Dr. Arvind Kumar Gupta

Professor

Dr. A. K. Gupta is working as an Professor in the Department of Mathematics, IIT Ropar. After obtaining his Master and Doctoral degree from IIT Roorkee, he joined BITS Pilani in 2006 as an Assistant Professor in the Mathematics Group and later in 2010 joined Department of Mathematics, IIT Ropar. Dr. Gupta’s areas of research interests include Mathematical Modeling of Traffic flow, Asymmetric simple exclusion process, Lattice hydrodynamics and Cellular Automata.

Traffic flow Modelling

In traffic flow modeling, we are interested in developing realistic models (Micro as well as Macro) to discover many interesting phenomenon of traffic dynamics in a network. The proposed models are analyzed and investigated theoretically and simulation is performed to test the analytical findings. These models plays a crucial role in understanding the complex mechanism of traffic congestion (jam) which is one of the serious problem for developed as well as developing countries nowadays.

Cellular Automata

Cellular automata (CA) is a modelling technique giving due consideration to individual properties and raising spatial and time discrete models of dynamical systems. CA are simple models to imitate many physical, biological or environmental complex phenomena. Typically, a two-dimensional CA comprise of two-dimensional array of identical objects called cells, having one of the possible finite states which changes in discrete time steps according to state update function.

Ribosome Flow Model (RFM)

Dynamical systems play a pivotal role in comprehending the diverse biophysical facets of complex transport phenomena. Within biological systems, intracellular transport stands as a fundamental process ubiquitous to all cells, thus requiring thorough investigation into its dynamics. Various mathematical models have been suggested based on a different paradigm, for example, Petri nets, probabilistic Boolean networks, and Kinetics-based ordinary differential equations. One such important model is the ribosome flow model (RFM) which is a deterministic model obtained via a mean-field approximation of ASEP. We extend the RFM by incorporating more intricate features to enhance our understanding of transport processes.

Machine learning approaches to mathematical modeling

We are also interested in modelling various physical phenomena under consideration, involving stochastic or partial differential equations, like stock market movement and traffic flow. The aim is to augment the physics behind such systems with machine learning and generate a predictive model that learns the evolution of these systems.

Current Semester

Previous Semesters

At IIT Ropar (2010-2025)

MA703 - Computational Partial differential equation (PG, PhD)

MA423 - Stochastic Process (PG)

MA456 - Fuzzy Logic & application (PG, UG)

MA202 - Operations Research (UG)

MA213 - Introduction to Probability & Stochastic Processes (UG)

MA211 - Complex Analysis (UG)

MA101 - Calculus (UG)

MA111 - Mathematics Laboratory (UG)

Preparatory Mathematics (UG)

At BITS Pilani (2006-2010)

Fuzzy Logic & its Applications (UG, PG)

Discrete Structure for Computer Science (UG, PG)

Numerical Analysis (UG, PG)

Probability & Statistics (UG)

Calculus (UG)

Linear Algebra & Complex Analysis (UG)

Differential Equations (UG, PG)

Optimization (UG)

Journal Articles

[101] S. N. Chattopadhyay and A. K. Gupta, "Predicting Jams in Heterogeneous Disordered Traffic: Insights from Tipping Point Theory", Applied Mathematical Modelling, (2025).

[100] N. K. Pande, P. Pasricha, and A. K. Gupta, "European Option Pricing in Regime Switching Framework via Physics-Informed Residual Learning", Expert Systems With Applications, 128226, (2025).

[99] S. N. Chattopadhyay and A. K. Gupta, "Anticipating critical transitions in a stochastic macrophage polarization model", Physical Review E, 111, 054415, (2025).

[98] A. K. Pandey, A. Gupta and A. K. Gupta, "Multilane bidirectional traffic in a strongly coupled exclusion model with constraint resources", Physical Review E, 111, 044131, (2025).

[97] S. N. Chattopadhyay and A. K. Gupta, "Unveiling critical transition in a transport network model: stochasticity and early warning signals", Nonlinear Dynamics, 1-26, (2025).

[96] N. Bhatia and A. K. Gupta, "Site-wise dynamic defects in a non-conserving exclusion process", SciPost Physics Core, 8, 009, (2025).

[95] M. Verma, A. K. Gupta, and S. Sharma, "Phase transitions in a multi-phase lattice hydrodynamic area occupancy model in mixed disorder traffic considering connected and human-driven vehicles", Physica A: Statistical Mechanics and its Applications, 658, 130264, (2025).

