Dr. Faqir M Bhatti

Associate Professor

Department of Mathematics, School of Arts and Sciences

Lahore University of Management Sciences, Sector U, DHA

Lahore 54792, PAKISTAN

 

 

www.lums.edu.pk

 

 

Education
Research
Research Collaborators
Publications
Conferences Organized
Teaching
Contact Me  E-mail

fmbhatti@lums.edu.pk
Department of Mathematics 
Lahore University of Management Sciences
Opposite Sector "U", DHA,
Lahore - 54792, Pakistan.
Phone: +92-42-5722670-79 ext: 2123,2121,2114
Fax: +92-42-5722591
 

Academic Qualifications

 

Ph.D (Applied/Computational Maths.)

University of London,  England

1986

 

Scholarships and Awards

 

1980-85


Prestigious Central Overseas Scholarship holder, awarded by Govt. of Pakistan for doctorate studies at the University of London, England.

1973-75

Merit Scholarship holder for postgraduate studies. 

1970-73

Merit Scholarship holder for undergraduate studies.

1964-69

Merit Scholarship holder

 

Academic Positions

 

  • Lecturer

28.4.76 to 7.01.77

Univ. of Balochistan, Quetta, Pakistan.
  • Lecturer

10.01.77 to 26.11.86

Shah Abdul Latif University, Khairpur
  • Assistant Prof.

27.11.86 to 4.3.88

Shah Abdul Latif University, Khairpur.
  • Associate Prof. 

 5.3.88 to 23.12.91

Shah Abdul Latif University, Khairpur.
  • In-charge(Computer Science Dept.)

9.7.87 to 23.12.91

Shah Abdul Latif University, Khairpur
  •  Senior Lecturer

25.12.91- 31.12.99 

University of Brunei Darussalam,  Brunei Darussalam
  • Senior Lecturer

11.01.2000-11.01.2003

Multimedia University, Melaka, Malaysia
  • Associate Professor

20.01.2003-onwards

Lahore University of Management Sciences, Lahore, Pakistan.

 

Short Term Visiting Fellowships

 

Dec, 93-Jan,1994
June-July,1996
July-August, 1998

Visiting Research  Fellow

Royal Holoway , University of London, Egham Hill, UK
July - August, 2007 Visiting Research Fellow Queen Mary's College, University of London, QMUL, UK

May 9- June 9, 2000

Visiting Associate Professor

Chuo University, Tokyo, Japan.
(also visited Kobe Univ., Nara Woman Univ., Univ. of Osaka, Japan)
June-July 2004 Visiting Professor Chiang Mai University, Thialand (Also visited King Mangut Institute of Technology, North Bangkok and Kasetsart University, Bangkok).
Dec 05 - August 2006 Visiting Professor Com^2Mac, Pohang University of Science and Technology, Pohang South Korea.
August 15-September 15, 2007 Visiting Professor Com^2Mac, Pohang University of Science and Technology, Pohang South Korea.

 

Teaching

 

 Undergraduate and Post-graduate Mathematics Courses.
  • Numerical Analysis (using Pascal)
  • Numerical Methods (using Pascal)
  • Numerical Optimization (using Pascal)
  • Numerical Solutions of Ordinary Differential Equations (With Pascal and Mathematica)
  • Differential Equations and Applications
  • Mathematical Methods
  • Vector Analysis and Mechanics
  • Introduction to Complex Analysis
  • Engineering Mathematics
  • Calculus with Analytic Geometry
  • Mathematical Statistics
  • Introduction to Scientific Computation.
  • Combinatorics.

Undergraduate Computer Science Courses/Information Technology.
  • Structured Programming (Pascal)
  • Programming with Pascal and C++
  •  Introduction to Computing
  • Basic mathematics for Computer Science
  • Mathematics for Information Technology.
  • Discrete Mathematics (i.e algorithm approach)
  • Mathematics with Mathematica
  • Discrete Structures
  • Resource Management Techniques.
  • Mathematical Techniques I and II
  • Numerical Mathematics

 

Computer Experience Since March 1982

Mainframe  (a). CDC-7600 
                     (b) Prime 570 
                     (c) Amdhal
                     (d) Cray-1(Super  Computer) 
                     (e). IBM 

Computer Languages

                    (a). Pascal
                    (b) Fortran F77
                    (c) C++ 
                    (d) Q-Basic
                    (e) Computer Packages including Mathematica and Maple.

