Department of Physics




Details of Dr. Md. Kamrul Hassan


"Everything should be as simple as possible, but no simpler" - Albert Einstein

Research statement:


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:

  • Percolation is a paradigmatic model for second order or continuous phase transition (CPT). It is expected that for every observable quantity in the CPT there is an equivalent counterpart. To this end we only knew the equilibrium counterpart of temperature, order parameter, susceptibility. However, we did not know the equivalent counterpart of entropy, specific heat. Besides, it has been well-known in the CPT that the critical exponents of specific heat, susceptibility and order parameter are bound by Rushbrooke inequality albeit remained elusive in percolation. Recently we have resolved all these issues.


  •  We have shown that percolation on scale-free weighted planar stochastic lattice does not belong to the universality class where all the other known planar lattice belong. It is the only exception in the history of percolation.


  • We proposed a mediation-driven attachment (MDA) rule that generate scale-free network with a spectrum of exponents. We, for the first time, looked at the leadership persistence probability in the network and found that the probability P(t) that the leader (nodes with highest connectivity or degree) retains its leadership up to t exhibits power-law.


  • 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.



Academic Degrees Obtained:


  •  1993-1996: Doctor of Philosophy, Degree awarded in Nov. 1996, Department of Physics, Brunel University, United Kingdom, Thesis Title: Kinetics of Fragmentation of particles with one or more than one degree of freedom, Supervisor: Dr. G. J. Rodgers
  •  1991-1992: Post Graduate Diploma in Condensed Matter Physics at International Centre for Theoretical Physics (ICTP), P. O. Box: 686, Trieste, Italy, Thesis Title: On Mixed Valence in Rare Earth materials, Supervisor: Professor P. Fazekas.
  •  1989-1090: Master of Science (First Class), Dhaka University, Department of Physics, Dhaka, Bangladesh. Thesis Title: Electronic Structure Calculation of Disordered Systems,

           Supervisor: Professor Mesbahuddin Ahmed.

  •  1982-1989: Bachelor of Science (Hon.) (First Class), Dhaka University, Department of Physics, Dhaka, Bangladesh.


Scholarships and Awards Obtained:


Post-doctoral Fellowship:


  • 2000-2002: Humboldt  Research Fellow: Awarded by the Alexander Von Humboldt Foundation, Germany (One of the most prestigious research fellowship in Germany)

         Academic host: Prof. Dr. J. Kurths, University of Potsdam, Germany

  • 1994: Overseas Research Studentship (ORS) award: Awarded by the Committee for Vice-chancellor and Principals (CVCP) of  United Kingdom.
  • ·1993: Brunel Departmental Scholarship: Offered by the Department of Physics, Brunel University.
  • 1991: ICTP Diploma Scholarship: Awarded by the Abdus Salam International Centre for Theoretical Physics (AS-ICTP) , Trieste, Italy.
  • 1989: Bose Research Fellowship:  Awarded by the S. N. Bose Centre for Basic

            Science, University of Dhaka, Dhaka 1000, Bangladesh



The Lists of Courses Taught:


  1. Introductory Solid State Physics.
  2. Elementary Quantum Mechanics
  3. Elementary Statistical Mechanics.
  4. Non-equilibrium Statistical Mechanics
  5. Waves and Vibrations.
  6. Heat and Thermodynamics.
  7. Vector Analysis.
  8. Electricity and Magnetism.
  9. Elementary Mathematical Physics (designed as the foundation course for Physics Major student).


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.


Highlights of my research:


  • Percolation transition and critical phenomena.
  •  Complex and scale-free network theory
  •  Stochastic Random Walk Problem
  • Kinetics of Aggregation (Smoluchowski equation).
  •  Kinetics of Fragmentation
  •  Fractals and Multifractals.
  •  Random Sequential Diposition of Particles (RSA).
  •  Kinetics of Nucleation and Growth of a stable phase in first-order phase transition (Kolmogorov-Johnson-Mehl-Avrami)




List of publications and 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. HassanMulti-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).



 M. K. Hassan, Fractal Dimension and the Science of Complexity, Published in Virtual Physics – Number 07, August 1, 1996; available at

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