Model reduction in Smoluchowski-type equations

References

[1] R. C. Ball, C. Connaughton, P. P. Jones, R. Rajesh, and O. Zaboronskl, Collective oscillations In Irreversible coagulation driven by monomer inputs and large-cluster outputs. Physical Review Letters 109 (2012), No. 16,168304.10.1103/PhysRevLett.109.168304Search in Google Scholar PubMed

[2] P. J. Blatz and A. V. Tobolsky, Note on the kinetics of systems manifestingsimultaneous polymerization-depolymerization phenomena. J. Phys. Chemistry 49 (1945), No. 2, 77-80.10.1021/j150440a004Search in Google Scholar

[3] A. Boje, J. Akroyd, and M. Kraft, A hybrid particle-number and particle model for efficient solution of population balance equations. J. Comput. Phys. 389 (2019), 189-218.10.1016/j.jcp.2019.03.033Search in Google Scholar

[4] A. Boje, J. Akroyd, S. Sutcliffe, and M. Kraft, Study of industrial titania synthesis using a hybrid particle-number and detailed particle model. Chemical Engrg. Sci. (2020), 115615.10.1016/j.ces.2020.115615Search in Google Scholar

[5] N. V. Brilliantov, P. L. Krapivsky, A. Bodrova, F. Spahn, H. Hayakawa, V. Stadnichuk, and J. Schmidt, Size distribution of particles in Saturn's rings from aggregation and fragmentation. PNAS112 (2015), No. 31, 9536-9541.10.1073/pnas.1503957112Search in Google Scholar PubMed PubMed Central

[6] N. V. Brilliantov, W. Otieno, S. A. Matveev, A. P. Smirnov, E. E. Tyrtyshnikov, and P. L. Krapivsky, Steady oscillations in aggregation-fragmentation processes. Phys. Rev. E98 (2018), No. 1, 012109.10.1103/PhysRevE.98.012109Search in Google Scholar PubMed

[7] A. Chaudhury, I. Oseledets, and R. Ramachandran, A computationally efficient technique for the solution of multi-dimensional PBMs of granulation via tensor decomposition. Computers & Chemical Engrg. 61 (2014), 234-244.10.1016/j.compchemeng.2013.10.020Search in Google Scholar

[8] L. W. Esposito, N. Albers, B. K. Meinke, M. Sremcevic, P. Madhusudhanan, J. E. Colwell, and R. G. Jerousek, A predator- prey model for moon-triggered clumping in Saturn's rings. Icarus 217 (2012), No. 1,103-114.10.1016/j.icarus.2011.09.029Search in Google Scholar

[9] L. W. Esposito, B. K. Meinke, J. E. Colwell, P. D. Nicholson, and M. M. Hedman, Moonlets and clumps in Saturn's F ring. Icarus 194 (2008), No. 1, 278-289.10.1016/j.icarus.2007.10.001Search in Google Scholar

[10] H. Hayakawa, Irreversible kinetic coagulations in the presence of a source. J. of Physics A: Mathematical and General 20 (1987), No. 12, L801.10.1088/0305-4470/20/12/009Search in Google Scholar

[11] P. L. Krapivsky and C. Connaughton, Driven brownian coagulation of polymers. J. Chem. Phys. 136 (2012), No. 20, 204901.10.1063/1.4718833Search in Google Scholar

[12] F. Leyvraz, Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Physics Reports 383 (2003), No. 2-3, 95-212.10.1016/S0370-1573(03)00241-2Search in Google Scholar

[13] S. A. Matveev, A. P. Smirnov, and E. E. Tyrtyshnikov, A fast numerical method for the Cauchy problem for the Smolu- chowski equation. J. Comput. Phys. 282 (2015), 23-32.10.1016/j.jcp.2014.11.003Search in Google Scholar

[14] S. A. Matveev, V. I. Stadnichuk, E. E. Tyrtyshnikov, A. P. Smirnov, N. V. Ampilogova, and N. V. Brilliantov, Anderson accel-eration method of finding steady-state particle size distribution for a wide class of aggregation-fragmentation models. Computer Physics Communications 224 (2018), 154-163.10.1016/j.cpc.2017.11.002Search in Google Scholar

[15] S. A. Matveev, A. A. Sorokin, A. P. Smirnov, and E. E. Tyrtyshnikov, Oscillating stationary distributions of nanoclusters in an open system. Mathematical and Computer Modelling of Dynamical Systems (2020), 95-109.10.1080/13873954.2020.1793786Search in Google Scholar

[16] H. Müller, Zur allgemeinen Theorie ser raschen Koagulation. Fortschrittsberichte über Kolloide und Polymere, 27 (1928), No. 6, 223-250.10.1007/BF02558510Search in Google Scholar

[17] R. L. Pego and J. J. L. Velazquez, Temporal oscillations in becker-döring equations with atomization. Nonlinearity33 (2020), No. 4, 1812.10.1088/1361-6544/ab6815Search in Google Scholar

[18] R. Pinnau, Model reduction via Proper Orthogonal Decomposition. In: Model Order Reduction: Theory, Research Aspects and Applications. Mathematics in Industry, Vol. 13 (Eds. W. H. A. Schilders, H. A. van der Vorst, and J. Rommes). Springer, Berlin-Heidelberg, 2008.10.1007/978-3-540-78841-6_5Search in Google Scholar

[19] V. Privman, D. V. Goia, J. Park, and E. Matijevic, Mechanism of formation of monodispersed colloids by aggregation of nanosize precursors. J. Colloid Interface Sci. 213 (1999), 36-45.10.1006/jcis.1999.6106Search in Google Scholar PubMed

[20] K. Semeniuk and A. Dastoor, Current state of atmospheric aerosol thermodynamics and mass transfer modeling: A review. Atmosphere 11 (2020), No. 2,156.10.3390/atmos11020156Search in Google Scholar

[21] A. Shalova and I. Oseledets, Deep Representation Learning for Dynamical Systems Modeling. arXiv:2002.05111 2020.Search in Google Scholar

[22] L. Sirovich, Turbulence and the dynamics of coherent structures. I-III. Quart. Appl. Math. 45 (1987), No 3, 561-590.10.1090/qam/910462Search in Google Scholar

[23] J. Stomka and R. Stocker, Bursts characterize coagulation of rods in a quiescent fluid. Physical Review Letters 124 (2020), No. 25, 258001.10.1103/PhysRevLett.124.258001Search in Google Scholar PubMed

[24] M. V. Smoluchowski, Drei vortrage uber diffusion, Brownsche bewegung und koagulation von kolloidteilchen. Zeitschrift furPhysik 17 (1916), 557-585.Search in Google Scholar

[25] I. V. Timokhin, S. A. Matveev, N. Siddharth, E. E. Tyrtyshnikov, A. P. Smirnov, and N. V. Brilliantov, Newton method for stationary and quasi-stationary problems for Smoluchowski-type equations. J. Comput. Phys. 382 (2019), 124-137.10.1016/j.jcp.2019.01.013Search in Google Scholar

[26] I. Timokhin, Tensorisation in the solution of Smoluchowski type equations. In: Int. Conf. on Large-Scale Scientific Computing. Lecture Notes in Computer Science, Vol. 11958. Springer, 2019, pp. 181-188.10.1007/978-3-030-41032-2_20Search in Google Scholar