 

 

Statement of Research

A major part of my research has been to establish computational techniques in Percolation Theory—i.e. numerical models to study the passage of fluid through a random ‘medium’. Markov processes and critical probability are used to study Directed Percolation Models.  This work has many different applications—e.g., traffic in a telephone network or charge in a disordered-conductor. 
Series Expansions are main tools used throughout my research. I have established a unique technique called ‘The Extended Perimeter Method’, and a computational method to find the coefficients of the series for all Percolation Models, whether Directed or Directed Compact. This involves a very large matrix inversion (say a 15000 by 15000 matrix or larger). The terms of the powers series are fitted to a recurrence relation of some order (say n), with polynomial coefficients. This is then used to obtain differential equations with polynomial coefficients of degree n. The numerical solution of the relevant differential equations gives the critical exponents, and determines various scaling relations between these exponents. I have established many algorithms to solve the differential equations. The coefficients in these expansions have graph theoretical interpretations which are of particular interest to researchers in the field.
My other contributions to Percolation Theory have been to analyze the series without forming recurrence relations and differential equations. For this purpose Pade’ approximant techniques (using Pascal Programming and Mathematica) are  used to analyze the power series, and to determine the numerical values of critical exponents for various Percolation Models. Very recently, the correction to scaling concept has been used to determine the exponent and critical points.

Another major part of my research has been concerned with graph theoretic problems arising in this area of research, where I have generated sub-graphs of both square lattice and directed square lattice, with up to 16 and 17  edges respectively. In all  of my research work, I have developed computer software to perform both numeric and non-numeric tasks. Moreover, I have active research interests in the following fields:

(i)  Enumerative Combinatroics
(ii) Percolation Theory (Directed & Undirected)
(iii) Applied Graph Theory
(iv) Scientific Computing

 

Scientific Publications

Chapter in Book (published in 1988)

  • Bhatti FM and Essam JW, Applications of Graphs in Chemistry and  Physics (1988) (edited by Kennedy JW  and Quintas, USA)’, 85-112 (North-Holland).
     

  • Book on Enumeration Combinatorics with J. H. Kwak (Underprepration) "expected to be publish in 2008".

Editor of Proceedings

  • Edited the ‘Proceedings of 7th Asian Technology Conference in Mathematics, December, 2002 (with Wei-Chi Yang, Sung Chi Chu, Tilak De Alwis) (published by ATCM Inc, USA.
     

  • A D R Coudary and F M Bhatti(editor) ‘Proceedings of World Conference    on 21st Century Mathematics 2004, September, 2004, Pakistan.
     

  • Editor-in-chief  A.D.R. Choudary and FM Bhatti Journal of Prime Research in Mathematics’ (since 2005).
     

  • Gullaya Dhompongsa, F M Bhatti and Quentin C. Kitson  Proceedings for International Conf. on 21st Century Information Technology in mathematics Education 2006.


 

Research Papers published in International refereed Journals.

 

