My main research areas are problems which are far from equilibrium. In particular, I have been involved in the study of a number of non-equilibrium phenomena, including theory of phase transition (percolation) and critical phenomena, complex network theory, stochastic fractals and multifractals, kinetics of aggregation and fragmentation, monolayer growth by deposition, nucleation and growth processes. My recent interest, however, on the theory of percolation and on complex network theory.
The principal impediments to make any progress to these processes is due to their non-equilibrium nature since there exists hardly any systematic standard theoretical framework for describing such non-equilibrium systems. This is indeed in sharp contrast with its equilibrium counterpart. On the other hand, it covers a wide variety of broad field of research which makes it worthwhile of keeping up the continuous effort to understand basic mechanism behind these seemingly unrelated problems which makes it one of the fastest growing fascinating area of research.
The concept of symmetry, order, scaling, similarity and self-similarity, dynamic and finite-size scaling, fractal, power-law, data-collapse etc have been the key tools of my research. I have found them immensely powerful in my search of finding beauty, harmony and regularity in many seeming disordered phenomena.
Below I give some of the major findings of my recent works:
In 2010 we proposed '''weighted planar stochastic lattice (WPSL)''' which in one hand has the property of lattice and on the other hand has the property of scale-free network. We have shown that its growth is governed by infinitely many conservation laws. It is a disordered lattice yet has hierarchy of regularity as it is multi-multifractal. This is a unique lattice as there exist no other lattice which is so rich in properties.
Supervisor: Professor Mesbahuddin Ahmed.
Post-doctoral Fellowship:
Academic host: Prof. Dr. J. Kurths, University of Potsdam, Germany
Science, University of Dhaka, Dhaka 1000, Bangladesh
The Lists of Courses Taught:
I have designed a new syllabus titled `Non-equllibrium Statistical Mechanics and Stochastic Fractals’ for the M. Sc. Student of Dhaka University. The syllabus is designed to cover the latest development in statistical mechanics which are far from equilibrium in nature.
Pre-prints:
International peer reviewed Journals:
1. M. K. Hassan, and M. M. H. Sabbir “Product-Sum universality and Rushbrooke inequality in explosive percolation” Submitted to Phys. Rev. E (2017)
2. M. K. Hassan, M. D. Alam, Z. I. Jitu, and M. M. Rahman “On entropy, specific heat, susceptibility and Rushbrooke inequality in percolation” Phys. Rev. E 96, 050101(R) (2017)
3. M. M. Rahman and M. K. Hassan, “ Explosive percolation on a scale-free multifractal weighted planar stochastic lattice ” Phys. Rev, E 95 042133 (2017) .
4. M. K. Hassan, Liana Islam and Syed Arefinul Haque, “Degree distribution, rank-size distribution, and leadership persistence in mediation-driven attachment networks” Physica A 469 23 (2017) IF 1.785.
