and D. Xiao, Three-dimensional dielectric photonic crystals of bodycentered-tetragonal lattice structure, Applied Physics Letters, vol.80, issue.25, pp.4702-4704, 2002.

T. Ahamed, R. Sundarrajan, G. T. Prasaath, and V. Raviraj, Implementation of Magneto-rheological Dampers in Bumpers of Automobiles for Reducing Impacts during Accidents, Procedia Engineering, vol.97, pp.1220-1226, 2014.

X. Zhang, W. Li, and X. Gong, Study on magnetorheological shear thickening fluid, Smart Materials and Structures, vol.17, issue.1, p.15051, 2008.

G. Yang, B. F. Spencer, J. D. Carlson, and M. K. Sain, Large-scale MR fluid dampers: modeling and dynamic performance considerations. Engineering Structures, vol.24, pp.309-323, 2002.

B. A. Jackson, K. J. Terhune, and L. B. King, Ionic liquid ferrofluid interface deformation and spray onset under electric and magnetic stresses, Physics of Fluids, vol.29, issue.6, p.64105, 2017.

P. Brown, A. Bushmelev, C. P. Butts, J. Cheng, J. Eastoe et al., Magnetic Control over Liquid Surface Properties with Responsive Surfactants, Angewandte Chemie International Edition, vol.51, issue.10, pp.2414-2416, 2012.

M. Belkin, A. Snezhko, I. S. Aranson, and W. Kwok, Driven Magnetic Particles on a Fluid Surface: Pattern Assisted Surface Flows, Physical Review Letters, vol.99, issue.15, p.158301, 2007.

A. Tay, A. Sohrabi, K. Poole, S. Seidlits, and D. D. Carlo, A 3D Magnetic Hyaluronic Acid Hydrogel for Magnetomechanical Neuromodulation of Primary Dorsal Root Ganglion Neurons, Advanced Materials, vol.30, issue.29, p.1800927, 2018.

H. Joo, M. Kang, C. W. Super, R. M. Yung, K. Cooper et al., An extracorporeal blood-cleansing device for sepsis therapy, Nature Medicine, vol.20, issue.10, pp.1211-1216, 2014.

S. Reardon, Artificial spleen cleans up blood, Nature, 2014.

R. Di-corato, G. Béalle, J. Kolosnjaj-tabi, A. Espinosa, O. Clément et al., Combining Magnetic Hyperthermia and Photodynamic Therapy for Tumor Ablation with Photoresponsive Magnetic Liposomes, ACS Nano, vol.9, issue.3, pp.2904-2916, 2015.

E. F. Borra, D. Brousseau, M. Cliche, and J. Parent, Aberration correction with a magnetic liquid active mirror, Monthly Notices of the Royal Astronomical Society, vol.391, issue.4, pp.1925-1930, 2008.

A. J. Bandodkar, C. S. Lopez, A. M. Vinu-mohan, L. Yin, R. Kumar et al., All-printed magnetically self-healing electrochemical devices, Science Advances, vol.2, issue.11, pp.1601465-1601465, 2016.

I. S. Jacobs and C. P. Bean, Approach to elongated fine-particle magnets, Phys. Rev, vol.100, issue.4, pp.1060-1067, 1955.

P. G. De-gennes and P. A. Pincus, Pair correlations in a ferromagnetic colloid, Phys. kondens. Materie, vol.11, issue.3, pp.189-198, 1970.

J. M. Luttinger and L. Tisza, Theory of dipole interaction in crystals, Phys. Rev, vol.70, pp.954-964, 1946.

C. Thomas, W. Halsey, and . Toor, Structure of electrorheological fluids, Phys. Rev. Lett, vol.65, issue.22, pp.2820-2823, 1990.

C. Thomas, W. Halsey, and . Toor, Fluctuation-induced couplings between defect lines or particle chains, Journal of Statistical Physics, p.38, 1990.

R. Tao and J. M. Sun, Three-dimensional structure of induced electrorheological solid, Phys. Rev. Lett, vol.67, issue.3, pp.398-401, 1991.

J. Schönke and E. Fried, Stability of vertical magnetic chains, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, vol.473, p.20160703, 2017.

J. Schönke, T. M. Schneider, and I. Rehberg, Infinite geometric frustration in a cubic dipole cluster, Phys. Rev. B, vol.91, p.20410, 2015.

R. Messina, L. A. Khalil, and I. Stankovic, Self-assembly of magnetic balls: From chains to tubes, Phys. Rev. E, vol.89, p.11202, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01516911

R. Messina and I. Stankovi?, Comment on 'Self-assembly of magnetic balls: From chains to tubes, Phys. Rev. E, vol.91, issue.5, p.57202, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01515837

F. Deißenbeck, H. Löwen, and . O?uz, Ground state of dipolar hard spheres confined in channels, Physical Review E, vol.97, issue.5, p.52608, 2018.

R. Messina and I. Stankovi?, Self-assembly of magnetic spheres in two dimensions: The relevance of onion-like structures, Europhys. Lett, vol.110, issue.4, p.46003, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01515836

R. Messina and I. Stankovi?, Assembly of magnetic spheres in strong homogeneous magnetic field, Physica A: Statistical Mechanics and its Applications, vol.466, pp.10-20, 2017.

D. Vella, E. Du-pontavice, C. L. Hall, and A. Goriely, The magneto-elastica: from self-buckling to self-assembly, Proc. R. Soc. A, vol.470, 2014.

J. Hernández-rojas, D. Chakrabarti, and D. Wales, Self-assembly of colloidal magnetic particles: energy landscapes and structural transitions, Physical Chemistry Chemical Physics, vol.18, issue.38, pp.26579-26585, 2016.

