International Journal of Modern Physics C, May 6, 2022
In intracellular transport, the motor proteins may jump between the filaments due to structural d... more In intracellular transport, the motor proteins may jump between the filaments due to structural deformity where the motion is hindered by presence of bound proteins. This motivates us to study a system of two parallel disordered exclusion processes with Langmuir kinetics under symmetric and asymmetric coupling conditions. Theoretically, continuum mean-field approximation is employed to obtain steady-state equations which are further solved numerically. The steady-state system dynamics are examined for different values of coupling constant [Formula: see text], which indicates ratio of lane-changing rates. The effect of binding constant [Formula: see text] and defect parameters is also explored. Under the symmetric coupling case, the topological structure of phase diagram turns out to be similar to that in single-lane model, which differs significantly under fully asymmetric coupling. The asymmetric coupling increases magnitude of difference between densities in two lanes. At a very large attachment/detachment rate, the LK dynamics dominate the effect of asymmetric coupling in the lanes. The defect parameters are found to reduce particle flux in the steady state. The numerical results are validated through extensive Monte Carlo simulation.
Being inspired by the biological process of gene transcription, we investigate the phenomenology ... more Being inspired by the biological process of gene transcription, we investigate the phenomenology of transport on two-channel TASEP in the presence of dynamical defects under symmetric coupling conditions. The continuum mean-field equations are derived and then solved numerically to obtain steady-state phase diagrams. The role of various parameters namely defect (un-)binding constants, lane-changing rates has been thoroughly examined. The defect (un-)binding rates are found to affect the phase boundaries in the phase plane. The effect of system size on the steady-state dynamics of the system has also been analyzed. The theoretical results are validated by performing extensive Monte Carlo simulations.
In intracellular transport, the motor proteins may jump between the filaments due to structural d... more In intracellular transport, the motor proteins may jump between the filaments due to structural deformity where the motion is hindered by presence of bound proteins. This motivates us to study a system of two parallel disordered exclusion processes with Langmuir kinetics under symmetric and asymmetric coupling conditions. Theoretically, continuum mean-field approximation is employed to obtain steady-state equations which are further solved numerically. The steady-state system dynamics are examined for different values of coupling constant [Formula: see text], which indicates ratio of lane-changing rates. The effect of binding constant [Formula: see text] and defect parameters is also explored. Under the symmetric coupling case, the topological structure of phase diagram turns out to be similar to that in single-lane model, which differs significantly under fully asymmetric coupling. The asymmetric coupling increases magnitude of difference between densities in two lanes. At a very l...
We study a single-channel dynamically disordered totally asymmetric simple exclusion process with... more We study a single-channel dynamically disordered totally asymmetric simple exclusion process with bulk particle attachment and detachment. The continuum mean-field equations are derived and solved numerically to obtain steady-state phase diagrams and density profiles. The effects of various parameters, namely particle attachment rate, defect binding and unbinding rates, and binding constant, have been investigated. An increase in the attachment rate of particles reduces the number of steady-state phases, whereas a variation in defect binding and unbinding rates shifts the phase boundaries. One of the important consequences of introducing particle nonconserving dynamics is the appearance of shock in the steady state. The shock dynamics have been thoroughly examined and the defect strength is found to have a significant effect on the shock position. The mean-field solutions are validated using extensive Monte Carlo simulations.
In order to understand the complexity of real world processes, one need to model these processes ... more In order to understand the complexity of real world processes, one need to model these processes mathematically. In this thesis, we review a epidemic compartmental models and their classifications. The aim of our approach is to develop an intuitive understanding of epidemic models and adapt a new technique Monte Carlo simulations for the validation of various epidemic model. A new model SEIQR has been introduced and results are validated using Runge Kutta method and Monte Carlo simulations
The steady-state dynamics of a two-channel TASEP coupled with Langmuir kinetics in the presence o... more The steady-state dynamics of a two-channel TASEP coupled with Langmuir kinetics in the presence of a localized bottleneck are investigated under a fully asymmetric lane-changing rule. A hybrid mean-field approach is adopted to generate the density profiles as well as phase diagrams. The effect of lane-changing rate and strength of bottleneck on the stationary dynamics of the system has also been investigated. It is observed that an increase in lane-changing rate weakens the effect of bottleneck. As a part of studying the shock dynamics, we have identified and analyzed turning effect in the movement of shock with respect to lane-changing rate. Our theoretical arguments are in good agreement with extensively performed Monte-Carlo simulations.
