Researches Mathematical Modelling and Simulations

Mathematical Modelling and Simulations


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Introduction:

Mathematics plays a very vital role in all branches of science and engineering, especially in conducting research activities.  Since Mathematical Modelling and Simulations is a very board area, which is applicable to almost all fields of research whether it is Natural Sciences, Engineering, Social Sciences or Medical Sciences. Therefore, this group (Mathematical Modelling and Simulations) plays an active role in providing Mathematical support to the researchers of other departments. However, the main focus of research group members include diversified areas of Pure & Applied Mathematics.

1.   ​Research Areas:

  • Mathematical modelling in fluid dynamics
  • Peristaltic transport of Newtonian and Non-Newtonian fluids
  • Magneto hydrodynamics
  • Heat and mass transfer effects
  • Nanofluid in Newtonian and Non-Newtonian fluids
  • Complaint wall problems in Newtonian and Non-Newtonian fluids
  • Cryptography
  • Coding theory
  • Network security
  • Canonical number systems
  • Theory of finite fields, irreducible polynomials and theory of primes in higher dimensional fields
  • Algebraic Number Theory​

2.   Research ​Group Members (Faculty):​

​S​​. No. Name​​ Designation​ Qualific​ation ​ Specialization Contact Details
​1. ​Dr. Muhammad Ashiq (Group Head) ​Assistant Professor ​Ph.D ​Group Theory ​m.ashiq@mcs.edu.pk
+92-346-5274852
​2. ​Dr. Abdul Hameed ​​Assistant Professor ​Ph.D ​Monogenity of Algebraic Number Fields and its Applications ​hameed.lamp@mcs.edu.pk
+92-301-8162543
​3. ​Dr. Saeed Murtaza (Focal Person) ​Associate Professor ​Ph.D ​Mathematical Modelling & Simulations ​smurtaza@mcs.edu.pk
+92-333-5142654
​4. ​Dr. Safia Akram ​​Associate Professor ​Ph.D ​Mathematical Modelling & Simulations (Fluid Mechanics) ​drsafiaakram@mcs.edu.pk
+92-300-9825620​
​5. ​Dr. Farkhanda Afzal ​​Assistant Professor ​Ph.D ​Mathematical Modelling & Simulations ​farkhanda@mcs.edu.pk
+92-331-0046177
​6. ​Mr. Muhammad Naeem ​​Assistant Professor ​MPhil​ ​Group Theory ​muhammad.naeem@mcs.edu.pk

Journal & Conference Papers by Group Members:

Dr. Muhammad Ashiq:

  • ​The Symmetric Groups as Quotients of G3,8,720, Math. Japonica, 37, 1(1992), 9-16. (co-authors Q.Mushtaq and T. Maqsood). MR 1148511
  • Factor Groups of G5,5,120, Communications in Algebra, 20, 12(1992), 3759-3767 (co-authors Q.Mushtaq and T. Maqsood). MR 1191978
  • The Quotients of G5,7,84, Math. Japonicae, 40, 2 (1994), 349-353 (co-authors Q.Mushtaq  and T. Maqsood). MR 1297253
  • On the Group G4,5,276, Kobe Jour. Math., 12 (1995), 1-7 (co-author T. Maqsood and Q.Mushtaq). MR 1362219
  • Alternating or Symmetric Groups as Quotients of G5,5,60, Algebra Colloquium, 4,3 (1996), 379-382 (co-author Q.Mushtaq). MR 1422976
  • The Quotients of  ,   European Jour.  Combinatorics,   22, 7(2001),  905-909 (co-authors: M.Aslam, Q.Mushtaq, T.Maqsood). MR 1857253
  • The CoxeterGroup  ,Communications in Algebra, 30, 5(2002), 2175-2182 (co-authors: Q.Mushtaq, T. Maqsood, and M.Aslam). MR 1904532
  • Parametrization of   on    Advances in Algebra – Proc. of ICM SattelliteCoference in Algebra and Related Topics (2002), 264-270, (co-author Q.Mushtaq). MR 2088447
  • Homomorphic Images of    as Subgroups of  , Algebras, Groups and Geometries, 20,4(2003), 485-500 (co-authors: M.Aslam, Q.Mushtaq, T.Maqsood). MR 2030402
  • Real Quadratic Irrational Numbers and the Group  , Southeast Asian Bulletin of Mathematics, Springer-Verlag, 27: (2003), 409-415, (co-authors: M.Aslam, Q.Mushtaq, T.Maqsood). MR 2045552
  • Finite Presentation of a Linear-Fractional Group, Algebra Colloquium,  (co-author Q. Mushtaq). MR 2183507
  • Action of a two Generator Group on a Real Quadratic Field, Southeast Asian Bulletin of Mathematics, 30: (2006), 399 – 404. MR 2243682
  • Action of a Subgroup of the Modular Group on an Imaginary Quadratic Field,  Quasigroups and Related Systems, 14(2006), 133 – 146, (co-author Q. Mushtaq).
  • Action of a 2-generated group on  : The Parametrization Problem,  Algebras, Groups and Geometries, 24(2007), 187 – 202, (co-author Q. Mushtaq).
  • Triangle Groups  , The Egyptian mathematical Society, Cairo, 1(2007), 35 – 43.
  • Coset Diagrams for a Homomorphic image of  , Acta Mathematica Scientia, 28B(2008), 363 – 370, (co-author Q. Mushtaq).
  • Parametrization of Actions of a Subgroup of the Modular Group, Quasigroups and Related Systems, 20: 1(2012), 21 – 28, (co-author Q. Mushtaq).
  • The Coxeter group G5,5,12, Quasigroups and Related Systems, 23(2015), 175 – 180, (co-author T. Imran).
  • Defining Relations of a group   and its action on real quadratic field, Bulletin of the Iranian Mathematical Society,43,6(2017), 1811 – 1820, (co-author, T. Imran and M. A. Zaighum).
  • Actions of   on Projective Line, Transactions of A. Razmadze Mathematical Institute, 172 (2018), 1 – 6, (co-author, T. Imran and M. A. Zaighum).

Dr. Safia Aram:

  • ​S. Nadeem, Safia Akram, “Peristaltic transport of a hyperbolic tangent fluid model in an    asymmetric channel.” Zeitschrift für Naturforschung A. 64a, 559-567(2009).  ISSN: 0932-0784, Impact Factor (1.363).
  •  S. Nadeem, Safia Akram, “Heat transfer in a peristaltic flow of MHD fluid with partial slip”. Communications in Nonlinear Science and Numerical Simulation. 15(2010)312-321. ISSN: 1007-5704, Impact Factor (2.773)
  • S. Nadeem, Safia Akram, “Peristaltic flow of a Williamson fluid in an asymmetric channel.” Communications in Nonlinear Science and Numerical Simulation. 15(2010)1705-1716.  ISSN: 1007-5704, Impact Factor (2.773)
  • S. Nadeem, Safia Akram, “Slip effects on the peristaltic flow of a Jeffrey fluid in an asymmetric channel under the effect of induced magnetic field.” International Journal for Numerical methods in fluids. 63(2010)374-394. ISSN: 0271-2091, online ISSN: 1097-0363, Impact Factor (1.352)
  • S. Nadeem, Safia Akram, “Influence of heat transfer and magnetic field on a peristaltic transport of a Jeffrey fluid in an asymmetric channel with partial slip.” Zeitschrift für Naturforschung A. 65a (2010) 483-494. ISSN: 0932-0784, Impact Factor (1.363).
  • S. Nadeem, Safia Akram, “Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric and asymmetric channel.” Mathematical and Computer Modelling.52 (2010)107-119. ISSN: 0895-7177,  Impact factor (1.420).
  • S. Nadeem, Safia Akram, “Peristaltic flow of a Jeffrey fluid in a rectangular duct.”Non-linear Analysis Real World Applications. 11(2010)4238-4247. ISSN: 1468-1218, Impact factor (2.201).
  • S. Nadeem, Safia Akram, “Peristaltic flow of a couple stress fluid under the effects of induced magnetic field in an asymmetric channel.’’ Archive of Applied Mechanics. 81(2011)97-109. ISSN: 0939-1533, Impact factor(1.035)
  • S. Nadeem, Safia Akram, “Peristaltic flow of a Maxwell model through porous boundaries in a porous medium.” Transport in porous media. 86(2011)895-909 ISSN: 0169-3913, Impact factor (1.551).
  • S. Nadeem, Safia Akram, “Magnetohydronamic peristaltic flow of a hyperbolic tangent   fluid in a vertical asymmetric channel with heat transfer” Acta Mechanica and Sinica. 27(2011)237-250. ISSN: 0567-7718, Impact factor (0.688)
  • S. Nadeem, Safia Akram, “Influence of inclined magnetic field on peristaltic flow of a Jeffrey fluid with heat and mass transfer in an inclined symmetric or asymmetric channel” Asia Pacific journal of chemical Engineering. 7(2012)33-44. ISSN: 1932-2135, 1932-2143, Impact factor (0.797)
  • S. Nadeem, Safia Akram, T. Hayat, Awatif A. Hendi, “Peristaltic flow of a Carreau fluid in a rectangular duct.”Journal of fluid engineering. 134(2012) 041201-041207. ISSN: 0098-2202, Impact factor (0.747).
  • Safia Akram, S. Nadeem, “Numerical and analytical solutions of peristaltic transport of a six constant Jeffreys model of Fluid in a symmetric or asymmetric channel.” International Journal of fluid Mechanics Research. 39(2012)238-260. ISSN:  1064-2277, Impact Factor (0.00).
  • Safia Akram, Abdul Ghafoor, S. Nadeem, “Mixed convective heat and Mass transfer on a peristaltic flow of a non-Newtonian fluid in a vertical asymmetric channel’’ Heat Transfer Asian Research. 41(2012)613-633. ISSN: 1523-1496, Impact Factor (0.00).
  • Safia Akram, S. Nadeem, Changhoon Lee, “Consequences of nanofluid on peristaltic flow in an asymmetric channel” International Journal of Basic &Applied Sciences.12 (2012)75-96, ISSN: 2077-1223(online), 2227-2720 (Print),  Impact Factor (0.4462).
  • Safia Akram, S. Nadeem, Changhoon Lee, “Influence of lateral walls on Peristaltic flow of a Jeffrey fluid in a rectangular duct with partial slip” International Journal of Applied Mathematics.14 (2012)449-463, ISSN: 2051-5227, Impact factor (2.072).
  • Safia Akram, S. Nadeem, “Simulation of heat and mass transfer on peristaltic flow of hyperbolic tangent fluid in an asymmetric channel.” International Journal for Numerical methods in fluids. 70 (2012)1475-1493, ISSN: 1097-0363, Impact Factor (1.352).
  • Safia Akram, S. Nadeem, “Influence of induced magnetic field and heat transfer on the peristaltic motion of a Jeffrey fluid in an asymmetric channel: Closed form solutions” Journal of Magnetism and Magnetic Materials. 328(2013) 11-20, ISSN: 0304-8853, Impact Factor (2.002).
  • Safia Akram, S. Nadeem, M. Hanif, “Numerical and analytical treatment on peristaltic flow of Williamson fluid in the occurrence of induced magnetic field” Journal of Magnetism and Magnetic Materials. 346(2013) 142-151, ISSN: 0304-8853, Impact Factor (2.002).
  • S. Nadeem, Safia Akram, Noreen Sher Akbar, “Simulation of heat and chemical reactions on peristaltic flow of a Williamson fluid in an inclined asymmetric channel” Iranian journal of chemistry and chemical engineering. Volume 32 No 2(2013)93-107.  ISSN: 1021-9986, Impact factor (0.250).