K. Butter, P. Bomans, P. Frederik, G. Vroege, and A. Philipse, Direct observation of dipolar chains in iron ferrofluids by cryogenic electron microscopy, Nature Materials, vol.2, issue.2, pp.88-91, 2003.

J. Biot and F. Savart, Note sur le magnetisme de la pile de volta, Ann. Chem. Phys, vol.15, p.222, 1820.

J. David and J. , Classical electrodynamics, 1999.

D. Griffiths, Introduction to electrodynamics, 2014.

K. Seleznyova, M. Strugatsky, and J. Kliava, Modelling the magnetic dipole, European Journal of Physics, vol.37, issue.2, p.25203, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01275891

, Wikipedia contributors. Magnetic field -Wikipedia, the free encyclopedia, vol.8, 2018.

J. P. Mc-tavish, Field pattern of a magnetic dipole, American Journal of Physics, vol.68, issue.6, pp.577-578, 2000.

F. Boyd, D. M. Edwards, J. Riffe, W. A. Ji, and . Booth, Interactions between uniformly magnetized spheres, vol.9, 2016.

P. W. Atkins, The Elements of Physical Chemistry: With Applications in Biology, p.11, 2001.

K. G. Kornev, D. Halverson, G. Korneva, Y. Gogotsi, and G. Friedman, Magnetostatic interactions between carbon nanotubes filled with magnetic nanoparticles, Appl. Phys. Lett, vol.92, issue.23, p.11, 2008.

M. J. Powell, A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation, vol.12, pp.51-67, 1994.

J. A. Nelder and R. Mead, A Simplex Method for Function Minimization, The Computer Journal, vol.7, issue.4, pp.308-313, 1965.

D. Kraft, A software package for sequential quadratic programming. Forschungsbericht / Deutsche Forschungs-und Versuchsanstalt für Luft-und Raumfahrt. Köln, 1988.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, vol.113, 1995.

G. Steven and . Johnson, The NLopt nonlinear-optimization package, 2014.

R. Messina and L. Spiteri, On the interaction of dipolar filaments

, Eur. Phys. J. E, vol.39, p.17, 2016.

R. Blakemore, Magnetotactic bacteria, Science, vol.190, pp.377-379, 1975.

T. Prozorov, D. A. Bazylinski, K. Surya, R. Mallapragada, and . Prozorov, Novel magnetic nanomaterials inspired by magnetotactic bacteria: Topical review, Materials Science and Engineering: R: Reports, vol.74, issue.5, pp.133-172, 2013.

M. Winklhofer, E. Holtkamp-rötzler, M. Hanzlik, G. Fleissner, and N. Petersen, Clusters of superparamagnetic magnetite particles in the upper-beak skin of homing pigeons: evidence of a magnetoreceptor?, European Journal of Mineralogy, vol.13, issue.4, p.17, 2001.

F. F. Torres-de-araujo, M. A. Pires, R. B. Frankel, and C. E. Bicudo, Magnetite and magnetotaxis in algae, Biophysical Journal, vol.50, issue.2, p.17, 1986.

Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, Applications of magnetic nanoparticles in biomedicine, Journal of Physics D: Applied Physics, vol.36, issue.13, p.167, 2003.

H. Wang, Y. Yu, Y. Sun, and Q. Chen, Magnetic nanochains: a review, Nano, issue.01, pp.1-17, 2011.

J. Park, G. Von-maltzahn, L. Zhang, M. P. Schwartz, E. Ruoslahti et al., Magnetic iron oxide nanoworms for tumor targeting and imaging, Adv. Mater, vol.20, issue.9, p.17, 2008.

C. Martinez-boubeta, K. Simeonidis, A. Makridis, M. Angelakeris, O. Iglesias et al., Learning from nature to improve the heat generation of iron-oxide nanoparticles for magnetic hyperthermia applications, Scientific Reports, vol.3, p.17, 2013.

A. Fert and . Piraux, Magnetic nanowires, Journal of Magnetism and Magnetic Materials, vol.200, issue.1-3, p.18, 1999.

M. Tanase, L. A. Bauer, A. Hultgren, D. M. Silevitch, L. Sun et al., Magnetic Alignment of Fluorescent Nanowires, Nano Letters, vol.1, issue.3, pp.155-158, 2001.

M. Skarabot, M. Ravnik, S. Zumer, U. Tkalec, I. Poberaj et al., Osterman, and I. Muvsevic. Two-dimensional dipolar nematic colloidal crystals

, Phys. Rev. E, vol.76, issue.5, p.51406, 2007.

Y. Gu, R. Burtovyy, J. Custer, I. Luzinov, and K. G. Kornev, A gradient field defeats the inherent repulsion between magnetic nanorods, Royal Society Open Science, vol.1, issue.2, p.140271, 2014.

C. Thomas and . Halsey, Electrorheological fluids, Science, vol.258, issue.5083, p.18, 1992.

E. M. Furst and A. P. Gast, Dynamics and lateral interactions of dipolar chains, Phys. Rev. E, vol.62, issue.5, pp.6916-6925, 2000.

T. Friedrich, I. Rehberg, and R. Richter, Self-assembly of magnetic balls: From chains to tubes, Phys. Rev. E, vol.91, issue.5, p.18, 2015.

A. O. Tsebers, Thermodynamic stability of a suspension of magnetic needles, Magnetohydrodynamics, vol.19, p.18, 1983.

R. P-i-belobrov, V. Gekht, and . Ignatchenko, Ground state in systems with dipole interaction, Zh. Eksp. Teor. Fiz, vol.84, p.18, 1983.

V. P-i-belobrov and V. A. Voevodin, Ground state of a dipole system in a plane rhombic lattice, Soviet Physics JETP, vol.88, pp.889-893, 1985.