[94] N. Bhatia and A. K. Gupta, "Local resetting in a dynamically disordered exclusion process", Physica A: Statistical Mechanics and its Applications, 130280, (2025).

[93] S. N. Chattopadhyay and A. K. Gupta, "B-tipping points in plankton dynamics: Stochasticity and early warning signals", Physical Review E, 110 (6), 064218, (2024).

[92] N. K. Pande, A.Jain, A. Kumar and A. K. Gupta, "Conservative deep neural networks for modeling competition of ribosomes with extended length", Physica D: Nonlinear Phenomena, 134415, (2024).

[91] M. Verma, A. K. Gupta, and S. Sharma, "Traffic flow dynamics and oscillation control in conserved fractal networks", The European Physical Journal B, 97 (10), 163, (2024).

[90] S. N. Chattopadhyay and A. K. Gupta, "Bistability and the emergence of oscillation in a multiple-loop traffic network", Nonlinear Dynamics, 1-13, (2024).

[89] N. Bhatia and A. K. Gupta, "Local resetting in a bidirectional transport system", Journal of Statistical Physics, 191 (7), 79, (2024).

[88] S. N. Chattopadhyay and A. K. Gupta, "Tipping Points, Multistability, and Stochasticity in a Two-Dimensional Traffic Network Dynamics", Chaos, 34 (7), 073107, (2024).

[87] N. K. Pande, A. Kumar and A. K. Gupta, "Forecasting Stock Indices: Stochastic and Artificial Neural Network Models", Computational Economics, 1--33, (2024).

[86] A. Jain, and A. K. Gupta, "A mathematical framework for analyzing particle flow in a network with multiple pools", Royal Society Open Science, 11 (5), 231588, (2024).

[85] A. Gupta and A. K. Gupta, "Competition for resources in an exclusion model with biased lane-changing mechanism", Physical Review E, 109 (2), 034132, (2024).

[84] M. Verma, T. Singla, A. K. Gupta, and S. Sharma "The role of occupancy on traffic flow in a multiple-loop networks", Physica A: Statistical Mechanics and its Applications, 638, 129617, (2024).

[83] N. Bhatia and A. K. Gupta, "Totally Asymmetric Simple Exclusion Process with Local Resetting in a Resource-Constrained Environment", Physical Review E, 109, 024109, (2024).

[82] A. Gupta and A. K. Gupta, "Reservoir crowding in a dynamically disordered bidirectional system with narrow entrances", Chaos, Solitons & Fractals, 178, 114318, (2024).

[81] A. Gupta and A. K. Gupta, "Exclusion processes on a roundabout traffic model with constrained resources", Physical Review E, 108 (6), 064116, (2023).

[80] A. Jain and A. K. Gupta, "Large-scale closed and generalized networks of ribosome flow model with different site sizes", Physica D: Nonlinear Phenomena, 455, 133881, (2023).

[79] A. Gupta, B. Pal and A. K. Gupta, "Interplay of reservoirs in a bidirectional system", Physical Review E, 107 (3), 034103, (2023).

[78] N. Bhatia and A. Gupta, "Role of site-wise dynamic defects in a resource-constrained exclusion process", Chaos, Solitons & Fractals 167, 113109, (2023).

[77] A. Gupta and A. K. Gupta, "Non-equilibrium processes in an unconserved network model with limited resources", The European Physical Journal Plus 138 (2), 108, (2023).

[76] A. Gupta, B. Pal, A. Jindal, N. Bhatia, and A. K. Gupta,"Modelling of Transport Processes: Theory and Simulations", MethodsX, 10, 101966, (2023).

[75] A. Jain, A. Kumar, A. K. Gupta, "A theoretical framework to analyze the flow of particles in a dynamical system with stochastic transition rates and site capacities", Royal Society Open Science, 9, 220698, (2022).

[74] B. Pal, A. K Gupta, "Reservoir crowding in a resource-constrained exclusion process with a dynamic defect", Physical Review E, 106 (4), 044130, (2022).

[73] D. Kaur, S. Sharma, A. K. Gupta, "Analyses of lattice hydrodynamic area occupancy model for heterogeneous disorder traffic", Physica A, 607, 128184, (2022).

[72] A. Jain, A. K. Gupta, "Modeling mRNA translation with ribosome abortions", IEEE/ACM Transactions on Computational Biology and Bioinformatics, 20, 1600-1605, (2022).

