Research

Research Interest:  

Computational Fluid Dynamics, Two-phase Flows, Drug Delivery, Computational Fluid Dynamics, Dispersion Phenomena, Heat and mass transfer, cancer modeling, electroporation, multi-scale modeling

Research Scholars

• Current:

1. Gopinath Sadhu

Theis title:  A Mathematical study on the impacts of oxygen heterogeneity on tumor growth and EMT dynamics (Submitted)

2. Tanay Kumar Karmakar

Theis title: Ongoing

3. Bikram Das

Theis title: Ongoing 

• Completed:

1. Jiten Ch. Kalita

Theis title: HOC schemes for incompressible viscous flows: Application and Development 

2. Swapan Kumar Pandit

Theis title: HOC schemes for the simulation of blood flows through Arterial Stenosis 

3. Akhilesh Kumar

Theis title: Analytical Study on Solute Transport in Streams with Transient Storage and Hyporheic Zones 

4. Chitralekha Sarkar

Theis title: Higher-order compact schemes and their applications to problems with complex geometries 

5. Koyel Chakravarty

Theis title: Mathematical Modelling of Drug Release Kinetics 

6. Swarup Barik

Theis title: Multi-scale analysis for dispersion in oscillatory flows 

7. Nilay Mondal

Theis title: Mathematical Modeling of Drug Delivery using Electroporation 

8. Kuldeep Singh Yadav

Theis title: Multiscale Modeling of Drug Delivery 

9. Rupchand Sutradhar

Theis title:  A Theoretical Study of Recycling Effects of rcDNA-containing Capsids on Hepatitis B Virus Infection 

Publications

• Journal Publications

50. Gopinath Sadhu and D.C. Dalal, "Effects of Non-linear Interaction Between Oxygen and Lactate on Solid Tumor Growth Under Cyclic Hypoxia", Bulletin of Mathematical Biology, 2025. doi: 10.1007/s11538-025-01420-6 

49. Rupchand Sutradhar and D C Dalal,  "On existence of traveling wave of an HBV infection dynamics model: a novel approach". The European Physical Journal Plus, 139(11), 963, 2024. 

48. Rupchand Sutradhar, D. C. Dalal, "Cytoplasmic Recycling of rcDNA containing Capsids Enhances HBV Infection", Nonlinear Dynamics, 112 (14) (2024) 12641–12666

47. Gopinath Sadhu and D.C. Dalal, "A mathematical study of the interaction between oxygen and lactate in an in vitro and in vivo tumor", International Journal of Biomathematics, 2024. doi: 10.1142/S1793524524501389 

46. Nilay Mondal and D. C. Dalal, "A model for reversible electroporation to deliver drugs into diseased tissues", The Journal of Membrane Biology, 257, 2024. https://doi.org/10.1007/s00232-024-00321-4 

45. Rupchand Sutradhar, D. C.  Dalal, "Fractional-order models of hepatitis Bvirus infection with recycling effects of capsids", Mathematical Methods in the Applied Sciences, 46 (14) (2023) 15599-15625

44. K. S. Yadav and D. C. Dalal. A multiscale computational study of the effects of fluid flow and drug metabolism on drug delivery, Computers and Mathematics with Applications, 130:58–68, 2023.

43. K. S. Yadav and D. C. Dalal. Effects of cell orientation on drug delivery into biological tissues: A computational study, Applied Mathematical Modelling, 119:156–173, 2023.

42. K. S. Yadav and D. C. Dalal. Penetration and distribution efficacy of chemotherapeutic drugs in biological tissues: A computational investigation, Mathematics and Computers in Simulation, 2023.

41. Nilay Mondal and D. C. Dalal, "Modelling of reversible tissue electroporation and its thermal effects in drug delivery", European Journal of Pharmaceutics and Biopharmaceutics, 190, 47-57, 2023. https://doi.org/10.1016/j.ejpb.2023.07.005 

40. Nilay Mondal, K. S. Yadav and D. C. Dalal, "Enhanced drug uptake on application of electroporation in a single-cell model", The Journal of Membrane Biology, 256(3), 243-256, 2023. https://doi.org/10.1007/s00232-023-00283-z 

39. K. S. Yadav and D. C. Dalal. The heterogeneous multiscale method to study particle size and partitioning effects in drug delivery, Computers and Mathematics with Applications, 92:134–148, 2021.

38.    K. S. Yadav and D. C. Dalal. The heterogeneous multiscale method to study particle size and partitioning effects in drug delivery, Computers and Mathematics with Applications, 92:134–148, 2021.