I. Peter, . Belobrov, V. Ivan, A. Ermilovit, and . Tsikh, Stable and Ground States of Dipolic, p.18, 1991.

Y. Gu, Composite Films with Magnetic Nanorods: Fundamentals, Processing and Applications. Dissertation, p.21, 2014.

M. B-r-jennings, P. Xu, and . Ridler, Structure in magneto-rheological fluids: a theoretical analysis, Journal of Physics D: Applied Physics, vol.34, issue.11, pp.1617-1623, 2001.

X. Xie, X. Mai, and . Zhou, Dispersion and alignment of carbon nanotubes in polymer matrix: A review, Materials Science and Engineering: R: Reports, vol.49, issue.4, p.36, 2005.

Y. Ye and B. Geng, Magnetic nanotubes: Synthesis, properties, and applications, Critical Reviews in Solid State and Materials Sciences, vol.37, issue.2, p.36, 2012.

, Magnetic (nano)materials as an useful tool for sample preparation in analytical methods. a review, Analytical Methods, vol.5, issue.18, p.36, 2013.

J. Velazquez, K. R. Pirota, and M. Vazquez, About the dipolar approach in magnetostatically coupled bistable magnetic micro and nanowires, IEEE Transactions on Magnetics, vol.39, issue.5, p.36, 2003.

J. Sang-jun-son, B. Reichel, M. He, S. B. Schuchman, and . Lee, Magnetic nanotubes for magnetic-field-assisted bioseparation, biointeraction, and drug delivery, J. Am. Chem. Soc, vol.127, issue.20, p.36, 2005.

C. Eisenmann, U. Gasser, P. Keim, and G. Maret, Anisotropic defectmediated melting of two-dimensional colloidal crystals, Phys. Rev. Lett, vol.93, issue.10, p.36, 2004.

G. Filipcsei, I. Csetneki, A. Szilágyi, and M. Zrínyi, Oligomers -Polymer Composites -Molecular Imprinting, of Advances in Polymer Science, chapter Magnetic Field-Responsive Smart Polymer Composites, vol.206, p.36, 2007.

P. Tierno, Recent advances in anisotropic magnetic colloids: realization, assembly and applications, Phys. Chem. Chem. Phys, vol.16, issue.43, p.36, 2014.

G. Lumay, S. Dorbolo, and N. Vandewalle, Compaction dynamics of a magnetized powder, Phys. Rev. E, vol.80, issue.4, p.36, 2009.

M. Sara-mehdizadeh-taheri, T. Michaelis, B. Friedrich, M. Förster, F. M. Drechsler et al., Self-assembly of smallest magnetic particles, Proc Natl Acad Sci, vol.112, issue.47, pp.14484-14489, 2015.

L. Spiteri and R. Messina, Columnar aggregation of dipolar chains

, Europhys. Lett, vol.120, issue.3, p.37, 2017.

E. Alphandery, Y. Ding, A. T. Ngo, Z. L. Wang, L. F. Wu et al., Assemblies of aligned magnetotactic bacteria and extracted magnetosomes: What is the main factor responsible for the magnetic anisotropy, ACS Nano, vol.3, issue.6, p.37, 2009.

B. Kiani, D. Faivre, and S. Klumpp, Elastic properties of magnetosome chains, New Journal of Physics, vol.17, issue.4, p.37, 2015.

M. Ewerlin, D. Demirbas, F. Brüssing, O. Petracic, A. A. Ünal et al., Magnetic dipole and higher pole interaction on a square lattice, Phys. Rev. Lett, vol.110, p.37, 2013.

A. T. Skjeltorp, One-and two-dimensional crystallization of magnetic holes, Phys. Rev. Lett, vol.51, p.37, 1983.

E. M. Furst and A. P. Gast, Micromechanics of dipolar chains using optical tweezers, Phys. Rev. Lett, vol.82, p.37, 1999.

H. Mirjam-e-leunissen, A. Rao-vutukuri, and . Van-blaaderen, Directing Colloidal Self-Assembly with Biaxial Electric Fields, Advanced Materials, vol.21, issue.30, pp.3116-3120, 2009.

J. E. Martin, K. M. Hill, and C. P. Tigges, Magnetic-fieldinduced optical transmittance in colloidal suspensions, Phys. Rev. E, vol.59, p.37, 1999.

J. Weis, Simulation of quasi-two-dimensional dipolar systems, Journal of Physics: Condensed Matter, vol.15, issue.15, pp.1471-1495, 2003.

J. Weis, Low density quasi-two-dimensional dipolar hard spheres in an external field, Molecular Physics, vol.103, issue.1, pp.7-10, 2005.

J. Faraudo, S. Jordi, C. Andreu, J. Calero, and . Camacho, Predicting the Self-Assembly of Superparamagnetic Colloids under Magnetic Fields

, Advanced Functional Materials, vol.26, issue.22, p.38, 2016.

J. E. Martin, R. A. Anderson, and C. P. Tigges, Simulation of the athermal coarsening of composites structured by a uniaxial field, J. Chem. Phys, vol.108, issue.9, pp.3765-3787, 1998.

R. Tao and J. M. Sun, Ground state of electrorheological fluids from monte carlo simulations, Phys. Rev. A, vol.44, issue.10, pp.6181-6184, 1991.

F. Weijia-wen, K. F. Kun, D. W. Pál, K. N. Zheng, and . Tu, Aggregation kinetics and stability of structures formed by magnetic microspheres, Phys. Rev. E, vol.59, p.38, 1999.

A. Taisia, V. A. Prokopieva, S. S. Danilov, C. Kantorovich, and . Holm, Ground state structures in ferrofluid monolayers, Phys. Rev. E, vol.80, p.31404, 2009.