[71] N. Bhatia, A. K. Gupta, "Far from equilibrium transport on TASEP with Pockets", The European Physical Journal Plus, 137, 892, (2022).

[70] B. Pal, A. K. Gupta, "Non-conserving exclusion process with a dynamic obstacle", Chaos, Solitons and Fractals, 162, 112471, (2022).

[69] B. Pal, A. K. Gupta, "Exclusion process with scaled resources: Delocalized shocks and interplay of reservoirs", Physical Review E 105, 054103, (2022).

[68] A. Jain, A. K. Gupta, "Modeling transport of extended interacting objects with drop-off phenomenon", Plos One, 17(5), e0267858, (2022).

[67] A. Gupta, A. K. Gupta, "Particle creation and annihilation in an exclusion process on network", Journal of Physics A: Mathematical and Theoretical, 55, 105001, (2022).

[66] A. Jain, M. Margaliot, A. K. Gupta, "Large-scale mRNA translation and the intricate effects of competition for the finite pool of ribosomes", Journal of the Royal Society Interface 19, 20220033, (2022).

[65] A. Jindal, N. Bhatia, A. B. Kolomeisky, A. K. Gupta, "The effect of local reversible dissociation of particles in interactive driven diffusive system", Physica A: Statistical Mechanics and its Applications, 588, 126555, (2022).

[64] A. Jindal, A. B. Kolomeisky, A. K. Gupta, "Steady-state dynamics of exclusion process with local reversible association of particles", Journal of Statistical Physics, 185, 17, (2021).

[63] . Verma, A. K. Gupta, "Evolutionary dynamics of rock-paper-scissors game in the patchy network with mutations", Chaos, Solitons and Fractals, 153(1), 111538, (2021).

[62] B. Pal, A. K. Gupta, "Reservoir crowding in a totally asymmetric simple exclusion process with Langmuir Kinetics", Chaos, Solitons and Fractals, 153(1), 111517, (2021).

[61] B. Pal, A. K. Gupta, "Persistence of spontaneous symmetry breaking in bidirectional transport system with reservoir crowding", Journal of Physics A, 54 (40), 405002, (2021).

[60] A. Jindal, A. K. Gupta, "Effect of local dissociation on symmetry breaking in exclusion model constituted by bridge lane and input-output TASEPs", Chaos, Solitons and Fractals, 152, 111354, (2021).

[59] N. Sharma, A. K. Verma, A. K. Gupta, "Spatial network based model forecasting transmission and control of COVID-19", Physica A: Statistical Mechanics and its Applications, 581(1), 126223, (2021).

[58] T. Verma, A. K. Gupta, "Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model", Communications in Nonlinear Science and Numerical Simulation, 102, 105927, (2021).

[57] A. Jindal, A. K. Gupta, "Exclusion process on two intersecting lanes with constrained resources: Symmetry breaking and shock dynamics", Physical Review E, 104, 014138, (2021).

[56] A. Jindal, A. K. Verma, A. K. Gupta, "Cooperative dynamics in bidirectional transport on flexible lattice", Journal of Statistical Physics, 182.1, 1-19, (2021).

[55] A. Jindal, A. B. Kolomeisky, A. K. Gupta, "Effect of local dissociations in bidirectional transport of driven particles", Journal of Statistical Mechanics 2020, 113202.

[54] B. Pal, A. K. Gupta, "Role of interactions in a closed quenched driven diffusive system", Journal of Physics A: Mathematical and Theoretical, 2020, 54, 025005.

[53] A. Jindal, A. B. Kolomeisky, A. K. Gupta, "The Role of Dynamic Defects in Transport of Interacting Molecular Motors", Journal of Statistical Mechanics, 2020 (4), 043206.

[52] A. Jindal, T. Midha, A. K. Gupta, "Analysis of interactions in totally asymmetric exclusion process with site-dependent hopping rates: theory and simulations", Journal of Physics A: Mathematical and Theoretical, 53 (23), 235001, (2020).

[51] A. K. Verma, N. Sharma, A. K. Gupta, "On the Role of Interacting Particles and Limited Resources in the Regulation of Lattice Length Dynamics", Journal of Statistical Physics, 179, 216–230, (2020).

[50] T. Verma, A. K. Gupta, "Mean-field dispersal induced synchrony and stability in an epidemic model under patchy environment", Physica A, 541, 123300, (2019).