37. Nilay Mondal, Koyel Chakravarty and D. C. Dalal, "A mathematical model of drug dynamics in an electroporated tissue", Mathematical Biosciences and Engineering, 18(6), 8641-8660, 2021. doi: 10.3934/mbe.2021428 

35. K. Chakravarty, D.C. Dalal., "A nonlinear mathematical model of drug delivery from polymeric matrix", Bulletin of Mathematical Biology , vol.81, pp.105-130, [2019]

34. S. Barik, D.C. Dalal., "Multi-scale analysis for concentration distribution in an oscillatory couette flow (In Press)", Proceedings of Royal Society A. [2019]

33. K. Chakravarty, D.C. Dalal., "Stability Analysis of Drug Dynamics Model : A Mathematical Approach (In Press).", International Journal of Biomathematics. [2019]

36. Nilay Mondal, Koyel Chakravarty and D. C. Dalal, "Mathematical modelling of drug delivery in tissue cells using electroporation, AIP Conference Proceedings", 1975(1), 030017, 2018. https://doi.org/10.1063/1.5042187 

32. Nilay Mondal, K. Chakravarty, D. C. Dalal. ., "Mathematical modeling of drug delivery in tissue cells using electroporation", AIP Conference Proceeding , vol.1975 ,pp.030017-030025, [2018]

31. S. Barik, D. C. Dalal. . :-., "Transvers concentration distribution in an open channel flow with bed absorption : A multi-scale approach.", Communications in Nonlinear Science and Numerical Simulation , vol.65 ,pp.1-19, [2018]

30. Koyel Chakravarty, D. C. Dalal., "Mathematical modelling of liposomal drug release to tumour.", Mathematical Biosciences. , vol.306 ,pp.82-96, [2018]

29. Koyel Chakravarty, D. C. Dalal., "A Nonlinear Mathematical Model of Drug Delivery from Polymeric Matrix doi.org/10.1007/s11538-018-0519-y (In Press).", Bulletin of Mathematical Biology. [2018]

28. Koyel Chakravarty, D. C. Dalal., "An analytical study of drug release kinetics from a degradable polymeric matrix (In Press).", International Journal of Biomathematics. [2017] , DOI/10.1142/S1793524518500110

27. Koyel Chakravarty, D. C. Dalal., "An analytical study of drug release to biological tissues through endocytosis(In Press).", International Journal of Dynamics and Control [2017] , DOI 10.1007/s40435-017-0307-9.

26. Koyel Chakravarty, D.C. Dalal., "A Two-Layer Mathematical Modelling of Drug Delivery to Biological Tissues", Journal of Physics: Conference Series , vol.J759 012023 [2016] , doi:10.1088/1742-6596/759/1/012023

25. Koyel Chakravarty, D.C. Dalal, "A two-phase model for drug release from microparticles with combined effects of solubilisation and recrystallisation.", Mathematical Biosciences. , vol.272 ,pp.24-33, [2016]

24. D.C. Dalal, A. Kumar., "Analytical solution and analysis for solute transport in streams with diffusive transfer in the hyporheic zone.", Journal of Hydro-environment Research, In Press. [2014]

23. D.C. Dalal, F. Hecht, O. Pironneau., "Implementation of a low order mimetic elements in freefem++.", Journal on Numerical Mathematics , vol.20 (3-4) ,pp.183-194, [2013]

22. D.C. Dalal, S.K. Pandit., "Transient solution of an incompressible viscous flow in a channel with sudden expansion/contraction.", World Academy of Sciences, Engineering and Technology , vol.67 ,pp.158-169, [2012]

21. D.C. Dalal, A. Kumar., "Analysis of solute transport in rivers with transient storage and lateral inflow:", An analytical study. Acta Geophysica, Published online. [2010]

20. S.K. Pandit, J.C. Kalita, D.C. Dalal., "A fourth-order accurate compact scheme for the solution of steady Navier-Stokes equations on non-uniform grids.", Computers and Fluids. , vol.37 (2) ,pp.121-134, [2008] , https://www.sciencedirect.com/science/article/pii/S0045793007000916

19. D.C. Dalal, S.K. Pandit., "Numerical study of transient natural convection in a cavity with multiple adiabatic blocks.", Proceedings in Applied Mathematics and Mechanics (PAMM). , vol.7 (1) ,pp.2100063-2100064, [2008]

18. Swapan K. Pandit, Jiten C. Kalita, D.C. Dalal., "A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular.", Journal of Computational Physics. , vol.225 (1) ,pp.1100-1124, [2007] , https://www.sciencedirect.com/science/article/pii/S0021999107000319