V. Danilov, T. Prokopyeva, and S. Kantorovich, Ground-state structures and structural transitions in a monolayer of magnetic dipolar particles in the presence of an external magnetic field, Phys. Rev. E, vol.86, p.38, 2012.

F. Guzmán-lastra, A. Kaiser, and H. Löwen, Fission and fusion scenarios for magnetic microswimmer clusters, Nature Communications, vol.7, p.13519, 2016.

A. Grzybowski and A. Brodka, Lekner type method for summing the dipoledipole interactions in computer simulations of one-and two-dimensionally periodic systems, Molec. Phys, vol.101, pp.1079-1088, 2003.

C. Park and R. E. Robertson, Alignment of particles by an electric field, Materials Science and Engineering: A, vol.257, issue.2, pp.295-311, 1998.

A. David, R. E. Norman, and . Robertson, The effect of fiber orientation on the toughening of short fiber-reinforced polymers, Journal of Applied Polymer Science, vol.90, issue.10, pp.2740-2751, 2003.

C. Park, J. Wilkinson, S. Banda, Z. Ounaies, K. E. Wise et al., Aligned single-wall carbon nanotube polymer composites using an electric field, Journal of Polymer Science Part B: Polymer Physics, vol.44, issue.12, pp.1751-1762, 2006.

L. Spiteri and R. Messina, Dipolar crystals: The crucial role of the clinohexagonal prism phase, Phys. Rev. Lett, vol.119, p.155501, 2017.

G. T. Pickett, M. Gross, and H. Okuyama, Spontaneous chirality in simple systems, Phys. Rev. Lett, vol.85, pp.3652-3655, 2000.

. Ec-o?uz, H. Messina, and . Löwen, Helicity in cylindrically confined yukawa systems, Europhys. Lett, vol.94, issue.2, p.28005, 2011.

I. Stankovi?, M. Da?i?, and R. Messina, Structure and cohesive energy of dipolar helices, Soft Matter, vol.12, issue.12, p.46, 2016.

L. Spiteri, I. Stankovi?, and R. Messina, Interaction of dipolar helical chains including linear-and zigzag-chains, The Journal of chemical physics, vol.47, 2018.

A. Wada, The alpha-helix as an electric macro-dipole, Advances in biophysics, p.48, 1976.

J. , M. Scholtz, and R. L. Baldwin, The mechanism of alpha-helix formation by peptides, Annual Review of Biophysics and Biomolecular Structure, vol.21, issue.1, p.48, 1992.

H. Andrew, . Wang, J. Gary, F. J. Quigley, J. L. Kolpak et al., Molecular structure of a left-handed double helical DNA fragment at atomic resolution, Nature, vol.282, issue.5740, p.48, 1979.

C. Howard and . Berg, The Rotary Motor of Bacterial Flagella, Annual Review of Biochemistry, vol.72, issue.1, p.48, 2003.

M. Iain, A. Cheeseman, and . Desai, Molecular architecture of the kinetochore-microtubule interface, Nature Reviews Molecular Cell Biology, vol.9, issue.1, p.48, 2008.

S. Iijima, Helical microtubules of graphitic carbon, Nature, vol.354, issue.6348, p.48, 1991.

X. X-b-zhang, D. Zhang, . Bernaerts, S. Van-tendeloo, . Amelinckx et al., The Texture of Catalytically Grown Coil-Shaped Carbon Nanotubules, Europhys. Lett, vol.27, issue.2, p.48, 1994.

T. Shimada, J. Okuno, and T. Kitamura, Chiral Selectivity of Unusual Helimagnetic Transition in Iron Nanotubes: Chirality Makes Quantum Helimagnets, Nano Letters, vol.13, issue.6, p.48, 2013.

Y. Kondo and K. Takayanagi, Synthesis and Characterization of Helical Multi-Shell Gold Nanowires, Science, vol.289, issue.5479, p.48, 2000.

F. Li, X. Badel, J. Linnros, and J. Wiley, Fabrication of Colloidal Crystals with Tubular-like Packings, J. Am. Chem. Soc, vol.127, issue.10, p.48, 2005.

M. Lohr, A. M-alsayed, B. Chen, Z. Zhang, R. D-kamien et al., Helical packings and phase transformations of soft spheres in cylinders, Phys. Rev. E, vol.81, issue.4, p.48, 2010.

Z. Mahdi, R. K. Yamchi, and . Bowles, Helical defect packings in a quasi-one-dimensional system of cylindrically confined hard spheres, Phys. Rev. Lett, vol.115, p.48, 2015.

Y. Yin and Y. Xia, Self-Assembly of Spherical Colloids into Helical Chains with Well-Controlled Handedness, J. Am. Chem. Soc, vol.125, issue.8, p.48, 2003.

Y. Hayase, T. Sakaue, and H. Nakanishi, Compressive response and helix formation of a semiflexible polymer confined in a nanochannel, Phys. Rev. E, vol.95, issue.5, p.48, 2017.

S. A. Sabeur, F. Hamdache, and F. Schmid, Kinetically driven helix formation during the homopolymer collapse process, Phys. Rev. E, vol.77, p.48, 2008.

W. Zhao, S. Dong, and J. Hao, Colloidal Wormlike Micelles with Highly Ferromagnetic Properties, Langmuir, vol.31, issue.41, p.48, 2015.

D. Zerrouki, . Baudry, . Pine, J. Chaikin, and . Bibette, Chiral colloidal clusters, Nature, vol.455, issue.7211, pp.380-382, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00345989

G. Singh, H. Chan, A. Baskin, E. Gelman, N. Repnin et al., Self-assembly of magnetite nanocubes into helical superstructures, Science, vol.345, issue.6201, pp.1149-1153, 2014.