  • Muhammad Imran, Abdul Ghafoor, Safia Akram, Victor Sreeram, “Limited frequency interval Gramians based model reduction for nonsingular generalized systems” Control Conference (AUCC), 2013 3rd Australian.  2013/11/4, pages 441-444.publisher IEEE.
  • Safia Akram, S. Nadeem “Analytical Analysis of Peristaltic Flow of a Six Constant Jeffrey’s Model of Fluid in an Inclined Planar Channel” Walailak Journal of Science and Technology. Volume 11 No .2 (2014)129-148.  ISSN: 1686-3933, Impact Factor (0.108).
  • Safia Akram, Kh.S. Mekheimer , S. Nadeem “Influence of lateral walls on peristaltic flow of a couple stress fluid in a non-uniform rectangular duct” Applied Mathematics & Information Sciences, No. 3 volume 8(2014) 1127-1133, ISSN: 1935-0090, Impact Factor (1.232).
  • Safia Akram, S. Nadeem “Consequence of nanofluid on Peristaltic transport of a hyperbolic Tangent fluid model in the occurrence of apt (tending) magnetic field” Journal of Magnetism and Magnetic Materials. Volume 358–359(2014)183-191. ISSN: 0304-8853, Impact Factor (2.002).
  • Safia Akram, S. Nadeem, “Significance of nanofluid and partial slip on the peristaltic transport of a Jeffrey fluid model in an asymmetric channel with different wave forms” IEEE Transactions on Nanotechnology. Volume 13(2014) 375 – 385, ISSN: 1536-125X, Impact Factor (1.619).
  • Safia Akram, S. Nadeem, Anwar Hussain, “Effects of heat and mass transfer on peristaltic flow of a Bingham fluid in the presence of inclined magnetic field and channel with different wave forms” Journal of Magnetism and Magnetic Materials. Volume 362(2014) 184 – 192 ISSN: 0304-8853, Impact Factor (2.002).
  • Safia Akram, “Effects of nanofluid on peristaltic flow of a Carreau fluid model in an inclined magnetic field” Heat Transfer Asian Research. Volume 43(2014) 368– 383  ISSN: 1523-1496, Impact Factor (0.00).
  • Safia Akram, “Effects of slip and heat transfer on a peristaltic flow of a Carreau fluid in a vertical asymmetric channel” Computational Mathematics and Mathematical Physics Volume 54(2014) 1886–1902. ISSN: 0965-5425(Print version), 1555-6662 (electronic version) Impact Factor (0.789).
  • Safia Akram, M. Hanif, S. Nadeem, “Peristaltic transport of a Maxwell fluid in a porous asymmetric channel through a porous medium” Cogent engineering Volume 1(2014) 980770 ISSN: 2331-1916, (0.0).
  • Safia Akram, S. Nadeem,  Anwar Hussain “Influence of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluid in an asymmetric channel” Iranian journal of chemistry and chemical engineering. Volume 33 (2014)43-52 ISSN: 1021-9986, Impact factor (0.250).
  • Safia Akram, S. Nadeem, Anwar Hussain “Influence of lateral walls on peristaltic flow of a third grade fluid in a rectangular duct” Journal of Applied Mechanical Engineering ISSN: 2168-9873, Volume 3 (2014) 1000140 ISSN: 2168-9873 Impact Factor (0.0).
  • Safia Akram, E. H. Aly, S. Nadeem, “Effects of metachronal wave on biomagnetic Jeffery fluid with inclined magnetic field” Revista Tecnica de la Facultad de Ingenieria Universidad del Zulia, Volume 38 (2015)18-28, ISSN: 0254-0770  Impact factor (0.047).
  • Safia Akram, S. Nadeem, Anwar Hussain “Partial Slip Consequences on Peristaltic Transport of Williamson Fluid in an Asymmetric Channel” Walailak Journal of Science and Technology. Volume 12(2015)885-908.  ISSN: 1686-3933, Impact Factor (0.108).
  • Safia Akram, S. Nadeem, “Effects of partial slip on the peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel” Computational Mathematics and Mathematical Physics Volume 55(2015) 1899–1912. ISSN: 0965-5425(Print version), 1555-6662 (electronic version) Impact Factor (0.789).
  • Safia Akram, “Nanofluid effects on peristaltic transport of a fourth grade fluid in the occurrence of inclined magnetic field” Scientia Iranica 23(2016) 1502–1516 .ISSN: 1026-3098 Impact factor (1.025).
  • Safia Akram, M. Zafar, Anwar Hussain, M. A.Rana, “ Effects of inclined magnetic field on peristaltic flow of a hyperbolic tangent fluid model with double-diffusive convection in nanofluids” Revista Tecnica de la Facultad de Ingenieria Universidad del Zulia, Volume 39 (2016)186-207, ISSN: 0254-0770  Impact factor (0.047).
  • Safia Akram, S. Nadeem, “Influence of nanoparticles phenomena on the peristaltic flow of pseudoplastic fluid in an inclined asymmetric channel with different wave forms” Iranian journal of chemistry and chemical engineering. Volume 36(2017)107-124, ISSN: 1021-9986, Impact factor (0.606).
  • Safia Akram, Kh.S. Mekheimer , Y. Abd elmaboud “Particulate suspension slip flow induced by peristaltic waves in a rectangular duct: Effect of lateral walls” Alexandria Engineering Journal. Volume 57(2018)407-414, ISSN: 1110-0168, Impact factor (2.33).

