Abstract
Molecular rotors are microscopic structures composed of two coupled parts that can rotate mutually. They have promising applications in viscosity measurement and flow detection in micro-sized and complex geometries. We propose a model for studying molecular rotors as classical systems moving in viscous environments, subjected to internal interactions and stochastic forces. Our model is expressed as a set of non-linear stochastic Langevin equations that are solved numerically using a Brownian Dynamics procedure. Attention is focused on the calculation of the two-time correlation function of the internal angular variable. For small internal forces, this correlation turns out to have a very slow time decay and its correct estimation requires long numerical experiments. We propose a CUDA implementation for a computer cluster with TESLA GPUs that calculates angular correlation functions in parallel. The implementation reduces the used computational time considerably in comparison with the one consumed by a usual serial scheme. It allows for the simulation of massive molecular rotors ensembles from which reliable results can be obtained. It is discussed how the GPU implementation can be improved in modern GPUs architectures.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kottas, G.S., Clarke, L.I., Horinek, D., Mich, J.: Artificial molecular rotors. Chem. Rev. 105, 1281–1376 (2005)
Cao, J., Lu, H.-Y., Chen, C.-F.: Synthesis, structures, and properties of peripheral o-dimethoxy-substituted pentiptycene quinones and their o-quinone derivatives. Tetrahedron 65, 8104–8112 (2009)
Khuong, T.V., Dang, H., Jarowski, P.D., Maverick, E.F., Garcia-Garibay, M.A.: Rotational dynamics in a crystalline molecular gyroscope by variable-temperature 13C NMR, 2H NMR, X-ray diffraction, and force field calculations. J. Am. Chem. Soc. 129(4), 839–845 (2007). PMID: 17243820
Akers, W., Haidekker, M.A.: A molecular rotor as viscosity sensor in aqueous colloid solutions. J. Biomech. Eng. 126(3), 340–345 (2004)
Comotti, A., Bracco, S., Ben, T., Qiu, S., Sozzani, P.: Molecular rotors in porous organic frameworks. Angew. Chem. Int. Ed. 53, 1043–1047 (2014)
Armspach, D., et al.: Catenated cyclodextrins. Chem. A Eur. J. 1(1), 33–55 (1995)
Kim, K., Lee, J.W.: Rotaxane dendrimers. Top. Curr. Chem. 228, 111–140 (2003)
Haidekker, M.A., Theodorakis, E.A.: Environment-sensitive behavior of fluorescent molecular rotors. J. Biol. Eng. 4, 11 (2010)
López-Duarte, I., Vu, T.T., Izquierdo, M.A., Bull, J.A., Kuimova, M.K.: A molecular rotor for measuring viscosity in plasma membranes of live cells. Chem. Commun. 50, 5282–5284 (2014)
Haidekker, M.A., Akers, W., Lichlyter, D., Brady, T.P., Theodorakis, E.A.: Sensing of flow and shear stress using fluorescent molecular rotors. Sens. Lett. 3, 42–48 (2005)
Mustafic, A., Huang, H.-M., Theodorakis, E.A., Haidekker, M.A.: Imaging of flow patterns with fluorescent molecular rotors. J. Fluorescence 20, 1087–1098 (2010)
Dong, J., et al.: Ultrathin two-dimensional porous organic nanosheets with molecular rotors for chemical sensing. Nat. Commun. 8, 1142 (2017)
Valeur, B.: Molecular fluorescence. In: Digital Encyclopedia of Applied Physics, pp. 477–531 (2009)
Horinek, D., Michl, J.: Molecular dynamics simulation of an electric field driven dipolar molecular rotor attached to a quartz glass surface. J. Am. Chem. Soc. 125(39), 11900–11910 (2003)
Kudernac, T., et al.: Electrically driven directional motion of a four-wheeled molecule on a metal surface. Nature 479, 208–211 (2011)
Ambı́a, F., Hı́jar, H.: Stochastic dynamics of a brownian motor based on morphological changes. Rev. Mex. Fis. 63, 314–327 (2017)
Hı́jar, H.: Operation of theoretical brownian motors based on morphological adaptations. Physica A 513, 781–797 (2019)
Marchesoni, F., Vij, J.K., Coffey, W.T.: Nonlinear budó model for dielectric relaxation: comparison with new experimental data. Z. Phys. B – Condens. Matter 61, 357–366 (1985)
Gutiérrez-Garibay, D.: Análisis teórico y numérico de la dinámica estocástica de giroscopios moleculares. Master’s thesis, La Salle University Mexico, Mexico City, Mexico (2019, in progress)
Marchesoni, F., Vij, J.K.: Brownian motion in a periodic potential: application to dielectric relaxation. Z. Phys. B – Condens. Matter 58, 187–198 (1985)
NVIDIA Corporation. Programming guide v10.0.130. https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html#cuda-general-purpose-parallel-computing-architecture. Accessed 18 Feb 2019
NVIDIA Corporation. Programming guide v10.0.130. https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html#from-graphics-processing-to-general-purpose-parallel-computing__memory-bandwidth-for-cpu-and-gpu. Accessed 18 Feb 2019
NVIDIA Corporation. Tesla v100 performance guide. https://images.nvidia.com/content/pdf/v100-application-performance-guide.pdf. Accessed 18 Feb 2019
Barda, D., Bellisbc, M., Allend, M.T., Yepremyane, H., Kratochvilf, J.M.: Cosmological calculations on the GPU. Astron. and Comput. 1, 17–22 (2013)
Alonso, D.: CUTE solutions for two-point correlation functions from large cosmological datasets. arXiv:1210.1833 [astro-ph.IM] (2013)
Ponce, R., Cardenas-Montes, M., Rodriguez-Vazquez, J.J., Sanchez, E., Sevilla, I.: Application of GPUs for the calculation of two point correlation functions in cosmology. arXiv:1204.6630 [astro-ph.IM] (2012)
Gembris, D., Neeb, M., Gipp, M., et al.: Correlation analysis on GPU systems using NVIDIA’s CUDA. J. Real-Time Image Proc. 6, 275–280 (2011). https://doi.org/10.1007/s11554-010-0162-9
Acknowledgments
H.H. thanks La Salle University Mexico for financial support under grant NEC-08/18. D.G-G. thanks La Salle University Mexico for financial support.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Gutiérrez-Garibay, D., Híjar, H. (2019). Molecular Rotors in Viscous Fluids: A Numerical Analysis Aid by GPU Computing. In: Torres, M., Klapp, J. (eds) Supercomputing. ISUM 2019. Communications in Computer and Information Science, vol 1151. Springer, Cham. https://doi.org/10.1007/978-3-030-38043-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-38043-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38042-7
Online ISBN: 978-3-030-38043-4
eBook Packages: Computer ScienceComputer Science (R0)