Q. Chen, J. K. Whitmer, S. Jiang, S. C. Bae, E. Luijten et al., Supracolloidal Reaction Kinetics of Janus Spheres

, Science, vol.331, issue.6014, pp.199-202, 2011.

V. Sobrino-fernández, F. Misko, and . Peeters, Self-assembly of Janus particles into helices with tunable pitch, Phys. Rev. E, vol.92, issue.4, p.42309, 2015.

R. Guo, J. Mao, X. Xie, and L. Yan, Predictive supracolloidal helices from patchy particles, Scientific Reports, vol.4, issue.1, p.2418, 2014.

H. Helmut, R. Strey, . Podgornik, C. Donald, . Rau et al., DNA-DNA interactions, Current Opinion in Structural Biology, vol.8, issue.3, p.48, 1998.

. H-m-harreis, C. Kornyshev, H. N-likos, G. Löwen, and . Sutmann, Phase Behavior of Columnar DNA Assemblies, Phys. Rev. Lett, vol.89, issue.1, p.48, 2002.

M. Kandu?, R. Dobnikar, and . Podgornik, Counterion-mediated electrostatic interactions between helical molecules, Soft Matter, vol.5, issue.4, p.48, 2009.

A. Cherstvy, Electrostatic interactions in biological DNA-related systems, Physical Chemistry Chemical Physics, vol.13, issue.21, p.48, 2011.

A. P. Philipse and D. Maas, Magnetic Colloids from Magnetotactic Bacteria: Chain Formation and Colloidal Stability, Langmuir, vol.18, issue.25, p.53, 2002.

K. Stoyan, S. Smoukov, M. Gangwal, O. Marquez, and . Velev, Reconfigurable responsive structures assembled from magnetic Janus particles, Soft Matter, vol.5, issue.6, p.68, 2009.

J. Domingos, M. François, W. Peeters, and . Ferreira, Self-assembly of rigid magnetic rods consisting of single dipolar beads in two dimensions, Phys. Rev. E, vol.96, issue.1, p.53, 2017.

E. D-a-rozhkov, E. Pyanzina, J. Novak, T. Cerdà, M. Sintes et al., Self-assembly of polymer-like structures of magnetic colloids: Langevin dynamics study of basic topologies, Molecular Simulation, vol.44, issue.6, p.53, 2018.

A. Ivan, C. Sergienko, E. ?en, and . Dagotto, Ferroelectricity in the Magnetic E-Phase of Orthorhombic Perovskites, Phys. Rev. Lett, vol.97, issue.22, p.220401, 2006.

J. and G. Guo, Systematic ab initiostudy of the magnetic and electronic properties of all 3dtransition metal linear and zigzag nanowires, Phys. Rev. B, vol.76, issue.9, p.55, 2007.

G. G-e-astrakharchik, G. D. Morigi, J. Chiara, and . Boronat, Ground state of low-dimensional dipolar gases: Linear and zigzag chains

, Phys. Rev. A, vol.78, issue.6, p.63622, 2008.

D. Wang, H. He, X. Chen, S. Feng, Y. Niu et al., A 3D porous metal-organic framework constructed of 1D zigzag and helical chains exhibiting selective anion exchange, CrystEngComm, vol.12, issue.4, p.55, 2010.

. Arthur-v-straube, P. Roel, L. Dullens, A. Schimansky-geier, and . Louis, Zigzag transitions and nonequilibrium pattern formation in colloidal chains, J. Chem. Phys, vol.139, issue.13, p.55, 2013.

S. Sacanna, L. Rossi, and D. J. Pine, Magnetic Click Colloidal Assembly, J. Am. Chem. Soc, vol.134, issue.14, pp.6112-6115, 2012.

L. Becu, M. Basler, L. Miodrag, I. M. Kuli?, and . Kuli?, Resonant reshaping of colloidal clusters on a current carrying wire, The European Physical Journal E, vol.40, issue.12, p.68, 2017.

J. Yan, K. Chaudhary, S. C. Bae, J. A. Lewis, and S. Granick, Colloidal ribbons and rings from Janus magnetic rods, Nature Communications, vol.4, p.68, 2013.

J. Timothy, F. M. Richmond, and . Richards, Packing of ?-helices: Geometrical constraints and contact areas, Journal of Molecular Biology, vol.119, issue.4, p.68, 1978.

W. Hol, P. T-van-duijnen, and H. Berendsen, The ?-helix dipole and the properties of proteins, Nature, vol.273, issue.5662, p.68, 1978.

G. Vernizzi, L. Kevin, M. Kohlstedt, and C. Olvera-de-la, The electrostatic origin of chiral patterns on nanofibers, Soft Matter, vol.5, issue.4, p.68, 2009.

Y. Ding, H. Öttinger, A. Schlüter, and M. Kröger, From atomistic simulation to the dynamics, structure and helical network formation of dendronized polymers: The Janus chain model, The Journal of Chemical Physics, vol.127, issue.9, p.68, 2007.

M. Kröger, O. Peleg, Y. Ding, and Y. Rabin, Formation of double helical and filamentous structures in models of physical and chemical gels, Soft Matter, vol.4, issue.1, p.68, 2008.

F. Smallenburg and M. Dijkstra, Phase diagram of colloidal spheres in a biaxial electric or magnetic field, The Journal of Chemical Physics, vol.132, issue.20, p.204508, 2010.

L. Spiteri, R. Messina, D. Gonzalez-rodriguez, and L. Bécu, Ordering of sedimenting paramagnetic colloids in a monolayer, Physical Review E, vol.98, issue.2, p.71, 2018.

P. N. Pusey and W. Van-megen, Phase behaviour of concentrated suspensions of nearly hard colloidal spheres, Nature, vol.320, issue.6060, p.71, 1986.