5. M. K. Hassan and M. M. Rahman, “Universality class of site and bond percolation on multi-multifractal scale-free planar stochastic lattice” Phys. Rev. E 94 042109 (2016) IF 2.28
6. F. R. Dayeen and M. K. Hassan “Multi-multifractality, dynamic scaling and neighbourhood statistics in weighted planar stochastic lattice” Chaos, Solitons & Fractals 91 228 (2016) IF 1.45
7. M. K. Hassan and M. M. Rahman, “Percolation on a multifractal scale-free planar stochastic lattice and its universality class” Phys. Rev. E (Rapid Communication) 92 040101(R) (2015) IF 2.28
8. M. K. Hassan, N. I. Pavel, R. K. Pandit and J. Kurths, “Dyadic Cantor set and its kinetic and stochastic counterpart” Chaos, Solitons & Fractals 60 31-39 (2014) IF 1.45
9. M. K. Hassan, M. Z. Hassan and N. Islam, “Emergence of fractal in aggregation with stochastic self-replication” Phys. Rev. E 88, 042137 (2013). IF=2.28
10. M. K. Hassan, M. Z. Hassan and N. I. Pavel, Scale-free coordination number disorder and multifractal size disorder in weighted planar stochastic lattice, J. Phys: Conf. Ser, 297 012010 (2011)
11. M. K. Hassan, M. Z. Hassan and N. I. Pavel, “Dynamic scaling, data-collapseand Self-similarity in Barabasi-Albert networks” J. Phys. A: Math. Theor. 44 175101 (2011). IF=1.933
12. M. K. Hassan, M. Z. Hassan and N. I. Pavel, “Scale-free network topology and multifractality in a weighted planar stochastic lattice” New Journal of Physics 13 093045 ( 2010) IF 3.57
12. M. K. Hassan and M. Z. Hassan, “Emergence of fractal behavior in condensation-driven aggregation”, Phys. Rev. E 79, 021406 (2009). IF=2.28
14. M. K. Hassan and M. Z. Hassan, “Condensation-driven aggregation in one dimension”, Phys. Rev. E 77, 061404 (2008). IF=2.28
15. M. K. Hassan, N. Wessel, and J. Kurths, Analytical model for a cooperative ballistic deposition in one dimension, Phys. Rev. E 67, 061109 (2003). IF=2.28
16. M. K. Hassan , J. Schmidt, B. Blasius and J. Kurths, Jamming and asymptotic behaviour in competitive car parking of bidisperse cars. Physica A 315, 163-173 (2002).IF 1.785
17. M. K. Hassan and J. Kurths, Can Randomness alone tune the Fractals dimensions? Physica A 315, 342-352 (2002). IF=1.785
18. M. K. Hassan, J. Schmidt, B. Blasius and J. Kurths, Jamming coverage in competitive random sequential adsorption of a binary mixture, Phys. Rev. E 65, 045103 (Rapid Communication), (2002). IF=2.28
19. M. K. Hassan and J. Kurths, Competitive random sequential adsorption of points and fixed size particles: analytical results, J. Phys. A, 34, 7517-7525 (2001). IF=1.933
20. M. K. Hassan and J. Kurths, Transition from random to ordered fractals in fragmentation of particles with an open system, Phys. Rev. E 64, 016119 (2001). IF=2.28
21. M. K. Hassan, Fractal dimension and degree of order in sequential deposition of a mixture of particles, Phys. Rev. E 55, 5302-5310 (1997). IF=2.28
22. M. K. Hassan, Multifractality and the shattering transition in fragmentation processes, Phys. Rev. E 54, 1126-1133 (1996). IF=2.28
23. P. Singh and M. K. Hassan, Kinetics of multidimensional fragmentation, Phys. Rev. E 53, 3134-3144 (1996). IF=2.28
24. M. K. Hassan and G. J. Rodgers, Multifractality and multiscaling in two dimensional fragmentation, Physics Letters A 218 207-211 (1996). IF=1.677
25. G. J. Rodgers and M. K .Hassan, Stable distributions in fragmentation processes, Physica A 233, 19-30 (1996). IF=1.785
26. M. K. Hassan and G. J. Rodgers, “Models of fragmentation and stochastic fractals”, Physics Letters A 208 95 (1995). IF=1.677
27. G. J. Rodgers and M. K. Hassan, Fragmentation of particles with more than one degree of freedom, Phys. Rev. E 50, 3458-3463 (1994). IF=2.28
National peer reviewed Journals:
1. M. Ahmed and M. K. Hassan, Electrical resistivity of metallic spin glasses in the hierarchical model, Dhaka University Studies B, 40, 117-121 (1992).
2. M. K. Hassan and J. Kurths, Can Smoluchowski equation exhibits gelation transition?, Dhaka Univ. J. Sci, 56(1), 113 (2008).
Miscellaneous
M. K. Hassan, Fractal Dimension and the Science of Complexity, Published in Virtual Physics – Number 07, August 1, 1996; available at http://www.isisnet.com/MAX/vp.html
G. J. Rodgers and M. K. Hassan, The kinetics of fragmentation in the presence of source and sink , Brunel University Preprint, BRU/PH/203 (1995).
Md. Kamrul Hassan