[49] Atul Kumar Verma, A. K. Gupta, "Stochastic transport on flexible lattice under limited resources", Journal of Statistical Mechanics, 2019, 103210.

[48] L. Gomes, T. Midha, A. K. Gupta, A. B. Kolomeisky, "The effect of local dissociation on dynamics of interacting molecular motors", Journal of Physics A: Mathematical and Theoretical, 52 (36), 365001, (2019).

[47] T. Midha, A. B Kolomeisky, A. K. Gupta, "Theoretical Study of Network Junction Models for Totally Asymmetric Exclusion Processes with Interacting Particles", Journal of Statistical Mechanics, 2019 (8), 083202.

[46] N. Sharma, T. Midha, A. K. Gupta, "Interactive dynamics controlling symmetry breaking in bidirectional transport systems with narrow entrances", Physica A, 514, 412-425, (2019).

[45] A. K. Verma, N. Sharma, A. K. Gupta, "Cooperative motor action to regulate microtubule length dynamics", Physical Review E, 99 (3), 032411, (2019).

[44] T. Midha, A. B. Kolomeisky, and A. K. Gupta, "Interactions in nonconserving driven diffusive systems", Physical Review E , 98(4) , 042119, (2018).

[43] T. Midha, L. V F Gomes, A. B. Kolomeisky, A. K. Gupta, "Theoretical Investigations of Asymmetric Simple Exclusion Processes for Interacting Oligomers", Journal of Statistical Mechanics, (2018), 053209.

[42] I. Dhiman, A. K. Gupta, "Steady-state dynamics of an inhomogeneous two-channel TASEP with Langmuir kinetics", Int. J. of Modern Phys. C, 29(4), 1850037, (2018).

[41] N. Sharma, A. K. Verma and A. K. Gupta, "The robustness in dynamics of out of equilibrium bidirectional transport systems with constrained entrances", Physics Letters A, 382(21), 1383-1388, (2018).

[40] T. Midha, A. B Kolomeisky, A. K. Gupta, "Effect of Interactions for One-Dimensional Asymmetric Exclusion Processes under Periodic and Bath-Adapted Coupling Environment", Journal of Statistical Mechanics, (2018), 043205.

[39] A. K. Verma, A. K. Gupta, "Limited resources in multi-lane stochastic transport system", J. Phys. Commun., 2, 045020, (2018).

[38] A. K. Verma, N. Sharma, and A. K.Gupta, "Far-from-equilibrium bidirectional transport system with constrained entrances competing for pool of limited resources", Physical Review E, 97, 022105, (2018).

[37] T. Midha, A. K. Gupta, "Role of interactions and correlations on collective dynamics of molecular motors along parallel filaments", Journal of Statistical Physics, 169(4), 824–845, (2017).

[36] T. Midha, A. K. Gupta, A. B. Kolomeisky, "The Effect of Side Motion in the Dynamics of Interacting Molecular Motors", Journal of Statistical Mechanics: Theory and Experiment, 2017, 073202.

[35] N. Sharma, A. K. Gupta, "Phase segregation and Spontaneous Symmetry Breaking in a bidirectional two-channel non-conserving model with narrow entrances", Journal of Statistical Mechanics: Theory and Experiment, 2017(4), 043211.

[34] N. Sharma, A. K. Gupta, "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata", Physica A, 471, 114-125, (2017).

[33] P. Redhu, A K. Gupta, "The role of passing in a two-dimensional network", Nonlinear Dynamics, 86 (1), 389-399, (2016).

[32] I. Dhiman, A. K Gupta, "Origin and dynamics of a bottleneck-induced shock in a two-channel exclusion process", Physics Letters A, 380 (24), 2038-2044, (2016).

[31] A. K. Gupta, "Collective dynamics on a two-lane asymmetrically coupled TASEP with mutually interactive Langmuir Kinetics", Journal of Statistical Physics, 162(6), 1571 - 1586, (2016).

[30] I. Dhiman, A. K Gupta, "Collective dynamics of an inhomogeneous two-channel exclusion process: Theory and Monte Carlo simulations", Journal of Computational Physics, 309, 227-240, (2016).

[29] P. Redhu, A K. Gupta, "Effect of forward looking sites on a multi-phase lattice hydrodynamic model", Physica A, 445, 150-160, (2016).

[28] Y. Sharma, P. S. Dutta and A. K. Gupta, "Anticipating regime shifts in gene expression: The case of an autoactivating positive feedback loop", Physical Review E, 93, 032404, (2016).