K. Zahn, R. Lenke, and G. Maret, Two-stage melting of paramagnetic colloidal crystals in two dimensions, Phys. Rev. Lett, vol.82, pp.2721-2724, 1999.

K. Zahn and G. Maret, Dynamic criteria for melting in two dimensions, Phys. Rev. Lett, vol.85, p.71, 2000.

U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, Real-space imaging of nucleation and growth in colloidal crystallization, Science, vol.292, issue.5515, p.71, 2001.

J. P. Hoogenboom, D. Derks, P. Vergeer, and A. Van-blaaderen, Stacking faults in colloidal crystals grown by sedimentation, The Journal of Chemical Physics, vol.117, issue.24, p.71, 2002.

A. Merlin, J. Salmon, and J. Leng, Microfluidicassisted growth of colloidal crystals, Soft Matter, vol.8, issue.13, p.71, 2012.

U. Gasser, Crystallization in three-and two-dimensional colloidal suspensions, Journal of Physics: Condensed Matter, vol.21, issue.20, p.203101, 2009.

F. Juan, M. Galisteo-lópez, R. Ibisate, L. S. Sapienza, Á. Froufepérez et al., Self-Assembled Photonic Structures, Advanced Materials, vol.23, issue.1, p.71, 2011.

A. Sanford, J. H. Asher, and . Holtz, Polymerized colloidal crystal hydrogel films as intelligent chemical sensing materials, Nature, vol.389, issue.6653, p.71, 1997.

O. D. Velev and E. W. Kaler, Structured Porous Materials via Colloidal Crystal Templating: From Inorganic Oxides to Metals, Advanced Materials, vol.12, issue.7, p.71, 2000.

. P-n-pusey, S. Van-megen, P. Underwood, R. Bartlett, and . Ottewill, Colloidal fluids, crystals and glasses, Journal of Physics: Condensed Matter, vol.2, issue.S, p.71, 1990.

P. Pusey, Liquids, freezing and the glass transition, p.71, 1991.

L. Assoud, F. Ebert, P. Keim, R. Messina, G. Maret et al., Ultrafast quenching of binary colloidal suspensions in an external magnetic field, Phys. Rev. Lett, vol.102, p.238301, 2009.

J. Perrin, Mouvement brownien et molécules, J. Phys. Theor. Appl, vol.9, issue.1, pp.5-39, 1910.

A. Vrij, Sedimentation equilibrium in concentrated, multicomponent particle dispersions. hard spheres in the percus-yevick approximation, The Journal of Chemical Physics, vol.72, issue.6, p.72, 1980.

T. Biben, J. Hansen, and J. Barrat, Density profiles of concentrated colloidal suspensions in sedimentation equilibrium, J. Chem. Phys, vol.98, issue.9, pp.7330-7344, 1993.

T. Biben and J. Hansen, Sedimentation equilibrium in concentrated chargestabilized colloidal suspensions, Journal of Physics: Condensed Matter, vol.6, issue.23A, p.72, 1994.

T. Biben, H. Ohnesorge, and . Löwen, Crystallization in Sedimentation Profiles of Hard Spheres, Europhys. Lett, vol.28, issue.9, pp.665-670, 1994.

J. Patrick-royall, M. Dzubiella, A. Schmidt, and . Van-blaaderen,

, Phys. Rev. Lett, vol.98, issue.18, p.72, 2007.

A. Esztermann and H. Löwen, Colloidal Brazil-nut effect in sediments of binary charged suspensions, Europhys. Lett, vol.68, issue.1, p.72, 2004.

T. Kruppa, T. Neuhaus, R. Messina, and H. Löwen, Soft repulsive mixtures under gravity: Brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking, J. Chem. Phys, vol.136, issue.13, p.72, 2012.

M. Schmidt, M. Dijkstra, and J. Hansen, Floating Liquid Phase in Sedimenting Colloid-Polymer Mixtures, Physical Review Letters, vol.93, issue.8, p.72, 2004.

M. Schmidt, M. Dijkstra, and J. Hansen, Competition between sedimentation and phase coexistence of colloidal dispersions under gravity, Journal of Physics: Condensed Matter, vol.16, issue.38, p.72, 2004.

A. L. Thorneywork, J. L. Abbott, G. Dirk, R. Aarts, and . Dullens, Two-Dimensional Melting of Colloidal Hard Spheres, Phys. Rev. Lett, vol.118, issue.15, p.72, 2017.

. Ekaterina-a-elfimova, O. Alexey, E. V. Ivanov, A. F. Lakhtina, P. Pshenichnikov et al., Sedimentation equilibria in polydisperse ferrofluids: critical comparisons between experiment, theory, and computer simulation, Soft Matter, vol.12, p.72, 2016.

R. Piazza, Settled and unsettled issues in particle settling, Reports on Progress in Physics, vol.77, issue.5, p.72, 2014.

K. Zahn, J. M. Méndez-alcaraz, and G. Maret, Hydrodynamic interactions may enhance the self-diffusion of colloidal particles, Phys. Rev. Lett, vol.79, p.72, 1997.

E. Madelung, Das elektrische feld in systemen von regelmäßig angeordneten punktladungen, Phys. Z, vol.19, p.75, 1918.

M. Hurley, J. Sherwin, and . Singer, Domain energies of the dipolar lattice gas, The Journal of Physical Chemistry, vol.96, issue.4, p.75, 1992.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. N. Teller, and E. Teller, To fill, J. Chem. Phys, vol.21, p.77, 1953.