17. D. C. Dalal, B.S. Mazumder, R.N. Roy., "Size distributions of suspended particles in open channel flow over bed materials.", Environmetrics. , vol.16 (2) ,pp.149-165, [2005]

16. D. C. Dalal, B.S. Mazumder, K. Ghoshal., "Influence of bed roughness on sediment suspension : Experimental and Theoretical studies.", Journal of Hydraulic Research , vol.43 (3) ,pp.245-257, [2005]

15. J.C. Kalita, Anoop K. Dass,D.C. Dalal., "A transformation-free HOC scheme for steady convection-diffusion on non-uniform grids.", International Journal for Numerical Methods in Fluids. , vol.44 (1) ,pp.33-53, [2004] , http://www3.interscience.wiley.com/cgi-bin/abstract/106570639/ABSTRACT

14. D.C. Dalal, B.S. Mazumder, K. Ghoshal., "Effect of bed roughness on suspended sediment: experimental and theoretical studies.", Shallow Flows 2004, book edited by Jirka and Uijttewaal (Balkema publisher). ,pp.503-509, [2004]

13. D.C. Dalal, B.S. Mazumder., "Saltation layer of particles in water flows related to transport stage.", Nordic Hydrology. , vol.34 (4) ,pp.343-360, [2003]

12. J.C. Kalita, D.C. Dalal, Anoop K. Dass., "A class of Higher Order Compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients.", International Journal for Numerical Methods in Fluids , vol.38 ,pp.1111-1131, [2002] , https://onlinelibrary.wiley.com/doi/10.1002/fld.263

11. J. C. Kalita, Anoop K. Dass, D.C. Dalal., "A fully compact HOC simulation of the steady-state natural convection in a square cavity.", Physical Review E, 066703. , vol.64 (6) ,pp.1-13, [2001] , http://prola.aps.org/abstract/PRE/v64/i6/e066703

10. D.C. Dalal, B.S. Mazumder., "Fully Compact Higher-order Computation of Steady-state Natural Convection in a Sqaure Cavity.", Physical Review E. , vol.64 (6) ,pp.066703-066715, [2001]

9. D.C. Dalal, B.S. Mazumder, R.N. Bhattacharya, J.K. Ghosh., "Comparison of diffusion based approaches to sediment transport with a stochastic interpretation.", Stochastic Hydraulics 2000, edited by Wang and Hu (Balkema publisher). -. ,pp.255-261, [2000]

8. D.C. Dalal, B.S. Mazumder., "Contaminant Dispersion from an Elevated Time-dependent Source.", J. Computational and Applied Mathematics. , vol.126 (1-2) ,pp.185-205, [2000]

7. D.C. Dalal, B.S. Mazumder., "Unsteady Convective Diffusion in Viscoelastic Fluid Flowing through a Tube.", Int. J. Non-Linear Mechanics. , vol.33 (1) ,pp.135-150, [1998]

6. D.C. Dalal, N. Datta, S.K. Mukherjee., "Unsteady Natural Convection of a Dusty Fluid in an Infinite Rectangular Channel.", International Journal of Heat and Mass Transfer. , vol.41 (3) ,pp.547-562, [1998]

5. D.C. Dalal, H.P. Mazumder, U.N. Ganguly, S. Ghorai., "On the Distribution of Axial Velocity and Pressure Gradient in a Pulsatile Flow of Blood through a Constricted Artery.", Indian J. Pure Appl. Math. , vol.27 (11) ,pp.1137-1150, [1996]

4. D.C. Dalal, N. Datta., "Pulsatile Flow and Heat Transfer of a Dusty Fluid through an Infinitely Long Annular Pipe.", International Journal of Multiphase Flow. , vol.21 ,pp.515-528, [1995]

3. D.C. Dalal, N. Datta, S.K. Mishra., "Unsteady Heat Transfer to Pulsatile Flow of a Dusty Viscous Incompressible Fluid in a Channel.", International Journal of Heat and Mass Transfer. , vol.36 ,pp.1783-1788, [1993]

2. D.C. Dalal, N. Datta., "Unsteady Flow of a Dusty Fluid through a Circular Pipe with Impulsive Pressure Gradient.", Acta Mechanica. , vol.95 ,pp.51-57, [1992]

1. D.C. Dalal, N. Datta., "Generalized Couette Flow of a Dusty Gas", Indian Journal of Technology. , vol.30 ,pp.260-264, [1992]