[27] Y Sharma, K C Abbott, P S Dutta, A K Gupta, "Stochasticity and bistability in insect outbreak dynamics" , Theoretical Ecology, 8 (2), 163–174, (2015).

[26] A. K. Verma, A. K. Gupta, I. Dhiman, "Phase diagrams of three-lane asymmetrically coupled exclusion process with Langmuir kinetics" , Europhysics Letters, 112, 30008, (2015).

[25] P. Redhu, A. K. Gupta, "Delayed-feedback control in a Lattice hydrodynamic model", Communications in Nonlinear Science and Numerical Simulation, 27, 263-270, (2015).

[24] P. Redhu, A. K. Gupta, "Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing", Physica A, 421, 249-260, (2015).

[23] A. K. Gupta, S. Sharma, P. Redhu, "Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing", Nonlinear Dynamics, 80, 1091-1108, (2015).

[22] A. K. Gupta, Isha Dhiman, "Phase diagram of a continuum traffic flow model with a static bottleneck", Nonlinear Dynamics, 79 (1), 663-671, (2014).

[21] I. Dhiman & A. K. Gupta, "Effect of coupling strength on a two-lane partially asymmetric coupled totally asymmetric simple exclusion process with Langmuir kinetics", Physical Review E, 90, 012114, (2014).

[20] I. Dhiman & A. K. Gupta, "Two-channel totally asymmetric simple exclusion process with Langmuir kinetics: The role of coupling constant", Europhysics Letters, 107, 20007, (2014).

[19] A. K. Gupta, S. Sharma, P. Redhu, "Analyses of lattice traffic flow model on a gradient highway", Communication in theoretical Physics, 62, 393, (2014).

[18] A. K Gupta & I. Dhiman, "Asymmetric coupling in two-lane simple exclusion processes with Langmuir kinetics: Phase diagrams and boundary layers", Physical Review E, 89, 022131, (2014).

[17] P. Redhu & A. K. Gupta, "Phase transition in a two-dimensional triangular flow with consideration of optimal current difference effect" Nonlinear Dynamics, 78, 957-968, (2014).

[16] A. K. Gupta, Isha Dhiman, "Analyses of a continuum traffic flow model for a non-lane-based system", Int. J. Modern Physics C, 25 (9), 1450045, (2014).

[15 ]Bharti Sharma, V. K. Katiyar, A. K. Gupta, A. Singh, "The Automated Vehicle Detection of Highway Traffic Images by Differential Morphological Profile", Journal of Transportation Technologies, 4(02), 150, (2014).

[14 ]Bharti Sharma, V. K. Katiyar, A. K. Gupta, "Fuzzy Logic Model for the Prediction of Traffic Volume in Week Days", Int. J. of Computer Applications, 107(17), 1, (2014).

[13] A. K. Gupta, P. Redhu, "Analyses of a modified two-lane lattice model by considering the density difference effect", Communication in Nonlinear Science and Simulation, 19(5), 1600-1610, (2014).

[12] A. K. Gupta & P. Redhu, "Analyses of the driver's anticipation effect in a new lattice hydrodynamic traffic flow model with passing", Nonlinear Dynamics, 76(2), 1001-1011, (2014).

[11] A. K. Gupta, I. Dhiman, "Coupling of two asymmetric exclusion processes with open boundaries", Physica A, 392, 6314-6329, (2013).

[10] A. K. Gupta, "A section approach to a traffic flow model on networks", Int. J. Mod. Phys. C, 25(4) 1350018, (2013).

[9] A. K. Gupta, P. Redhu, "Jamming transition of a two-dimensional traffic dynamics with consideration of optimal current difference", Physics Letters A, 377, 2027, (2013).

[8] A. K. Gupta, P. Redhu, "Analyses of driver's anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system", Physica A, 392, 5622(2013)

[7] A. K. Gupta, S. Sharma, (2012), "Analysis of wave properties of a new two-lane continuum model with consideration of the coupling effect", Chin. Phys. B, 21(1) 015201.

[6] A. K. Gupta, S. Sharma, (2010), "Nonlinear analysis of traffic jams in an anisotropic continuum model", Chin. Phys. B, 19(11), 110503.

[5] A. K. Gupta and V. K. Katiyar, (2007), "A new multi-class continuum model for traffic flow", Transportmetrica, 3(1), 73-85.