P. Michael, D. J. Allen, and . Tildesley, Computer Simulation of Liquids, vol.1, p.77, 2017.

C. Sebastian, W. Kapfer, and . Krauth, Two-Dimensional Melting: From Liquid-Hexatic Coexistence to Continuous Transitions, Phys. Rev. Lett, vol.114, issue.3, pp.35702-35707, 2015.

L. Spiteri, H. Mohrbach, and R. Messina, Layered dipolar particles in external magnetic field, vol.83, 2018.

K. De, A. B. Bell, J. P. Macisaac, and . Whitehead, Dipolar effects in magnetic thin films and quasi-two-dimensional systems, Reviews of Modern Physics, vol.72, issue.1, p.83, 2000.

C. Chen and C. Li, Ordered microdroplet formations of thin ferrofluid layer breakups, Physics of Fluids, vol.22, issue.1, p.14105, 2010.

J. Yan, S. C. Bae, and S. Granick, Colloidal Superstructures Programmed into Magnetic Janus Particles, Advanced Materials, vol.27, issue.5, pp.874-879, 2015.

R. Seshadri and R. M. Westervelt, Statistical mechanics of magnetic bubble arrays. I. Topology and thermalization, Physical Review B, vol.46, issue.9, pp.5142-5149, 1992.

R. Seshadri and R. M. Westervelt, Statistical mechanics of magnetic bubble arrays. II. Observations of two-dimensional melting, Physical Review B, vol.46, issue.9, pp.5150-5161, 1992.

I. Musevic, Two-Dimensional Nematic Colloidal Crystals Self-Assembled by Topological Defects, Science, vol.313, issue.5789, pp.954-958, 2006.

F. Weijia-wen, K. F. Kun, D. W. Pál, K. N. Zheng, and . Tu, Aggregation kinetics and stability of structures formed by magnetic microspheres, Physical Review E, vol.59, issue.5, p.83, 1999.

J. Schockmel, E. Mersch, N. Vandewalle, and G. Lumay, Melting of a confined monolayer of magnetized beads, Phys. Rev. E, vol.87, issue.6, p.62201, 2013.

M. Golosovsky, Y. Saado, and D. Davidov, Self-assembly of floating magnetic particles into ordered structures: A promising route for the fabrication of tunable photonic band gap materials, Applied Physics Letters, vol.75, issue.26, p.83, 1999.

W. Wen, L. Zhang, and P. Sheng, Planar Magnetic Colloidal Crystals, Physical Review Letters, vol.85, issue.25, pp.5464-5467, 2000.

G. Helgesen and A. T. Skjeltorp, An experimental system for studying dynamic behavior of magnetic microparticles, Journal of Applied Physics, vol.69, issue.12, pp.8277-8284, 1991.

N. V. Dziomkina and G. J. Vancso, Colloidal crystal assembly on topologically patterned templates, Soft Matter, vol.1, issue.4, p.265, 2005.

. Ca-ross, Patterned Magnetic Recording Media, Annual Review of Materials Research, vol.31, issue.1, pp.203-235, 2001.

B. Trpi?ová and J. A. Brown, Ordering of Dipoles in Different Types of Microtubule Lattice, International Journal of Modern Physics B, vol.12, issue.05, pp.543-578, 1998.

E. Rufeil-fiori, N. Wilke, and A. J. Banchio, Dipolar interactions between domains in lipid monolayers at the air-water interface, Soft Matter, vol.12, issue.21, pp.4769-4777, 2016.

J. Caillol and J. Weis, Monte Carlo simulations of the two-dimensional dipolar fluid, Molecular Physics, vol.83, pp.2487-2495, 2015.

H. Schmidle, C. K. Hall, D. Orlin, S. H. Velev, and . Klapp, Phase diagram of two-dimensional systems of dipole-like colloids, Soft Matter, vol.8, issue.5, p.83, 2012.

J. J. Weis, Orientational structure in a monolayer of dipolar hard spheres, Molecular Physics, vol.100, issue.5, pp.579-594, 2002.

P. D. Duncan and P. J. Camp, Structure and dynamics in a monolayer of dipolar spheres, J. Chem. Phys, vol.121, issue.22, pp.11322-11331, 2004.

E. Lomba, F. Lado, and J. J. Weis, Structure and thermodynamics of a ferrofluid monolayer, Physical Review E, vol.61, issue.4, pp.3838-3849, 2000.

J. G. Brankov and D. M. Danchev, Ground state of an infinite two-dimensional system of dipoles on a lattice with arbitrary rhombicity angle, Physica A: Statistical Mechanics and its Applications, vol.144, issue.1, pp.128-139, 1987.

S. Fazekas, J. Kertész, and D. E. Wolf, Two-dimensional array of magnetic particles: The role of an interaction cutoff, Phys. Rev. E, vol.68, p.41102, 2003.

V. A. Froltsov, R. Blaak, C. N. Likos, and H. Löwen, Crystal structures of two-dimensional magnetic colloids in tilted external magnetic fields, Physical Review E, vol.68, issue.6, p.84, 2003.

S. W. De-leeuw, J. W. Perram, and E. R. Smith, Simulation of electrostatic systems in periodic boundary conditions. i. lattice sums and dielectric constants, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.373, pp.27-56, 1752.

J. Weis and D. Levesque, Simple Dipolar Fluids as Generic Models for Soft Matter, vol.95, pp.163-225, 2005.

C. Holm and J. Weis, The structure of ferrofluids: A status report. Curr

. Opin, Colloid Interface Sci, vol.10, p.93, 2005.

E. V. Dmitri-v-talapin, . Shevchenko, B. Christopher, A. V. Murray, P. Titov et al., Dipole-Dipole Interactions in Nanoparticle Superlattices, Nano Letters, vol.7, issue.5, p.93, 2007.