  • Bhatti FM, J. Phys. A: Math. & Gen. 17 (1984) ‘The resistive susceptibility of three dimensional diode-insulator Network’, 1771-1773 (UK).
  • Bhatti FM and Essam JW, J. Phys. A: Math. & Gen. 17 (1984) ‘The Resistive  Susceptibility of random diode-insulator Networks’, L67-L73 (UK).
  • Essam JW and Bhatti FM, J. Phys. A: Math. & Gen. 18 (1985) ‘Series  Expansions evidence supporting the Alexander-Orbach conjecture in two  dimensions’, 3577-3584 (UK).
  • Bhatti FM and Essam JW, J. Phys. A: Math. & Gen. 19 (1986) ‘Series  expansions study of the distribution of currents in the elements of a random  diode-insulator Networks’, L519-L525 (UK).
  • Essam JW, K. De’ Bell, Adler J, and Bhatti FM, Phys. Rev. B-33 (1986)  ‘Analysis of extended series of Bond Percolation on the Directed Square lattice’, 1982-1986 (USA).
  • Bhatti FM, Proc. of  the 9th All Pakistan Mathematical Conference Hyderabad’, (1987) ‘Disjoint Parallel Paths on the Directed Square lattice’,71-76 (Pakistan).
  • Bhatti FM and Essam JW, Discrete Applied Mathematics (Special Edition)           19 (1988) ‘Low Density Series expansion for Backbone properties of  Percolation Clusters’, 85-112 (Holland).
  • Bhatti FM and Khan MZ Mehran Univ. Res. Journal(1990) ‘On theorem for Some Classes of Operators in Lorentz Space’, 35-40 (Pakistan).
  • Bhatti FM, Algebraic Combinatorics and Related Topics(1994)’Embedding  Algorithm for Two-rooted Acyclic Directed Graphs’, 12-20 (Philippines).
  • Bhatti FM, Brak R, Essam J W, and Lookman T, J. Phys. A: Math. & Gen  30(1997)’ Series Expansion Analysis of the Backbone Properties of Two  Dimensional  Percolation Clusters’, 6215-6232 (UK).
  • Tandon PN and Bhatti FM, Asean Journal on Science & Technology Development 15(2) (1998)’ A Simple Mathematical Model for the Oxygen Diffusion in an Artificial Heart-Lung Device’, 13-26 (Philippines).
  • Bhatti FM, Khan MZ and Jalbani S.U Res. Journal (Sc. Series) (1998) ‘On Theorems For Estimating Eigenvalues of Some Class of Operators in Banach Spaces’, Volume 30.
  • Faqir M Bhatti(2000) Journal of the Physical Society of Japan, Vol 69, No.10, October’ Estimates of Resistance and Conductive Exponents in Two   and Three dimensions Using Extended Perimeter Method’,  Page No. 3223-3227(printed in Japan)
  • Norio Inui, M. Katori and Faqir M Bhatti(2001) Journal of Physical Society of Japan, Volume No. 70, No.2, February, 2001"Low-Density Series Expansions for the Domany-Kinzel Model., Page No. 359-366 (Printed in Japan)
  • Bhatti F M, Azman NA and Zuraifah Mohd Adnan (2001) “The Use of ICT as an Aid to Enrich Teaching and Learning Process of Mathematics at Secondary School level”, Proceeding of ICPSME (2001), 98-108 Malaysia.
  • Bhatti FM and Azman N A (2002) ‘Some Properties of Weight factors arising in Low-Density Expansion for Percolation Models’
  • Nur Azaman Abu and Bhatti F M (2002) ‘Pre-Calculus in Additional Mathematics’, Realities in Science Mathematics and Technical Education’, 300-309 (Brunei Darussalam)
  • Bhatti F M (2002) ‘Simple Technique for Computing the Resistance of Cover-able Two-Rooted Graph’, Proceedings of ATCM2002, 505-512 (USA).
  • Nur Azman Abu and Bhatti F M (2002) ‘The strength of Graphical Elements in Pre-Calculus’, Proceedings of ATCM2002, 235-243 (USA).
  • Nurhayati Yusoff and Bhatti F M (2002) ‘Survey on the Application of Large Graph Based Techniques in Visualization of Data Mining’, Prosiding Persidangan Mathematik Teknologi Asia, Malaysia, 111-122.

  • S. Tariq and Bhatti FM (2004)‘Computational Technique for Solving Nonlinear Schrödinger Equation Arising for  Modulation Instability in Fiber Optics’ Proceedings of the World Conference on 21st Mathematics 2004,        Lahore.234-243
  • F M Bhatti and J W Essam(2005) ‘Journal of Prime Research in Mathematics’, V-1, N0.1’ Fermi, Bose and Vicious Walk Configurations on the Directed Path’, 156-177(Pakistan).
  • F M Bhatti and J W Essam (2006) J.Physcis 42 Generating Function Rationality for Anisotropic Vicious Walk Configurations on the Directed Square Lattice.25-34 Australia
  • N A Abu, Bhatti F M and N.M Yousuf  Proceedings of Thailand International Conf. on 21st Century IT in Mathematics Edu.(2006) ‘Multimedia Learning System on Mathematics II’,51-65  Thailand.
  • Bhatti F M and Toor S K   Proceedings of Thailand International Conf. on 21st Century IT in Mathematics Edu.(2006) ‘The e-learning Methodology in Teaching and Assessment of University Level Mathematics in 21st Century’, II’,127-142  Thailand.
  • Bhatti FM Proceedings of Combinatorics Workshop 2006 ‘Fermi Walk and Bose Walk Configurations on Acyclic Two Rooted Directed Square Lattice’, 161-171 South Korea
  • D K Arrowsmith, FM Bhatti and J.W. Essam "Bose and Fermi Walk Configuration, POSETs and Young Tableaux" to be submitted in 2007.
  • FMBhatti "Somer Properties of Spectrum of Planar Honeycomb Graph Under Complete set of Invariants" to be submitted in 2007.