[4] A. K. Gupta and V. K. Katiyar, (2006), "A new anisotropic continuum model for traffic flow", Physica A: Statistical Mechanics and its Applications, 368 (2), 551-559.

[3] A. K. Gupta and V. K. Katiyar, (2006), "Phase transition of traffic states with an on-ramp", Physica A: Statistical Mechanics and its Applications, 371 (2), 674-682.

[2] A. K. Gupta and V. K. Katiyar, (2005), "Analyses of shock waves and traffic jams in traffic flow", Journal of Physics A: Mathematical and General, May (38), 4069-4083.

[1] V. K. Katiyar A. K. Gupta and Jaipal, (2005), "Effect of noise on blood pressure and heart rate", Biomechanics, Anamaya Publishers, New Delhi, 258-266.

Conference/Workshops Proceedings

[6] A. Jain, A. K. Gupta, "A Closed Network of RNA Polymerase Flow Models for Analyzing Intracellular Transport", Traffic and Granular Flow -22, 2024, pp 249-256, ISBN: 978-981-99-7975-2 (Springer, Singapore).

[5] N. Bhatia, A. K. Gupta, "Modified version of open TASEP with dynamic defects", Traffic and Granular Flow -22, 2024, pp 257-264, ISBN: 978-981-99-7975-2 (Springer, Singapore).

[4] S. Sharma, A. K. Gupta, "Numerical simulation of heat transfer of nanofluids in an enclosure", Seventh International Conference on CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia, 2009.

[3] B. Sharma, V. K. Katiyar, A. K. Gupta, "Intelligent traffic light control algorithm at the road intersection", Communication and computing systems, Proc. of the Int. Conf. on Comm. & Computing systems (ICCCS 2016), 861-866, 2016. DOI: 10.1201/9781315364094-155. (Taylor & Francis)

[2] A. K. Gupta, "Two-Channel Partially Coupled Exclusion Process with Mutually Interactive Langmuir Kinetics", Traffic and Granular Flow -15, 2016, pp 629-636, ISBN: 978-3-319-33481-3 (Springer).

[1] A. K. Verma, A. K. Gupta, "Effect of Binding Constant on Phase Diagram for Three-Lane Exclusion Process", Advanced Computing and Communication Technologies, Proceedings of the 9th ICACCT, 2015, ISBN 978-981-10-1021-7, 289-296.

Edited Volumes and Book Chapters

[3] A. K. Gupta, A. Kumar & N. K. Pande, (2024), "Machine learning assisted manufacturing", In: Industry 4.0. CRC Press. pp 77--108.

[2] A. Jindal, T. Midha & A. K. Gupta, (2022), "Theoretical Investigation of Interacting Molecular Motors", In: Zdravković, S., Chevizovich, D. (eds) Nonlinear Dynamics of Nanobiophysics. Springer, Singapore. pp 345–368.

[1] A. K. Gupta, (2011), "Mathematical Modeling of Traffic flow: A continuum approach", Lambert Academic Publishing, Germany (ISBN 978-3-8433-6881-0).

Poster Presentation

[3] A. K. Gupta, "Effect of Mutually Interactive Langmuir Kinetics on the Collective Dynamics in a Two-Lane Asymmetrically Coupled TASEP", STATPHYS 26 at Lyon during 18-22 July 2016.

[2] I Dhiman, A K Gupta, "Steady-state properties of a two-channel inhomogeneous exclusion process ", STATPHYS 26 at Lyon during 18-22 July 2016.

[1] A. K. Verma, A. K. Gupta, "Collective Dynamics on a Three-Channel Exclusion Processes with Langmuir-Kinetics", STATPHYS 26 at Lyon during 18-22 July 2016.

Professor, Indian Institute of Technology Ropar, India, 2025-Present
Associate Professor, Indian Institute of Technology Ropar, India, 2015-2025
Assistant Professor, Indian Institute of Technology Ropar, India, 2010-2015
Assistant Professor, BITS Pilani, India, 2006-2010

Present Members

Former Members

Completed projects

[5] "Investigation of Mechanisms of Biological Transport Phenomena on Cellular Network Utilizing Analytical and Computational Tools", under Core Research Grant of DST-SERB for three years (2020-2023).

[4] "Understanding disordered traffic dynamics on Indian roads: Modeling & simulation", under Mathematical Research Impact Centric Support (MATRICS) of SERB for three years (2020-2023).