• Conference Publications

16. Rupchand Sutradhar and D. C. Dalal, "Combination Therapy for Chronic Hepatitis B Using Capsid Recycling Inhibitor". Proceedings of the 2nd International Conference on Nonlinear Dynamics and Applications (ICNDA 2024), Volume 2: Complex Systems, Fractals and Nonlinear Flows 

15. Gopinath Sadhu and D.C. Dalal, "Role of Diffusivity of Lactate on Its Accumulation in Tumor Necrotic Core", Proceedings of the 2nd International Conference on Nonlinear Dynamics and Applications (ICNDA 2024), Volume 2, 2024. doi: 10.1007/978-3- 031-69134-8_22 

14. D.C. Dalal, Akhilesh Kumar., "Mathematical modeling of solute transport in rivers.", Proceedings of Recent Trends in Mathematical Modeling and simulation held in the Department of Mathematics, Institute of Technology, Banaras Hindu University, Varanasi. [2010]

13. D.C. Dalal, Akhilesh Kumar., "Analytical solution for continuous injection of solute in rivers with diffusive transfer in the hypoheic zone.", Proceedings of 11th International Conference on Wetland Systems for Water Pollution Control held in Indore. [2008]

12. D.C. Dalal, Akhilesh Kumar., "Analytical solution for instantaneous injection of conservative solutes in rivers with hypoheic zone.", Proceedings of 2nd World Aqua Congress held in New Delhi. [2008]

11. D.C. Dalal, J.C. Kalita, S.K. Pandit., "Numerical investigation of vertical evolution in a backward constricted channel flow.", Proceedings of 2nd International Congress on Computational Mechanics and Simulation (ICCMS- 06) held at the IIT Guwahati. , vol.2 ,pp.1274-1280, [2006]

10. J. C. Kalita, S. K. Pandit, D. C. Dalal., "Numerical investigation of vortical evolution in a backward constricted channel.", Proceedings of the second International conference on computational mechanics and simulation, IIT Guwahati, India. , vol.3 ,pp.1695-1700, [2006]

9. J. C. Kalita, S. K. Pandit, D. C. Dalal., "Higher order compact computation of incompressible viscous flows on nonuniform grids.", Proceedings of the International congress of computational and experimental engineering, IIT Madras, India. December. [2005]

8. J. C. Kalita, S. K. Pandit, D. C. Dalal., "HOC schemes for solving Navier-Stokes equations on curvilinear meshes.", Proceedings of the 50th congress of Indian society of theoretical and applied mechanics, IIT Kharagpur, India. [2005]

7. J. C. Kalita, S. K. Pandit, D. C. Dalal., "HOC schemes for rows in constricted tube.", Proceedings of the 50th congress of Indian society of theoretical and applied mechanics, IIT Kharagpur, India. [2005]

6. D.C. Dalal, B.S. Mazumder, K. Ghoshal., "Influence of bed roughness on sediment suspension: Experimental and Theoretical studies.", Proceedings of conference on Hydraulics, Water Resources and Ocean Engineering - HYDRO 2002 held at the Indian Institute of Technology Bombay, Mumba. . [2002]

5. D.C. Dalal, J.C. Kalita, Anoop K. Dass., "Buoyancy Ratio Effects on the Double-Diffusive Natural Convection in a Vertical Porous Annulus: An HOC Simulation.", Proceedings of International Symposium on Recent Trends in Heat and Mass Transfer held at the Indian Institute of Technology Guwahati, India, paper no. ISRTHMT 02-125. January. [2002]

4. Jiten C Kalita, D. C. Dalal, Anoop K. Dass., "Simulation of flow in a differentially heated square cavity at high Rayleigh Numbers.", proceedings of the International Conference on Mathematical Modelling of Non-linear Systems, at Indian Institute of Technology, Kharagpur, India. , vol.2 ,pp.114-133, [2000]

3. D.C. Dalal, J.C. Kalita, Anoop K. Dass., "Simulation of flow in a differentially heated square cavity for Ra=10^6 and 10^7.", Proceedings of the 27th National Conference on Fluid Mechanics and Fluid Power held at Palghat, India, December 2000. ,pp.229-235, [2000]

2. D.C. Dalal, R. N. Bhattacharya, J.K. Ghosh, B.S. Mazumder., "Comparison of diffusion based approaches to sediment transport with a stochastic interpretation.", Proceedings of 8th International Symposium on Stochastic Hydraulics in Beijing, China. . [2000]

1. D.C. Dalal, J.C. Kalita., "Application of HOC method in steady state natural convection in a square cavity: A numerical approach.", Proceedings of the International Conference on Mathematical Modelling of Nonlinear Systems held at Indian Institute of Technology, Kharagpur. [1999]