Research Projects  in Progress at International Level
  • Essam J W(UK) & Bhatti F M ‘Some Theoretical and Numerical Studies of Directed Compact Percolation Clusters
  • Essam JW (UK) and F M Bhatti Computational Methods for Percolation Models

 Research/Dissertation Supervision
  • 1993

Comparison Study of Some Computational Methods for Ordinary Differential  Equations. (Miss Sarina Yahya).
  • 1994

Numerical Methods for Percolation Models (Miss Sarinah Tampoi)
  • 1995

Some Properties of Directed Percolation Processes (Mr.Radzman Ibrahim ).
  • 1995 

Comparison Study of Some Computational Methods For Partial Differential  Equations (Miss Haslina Abdul Ghafar).
  • 1996 

Computational Methods For Unconstrained  Optimization (Mr. Mohammad  Salleh Tuah).
  • 1997

Comparison of Principal Methods of Power Series Analysis (Mr.Khoo Seng  Leong.
  • 1998

Some Computational Methods For Constrained Optimization (Miss Loo  Memeriahneh.
  • 1998 

Some Applications of Graphs (Miss Norhayati bte Hj Yahya).
  • 1999 

Some Applications of Digraphs Cyclic and Acyclic (Miss Fatimah Binye Hj. Muhamad Yousuf).
  • 1999 

Extrapolation Methods (Miss Faeizah bte Hj. Yakop).
  • 1999

Numerical Mathematics with Mathematica (Miss Jamilah Hj. Tengah).

 

Research Collaborators

 

  • Prof. John W Essam,  UK

  • Prof. D K Arrowsmith, UK

  • Prof. P N Tandon,  Brunei

  • Prof. Keith De Bell, Canada

  • Prof. Turab Lookman, USA

  • Dr. Richard Brak, Australia

  • Prof. Joan Adler, Australia (now somewhere else)

  • Prof. M Katori, Japan

  • Prof. Norio Anui, Japan

  • Prof. Jin Ho Kwak, South Korea

  • Nur Azman Abu,  Malaysia

  • N M Yousuf, Malaysia

  • Zuraifah Mohd Adnan Malaysia

  • Prof. Salim Tariq, Pakistan

  • Prof. M Z Khan, Pakistan

  • S K Toor, Pakistan

External Examiner and Professional Activities
  • Subject Specialist member of the selection committee of Mehran University of   Engineering and Technology, Pakistan, to recruit staff in Mathematics and  Computer Science.
  • External Examiner in Mathematics and Computer Science, Mehran University of Engineering and Technology, Pakistan.
  • External Examiner in Mathematics at the University of Balochistan, Pakistan
  • External Examiner in Mathematics at the University of Sindh.
  • Convener of the Computer Inspection Team appointed by the Sindh Board of Technical Education, Sindh, Pakistan.
  • Member Board of Studies in Mathematics, University of the Punjab, Lahore.

 

Administration

 

University of London, UK

Assistant Warden of Philpot Hall, Westfield College, University of London, from October, 1983 to March 1986.

Shah Abdul Latif University, Pakistan

My administrative experience at Shah Abdul Latif University has been quite      significant. I established the Computer Science department and was appointed the first In-charge (1987-1991).  I was responsible for recruiting staff and installation of IBM RISC System 6000 and generally to provide computer services to all other departments in the university.  I served as a member of the following academic committees: 
  • Academic Council
  • Advanced Studies and Research Board
  • Board of Studies in Mathematics
  • Board of Studies in Computer Science

Universiti Brunei Darussalam, Brunei
  • National Director of the Australian Mathematics Competition for Brunei Darussalam (1995-9)
  • Member, Board of the Faculty of Science (1991-9)
  • Chairman, Australian Mathematics Competition National Coordinating Committee Ministry of Education, Brunei Darussalam(1995-9)
  • Seminar Coordinator (January 1992-July 1997)
  • Chairman, Local Committee for travel, accommodation and hospitality: International  Conference on Mathematical Modeling (ICMM 1995)
  • Member, Organizing Committee and Programming Committee (ICMM 1995)