[3] "Organized a GIAN program titled: “Motor proteins & Molecular Motors", during 04-08 Feb 2019 and hosted Prof. Anatoly B. Kolomeisky, Rice University, USA.

[2] "Mathematical Modeling of Two-Channel Exclusion Processes Relevant to Real World: Analysis and Simulation", under DST Fast track scheme (2014-2017).

[1] "Analyses and Simulation of a continuum traffic flow model for large-scale traffic networks", under ISRD-IIT Ropar (2011-2014).

Workshop and Conferences

[11] Chaired a session in "Recent Advances in Theoretical & Computational Partial Differential Equations" at Punjab University, Punjab during 5-9th December, 2016.

[10] Chaired a session and presented a paper titled "Multi-forward looking effect in lattice hydrodynamic traffic flow model" in the international conference on modeling simulation and optimizing techniques (ICMSOT-15)" during 12-14 Feb 2015 at DAV College Jalandhar.

[9] Chaired a session and presented a paper titled "Phase transition in a three phase lattice hydrodynamic model with passing" in International Congress of Mathematician (ICM 2014) at Seoul during 13th August to 21st August 2014.

[8] Chaired a session and presented a paper titled, "Modeling of vehicular traffic Flow on highway interchange using section approach" in International Conferences on Engineering and Applied Sciences at Beijing during 23rd July 2012 to 27th July 2012.

[7] Presented a paper entitled, "Nonlinear Analysis of Traffic Jams in a Continuum Model Using Wavefront Expansion Technique" in 7th International Congress on Industrial and Applied Mathematics - ICIAM 2011, from July 18 - 22, 2011 at Vancouver, Canada.

[6] Presented a paper entitled "Traffic flow modeling using controlled traffic lights" in IMST 2009 - FIM XVIII in Jay Pee University, Solan during 2nd -4th August 2009.

[5] Presented a paper entitled "Continuum approach to traffic flow" in IMS - 05 in the Department of Mathematics, IIT Roorkee during Dec 26th - 29th, 2005.

[4] Participated in "Instructional school on computational PDE'S" in Department of Mathematics, IIT Bombay during June 5-24, 2005.

[3] Poster presentation on "Modeling drivers's behavior in traffic flow", in National conference on Biomechanics in Centre for Biomedical Engg., IIT Delhi during Nov 19-21, 2004.

[2] "International Conference and Instructional Workshop on Industrial Mathematics" in Department of Mathematics, IIT Bombay during Dec 7-9, 2002.

[1] "International Conference on Mathematical Modeling" in Department of Mathematics, University of Roorkee, Roorkee during Jan 29-31, 2001.

Administrative Responsibilities

Head Deptt. of Mathematics from (Jan 2019 – till date).

Associate Dean, Sponsored research (Oct. 2017-Jan 2019).

JAM, vice Chairman (2018, 2019, 2020).

Convener of Hindi Cell, IIT Ropar, (August 2010 - till date).

Member of the ACUGS, Course Evaluation Committee, Library Committee etc. at Mathematics Department, IIT Ropar.

Reviewer in International Journals

Communications in Nonlinear Science & Numerical Simulation (Elsevier)

Physics A (Elsevier)

PLOS One

Nonlinear Dynamics (Springer)

Modern Physics Letter B (World-scientific)

Physics Letters A (Elsevier)

Applied Mathematical Modeling (Elsevier)

Differential Equations and Dynamical Systems (Springer)

International Journal of Modern Physics C (World-scientific)

International Journal of Modern Physics B (World-scientific)

Transportation Research D (Elsevier)

Measurement (Elsevier)

Proceedings of the National Academy of Sciences (Springer)

Journal of Computational and Nonlinear Dynamics (ASME)

Mathematical Problems in Engineering (Hindawi)

Transport (Taylor & Francis)

Transportmetrica B (Taylor & Francis)

Chinese Physics B (IOP)

Invited Talks

An invited talk on "Dynamics of Stochastic Bidirectional Transport in Complex Systems" at Department of Physics, IIT Jammu on 04th Feb 2025.

An invited talk on "Cellular Automata Modeling of Physical Systems" on Mathematics Day at J.C. Bose University of Science & Technology, YMCA, Faridabad on 30th Jan 2025.

An invited lecture series on "Cellular Automata Modeling of Traffic flow" on Application of Mathematics at Guru Nanak College, Sri Muktsar Sahib, Punjab during 27-28 September, 2024.