Dr. Farkhanda Afzal:

Journal Papers:

  • ​Farkhanda Afzal, Deeba Afzal, Gerhard Pfister & Asad Yaqub: “Unimodular ICIS, a classifier”, Studia Scientiarum Mathematicarum Hungarica. (W category, HEC recognized, Thomson Reuters, ISI impact factor journal) 2017.
  • Farkhanda Afzal: “Generalized Characteristic Sets for Ordinary Differential Polynomial Sets”, Science International, Y category, HEC recognized, (Thomson Reuters, Zoological records) 2016
  • Farkhanda Afzal, Qamar Afzal & M Aslam Malik: “Quadratic Fields under the Action of Subgroup of M”, International Journal of Modelling and Optimization (X category, HEC recognized), 2013.
  • Farkhanda Afzal, Qamar Afzal: “Quadratic Irrationals and Symmetries of Continued Fraction”, International Journal of Mathematical Archive, (X category, HEC recognized), 2013.
  • Farkhanda Afzal, Qamar Afzal & M Aslam Malik: “A Classification of the Real Quadratic irrational numbers (a+√n)/c  of Q^* (√n  )   w.r.t modulo〖 3〗^r “, International Mathematical Forum (X category, HEC recognized), 2012.
  • Farkhanda Afzal, Imran Shaban Bhatti & M Aslam Malik: “Action of G and M on Q(√m  )& Algorithmic Implementation of Group Actions”, Journal of Hyperstructures, (X category, HEC recognized), 2012.
  • Farkhanda Afzal, Qamar Afzal & M Aslam Malik: “Modular Group Action on Quadratic Field by Linear congruence”, Novi Sad Journal Of Mathematics, (X category, HEC recognized), 2012.

Conference Papers:

  • ​Farkhanda Afzal: “Comparison of Char-Set with Generalized Char- Sets of Ordinary Differential Polynomial Sets”, ACME (2016) Johor Bahru, Malaysia, May 30-31, 2016.
  •  Farkhanda Afzal: “Some Applications of Generalized Char- Sets of Ordinary Differential Polynomial Sets”, ICMAE (2016) London United Kingdom, July 18-20, 2016. (Best Presentation Award).
  • Farkhanda Afzal, Qamar Afzal & M Aslam Malik: “Quadratic Fields under the Action of Subgroup of M”, ICPAM (2013) Moscow, Russia, July 20-21, 2013.