W. Dulmage and W. Lipscomb, The crystal structures of hydrogen cyanide, HCN. Acta Cryst, vol.4, p.93, 1951.

K. Aoki, B. J. Baer, H. C. Cynn, and M. Nicol, High-pressure raman study of one-dimensional crystals of the very polar molecule hydrogen cyanide, Phys. Rev. B, vol.42, p.93, 1990.

R. Tao and D. Xiao, Three-dimensional dielectric photonic crystals of bodycentered-tetragonal lattice structure, Applied Physics Letters, vol.80, issue.25, p.93, 2002.

A. Yethiraj, J. Thijssen, . Wouterse, and . Van-blaaderen, Large-Area Electric-Field-Induced Colloidal Single Crystals for Photonic Applications, Advanced Materials, vol.16, issue.7, p.93, 2004.

L. He, V. Malik, M. Wang, Y. Hu, F. E. Anson et al., Self-assembly and magnetically induced phase transition of three-dimensional colloidal photonic crystals, Nanoscale, vol.4, issue.15, p.93, 2012.

. René-van-roij, Theory of chain association versus liquid condensation, Phys. Rev. Lett, vol.76, p.94, 1996.

Y. Levin, What happened to the gas-liquid transition in the system of dipolar hard spheres?, Phys. Rev. Lett, vol.83, p.94, 1999.

J. Philip, G. N. Camp, and . Patey, Structure and scattering in colloidal ferrofluids, Phys. Rev. E, vol.62, p.94, 2000.

D. Peter, P. J. Duncan, and . Camp, Aggregation kinetics and the nature of phase separation in two-dimensional dipolar fluids, Phys. Rev. Lett, vol.97, p.94, 2006.

S. Kantorovich, A. O. Ivanov, L. Rovigatti, J. M. Tavares, and F. Sciortino, Nonmonotonic magnetic susceptibility of dipolar hard-spheres at low temperature and density, Phys. Rev. Lett, vol.110, p.94, 2013.

J. J. Weis and D. Levesque, Ferroelectric phases of dipolar hard spheres, Phys. Rev. E, vol.48, p.94, 1993.

M. Antti-pekka-hynninen and . Dijkstra, Phase diagram of dipolar hard and soft spheres: Manipulation of colloidal crystal structures by an external field, Phys. Rev. Lett, vol.94, issue.13, p.138303, 2005.

G. S-h-l-klapp and . Patey, Crystallization of dipolar spheres: A discussion of second-order density functional theory, J. Chem. Phys, vol.112, issue.24, p.94, 2000.

. Shl-klapp, Dipolar fluids under external perturbations, Journal of Physics: Condensed Matter, vol.17, issue.15, p.94, 2005.

B. Groh and S. Dietrich, Crystal structures and freezing of dipolar fluids, Phys. Rev. E, vol.63, issue.2, p.21203, 2001.

H. B. Lavender, K. A. Iyer, and S. J. Singer, Global orientational order in model polar clusters, J. Chem. Phys, vol.101, issue.9, p.104, 1994.

. F-cousin and . Dubois, Tuning the interactions of a magnetic colloidal suspension, Phys. Rev. E, vol.68, issue.2, p.105, 2003.

U. Dassanayake, . Fraden, and . Van-blaaderen, Structure of electrorheological fluids, The Journal of Chemical Physics, vol.112, issue.8, p.105, 2000.

A. Yethiraj, A. Wouterse, B. Groh, and A. Van-blaaderen, Nature of an Electric-Field-Induced Colloidal Martensitic Transition, Phys. Rev. Lett, vol.92, issue.5, p.105, 2004.

S. Priti, P. Mohanty, S. Bagheri, A. Nöjd, P. Yethiraj et al., Multiple path-dependent routes for phase-transition kinetics in thermoresponsive and field-responsive ultrasoft colloids, Physical Review X, vol.5, issue.1, p.105, 2015.

M. Antti-pekka-hynninen and . Dijkstra, Phase behavior of dipolar hard and soft spheres, Phys. Rev. E, vol.72, p.105, 2005.

G. T. Gao and X. C. Zeng, Freezing transition of a strongly dipolar simple fluid, Phys. Rev. E, vol.61, p.105, 2000.

A. Goyal, K. Carol, O. Hall, and . Velev, Phase diagram for stimulusresponsive materials containing dipolar colloidal particles, Phys. Rev. E, vol.77, issue.3, p.105, 2008.

C. Philip, A. V. Brandt, G. E. Ivlev, and . Morfill, Solid phases in electroand magnetorheological systems, J. Chem. Phys, vol.130, issue.20, p.105, 2009.

D. Gottwald, C. N. Likos, G. Kahl, and H. Löwen, Phase behavior of ionic microgels, Phys. Rev. Lett, vol.92, issue.6, p.105, 2004.

D. Gottwald, G. Kahl, and C. N. Likos, Predicting equilibrium structures in freezing processes, J. Chem. Phys, vol.122, issue.20, p.105, 2005.

M. Watzlawek, C. N. Likos, and H. Löwen, Phase diagram of star polymer solutions, Phys. Rev. Lett, vol.82, issue.26, p.105, 1999.

D. Kraft, Algorithm 733; TOMP-Fortran modules for optimal control calculations, ACM Transactions on Mathematical Software, vol.20, issue.3, p.111, 1994.

B. Robert and . Wilson, A simplicial algorithm for concave programming, p.111, 1963.

J. Nocedal, J. Stephen, and . Wright, Numerical Optimization. Springer Series in Operations Research and Financial Engineering, 2006.

K. Schittkowski, The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function -Part 2: An Efficient Implementation with Linear Least Squares Subproblems, Numerische Mathematik, vol.38, issue.1, p.113, 1982.

R. P. Brent, Algorithms for minimization without derivatives, p.114, 1973.