An invited lecture on "Modeling of stochastic biological transport" at BITS Pilani on 18th March 2024.

An invited talk on "Understanding various transportation systems: Theory & Simulation" , in a workshop on “Recent Advances in Mathematics”at PEC Chandigarh during 22-23rd Feb 2024.

An invited talk on "Modeling of transport in various systems" at IIT Ropar on 18th January 2024.

An invited talk on "Symmetry breaking in bidirectional transport: Theory & Simulation" in the "6th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM 2023)" at BITS DUBAI, UAE during 21-22nd December, 2023.

An invited talk on "Understanding stochastic biological transport" in the "International Conference on Advancements in Mathematics (ICAM-2023)" at TIET Patiala during 28 – 30th September, 2023.

An invited talk on "Mathematical modeling" in at Bela college, Punjab on January 25, 2017.

An invited talk on "Understanding Stochastic Transport Through Channels Utilizing Vertical Cluster Mean Field Approach" in TCPDE international Conference on Recent Advances in Theoretical & Computational Partial Differential Equations at Punjab University, Punjab during 5-9th December, 2016.

An invited talk on "The role of statistics in engineering" in TEQIP-II sponsored short term course on “Advances of Statistics in Sciences and Engineering” during 19-25 September, 2016 at NIT Jalandhar.

An invited talk on "Modeling with Differential Equation", in NPDE-TCA workshop during 15 May - 04 June, 2016 at IIT Ropar.

A key note address on topic "Multi-forward looking effect in lattice hydrodynamic traffic flow model" in the "international conference on modeling simulation and optimizing techniques (ICMSOT-15)" during 12-14 Feb 2015 at DAV College Jalandhar.

Given an invited talk on "Computational PDE's with MATLAB" in the National Workshop on "Research Tools in Mathematics" during 19th - 25th, December 2014 at Mata Gujri College, Fatehgarh Sahib.

Given an invited talk on "Fuzzy logic and applications" in the National Workshop on "Research Tools in Mathematics" during 19th - 25th, December 2014 at Mata Gujri College, Fatehgarh Sahib.

An invited talk on "Modeling Of Stochastic Transport Processes: Vertical Cluster Mean Field Approach for Two-Channel TASEP" in ASEP meeting on 8th Nov 2014 at Ramakrishna Mission Vivekananda University, Belur Math, West Bengal.

Given an invited talk on "A talk on continuum Approach to Non-lane-based traffic flow" at Beihang University of Aeronautics & Astronautics, Beijing China on 26th July 2012.

Given an invited talk on "Cellular automaton & its applications" at Chandigarh University, Punjab, India on 9th April 2014.

An invited talk on "An introduction to fuzzy sets and fuzzy numbers" in refresher course at Chandigarh University on 07/07/2014.

An invited talk on "Modeling & simulation of traffic flow through cellular automaton approach" in TEQIP-II sponsored FDP on Modeling & simulation of dynamical systems and optimization (MSDSO-2014) at Delhi Technical University, Delhi during 9-13 June 2014.

An invited talk on "Modeling of stochastic transport processes" in TEQIP-II sponsored FDP on Modeling & simulation of dynamical systems and optimization (MSDSO-2014) at Delhi Technical University, Delhi during 9-13 June 2014.

Master's Thesis Guided

Himanshu Nagpal, BS-MS, IISER Mohali, Analyses of Traffic Flow through Lattice Hydrodynamic Approach (2014)

Saksham Singh, BS-MS, IISER Mohali, A dynamic continuum model for traffic assignment in an urban city (2014)

Aditya Suman, MSc-Mathematics, IIT Ropar, Lattice hydrodynamic traffic flow models (2017)

Depinder Singh Sumal, MSc-Mathematics, IIT Ropar, Modeling on vehicular traffic flow (2017)

Himani Rajput, MSc-Mathematics, IIT Ropar, Mathematical Modeling of Vehicular Traffic (2019)

Extra Curricular Activities

Worked as a nucleus member in Educational Development Division, BITS Pilani.

Participated in Departmental functions at IIT Roorkee.

Worked as a member of DEAN's Organization of IIT Roorkee and hence involved in the organization of various activities.

Worked as an Assistant Warden of Govind Bhawan, IIT Roorkee from July, 2003 - July, 2006.

Worked as a Joint Secretary of the student representation at the Mathematics Department, IIT Roorkee during 2000-01.