Dr. Saeed Murtaza:

  • ​Sirhindi, R., Afzal, M., Murtaza, S.: An Extended Secret Sharing Scheme for Colour Images with Fixed Pixel Expansion. International Journal of Electronic Security and Digital Forensics, Inderscience, 2008.
  • Sirhindi, R., Murtaza, S., Afzal, M.: Improved Data Hiding Technique for Shares in Extended Visual Secret Sharing Schemes. International Conference on Information and Communication Security, ICICS 2008, LNCS Springer-Verlag, 2008.
  • Asma Basharat, Imtiaz Ahmed  and Saeed Murtaza, “Security analysis of Iterveave Division Multiple Access, Next Generation Competitor”, 4th International Conference on Wireless and Mobile Communication (ICWMC08), 27th July – 1st August 2008, Athens, Greece.
  • Asma Basharat, Imtiaz Ahmed  and Saeed Murtaza, “CDMA Vs IDMA for Subscriber Cell Density”, Innovation 2008, 16 – 18 December 2008, Dubai, UAE.
  • Samin Jan and Saeed Murtaza, “A Technique to Discourage the Relay Attack on CAPTCHA”, International Conference on Web Intelligent Systems (ICWIS09), 8 – 10 January 2009, Chennai, India.
  • Adnan Khan Akhunzada, Saeed Murtaza, Ahmad Raza Cheema and Arif Wahla, “Suggestion of New Core Point of Attacks on IEEE 802.16e Networks: A Survey”, International Journal of computer Networks and Security, Vol. 1, No. 2, 2009.

Dr. Abdul Hameed:

Journal Publications

  • ​A. Hameed and T. Nakahara, Integral Bases and Relative Monogenity pure fields, Bull. Math Soc. Sci. Math. Roumanie 58 (106) No. 4 (2015), 419-433. http://ssmr.ro/bulletin/pdf/58-4/articol_5.pdf
  • A. Hameed, T. Nakahara and S. Ahmad, Non-Monogenity of an Infinite Family of Pure Octic Fields, Elixir International Journal (Applied Mathematics), 1(113), (2017), 49328-49333.​http://www.elixirpublishers.com/articles/1515050063_ELIXIR2017095931A.pdf
  • S. Ahmad, T. Nakahara and A. Hameed, On Certain Pure Sextic Fields Related to a Problem of Hasse, International Journal of algebra and Computation, 3(26), (2016), 577-583. http://www.worldscientific.com/worldscinet/ijac
  • A. Hameed, T. Nakahara, S. M. Husnine and S. Ahmad, On the existence of CNS in certain classes of pure algebraic number fields, J. Prime Research in Math, 7(2011), 19-24. http://jprm.sms.edu.pk/media/pdf/jprm/volume_07/03.pdf
  • M. Ahmad, A. Hameed, N. Khan and T. Nakahara, On the Monogenity of Cyclic Sextic Fields of Composite Conductor, Punjab Univ J. Math,  50(3), (2018), 67-73. http://pu.edu.pk/images/journal/maths/PDF/Paper-6_50_3_2018.pdf
  • A. Hameed and S. M. Husnine, On Rationality of Zassenhause Groups, Punjab Univ J. Math , Vol. No. XXXII, (1999), 117-122.
  • A. Hameed and S. M. Husnine, On Rationality of Certain Groups, Punjab Univ J. Math , Vol. No. XXXV, (2002), 7-14

Conference Publications

  • ​A. Hameed, On Monogenity of Pure Octic Fields, Intl Conf on Recent Advances in Math. Model and Applications, LUMS, Lahore, April 2010.
  • A. Hameed,  Computational Complexities in Pure Octic Fields related to a problem of Hasse, 16th Intl Pure Math. Conf. Quaid-e-Azam Univ

 

Contact Research Group:

Dr. Saeed Murtaza (Research Group Coordinator)
Associate Professor
Telephone: +92-333-5142654
Email: smurtaza@mcs.edu.pk

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