We analyze the origin and characteristics of the bottleneck-induced shock in a two-channel totall... more We analyze the origin and characteristics of the bottleneck-induced shock in a two-channel totally asymmetric simple exclusion process with Langmuir kinetics under symmetric coupling conditions. The variation in height of the spike, which has been found to be a precursor to the bottleneck-induced shock, is analyzed with respect to lane-changing rate and bottleneck rate q. The critical value of q(q c), below which the effect of bottleneck turns from local to global, has been identified. A non-monotonic variation of q c with respect to is observed. The bottleneck-induced shock exhibits turning effect with respect to an increase in .
This letter studies a fully asymmetrically coupled three-lane totally asymmetric simple exclusion... more This letter studies a fully asymmetrically coupled three-lane totally asymmetric simple exclusion process with Langmuir kinetics under open boundary conditions. Phase diagrams and density profiles for different kinetic rates are obtained using a mean-field analysis along with a singular perturbation technique and are found to be in good agreement with Monte Carlo simulation results. Some mixed phases are observed in the middle lane resulting into bulk-induced phase transitions. We have found that a number of steady-state phases firstly increases then decreases with respect to an increase in lane changing rate. Critical values of the lane changing rate are identified at which the appearance or disappearance of certain phases is observed. We have identified the jumping effect in the position of shock in the middle lane with respect to an increase in the lane changing rate.
We analyze an open system comprised of two parallel totally asymmetric simple exclusion processes... more We analyze an open system comprised of two parallel totally asymmetric simple exclusion processes with particle attachment and detachment in the bulk under partially asymmetric coupling conditions. The phase diagrams are obtained using boundary layer analysis of continuum mean-field equations and characterized for different values of lane-changing rates. The structure of the phase diagram remains qualitatively the same as the one in fully asymmetric coupling conditions up to a certain critical order of lane-changing rates, after which significant changes are found in the phase diagram. The effect of system size on the steady-state dynamics has also been examined. To validate theoretical findings, extensive Monte Carlo simulations are carried out.
We develop a heterogeneous continuum model based upon a car-following model for a nonlane-based s... more We develop a heterogeneous continuum model based upon a car-following model for a nonlane-based system taking lateral separation into account. The criterion for linear stability analysis and traveling wave solution of the homogeneous case is studied. The consideration of the lateral separation not only stabilizes the flow but also shrinks the critical region. For heterogeneous case, the fundamental diagram is examined for two different equilibrium speed-density functions and the effect of lane width is investigated for different compositions of heterogeneous traffic. The theoretical findings agree well with the results of numerical simulation which justifies the applicability of the model to a nonlane-based system.
The phase transitions are investigated in a continuum speed-gradient model with a static bottlene... more The phase transitions are investigated in a continuum speed-gradient model with a static bottleneck under open boundary conditions. The bottleneck situation has been studied using two different approaches-explicit and implicit. The phase diagrams showing different traffic states are presented. The effect of strength of bottleneck has been analyzed, and it is found that the strength parameter has no qualitative effect in the explicit case while has considerable effect in the implicit case. Furthermore, the results of both the approaches are compared, and the consistency between them is discussed.
We study an open system composed of two parallel totally asymmetric simple exclusion processes wi... more We study an open system composed of two parallel totally asymmetric simple exclusion processes with particle attachment and detachment in the bulk. The particles are allowed to change their lane from lane-A to lane-B, but not conversely. We investigate the steady-state behavior of the system using boundary layer analysis on continuum mean-field equations to provide the phase diagram. The structure of the phase diagram is quite complex and provides a complete insight about the steady-state dynamics. We examine two kinds of transitions in the phase plane: bulk transitions and surface transitions, qualitatively as well as quantitatively. The dynamics of shock formation, localization and their dependence on the system parameters and boundary rates have been investigated. We also justify the non-existence of downward shock in both the lanes using fixed point theory. Further, we examine the effect of increasing lane-changing rate on the steady-state dynamics and observe that the number of steady-state phases reduces with increase in lane-changing rate. Our theoretical results are supported with extensive Monte-Carlo simulation results.
Physica A: Statistical Mechanics and its Applications, 2013
ABSTRACT We study the dynamics of a coupled two-channel ASEP in which intra-channel transition ra... more ABSTRACT We study the dynamics of a coupled two-channel ASEP in which intra-channel transition rates are dependent on the configuration of neighboring channel. The binding constant k, which signifies the ratio of inter-channel transition rates, is introduced and the symmetric and asymmetric coupling conditions are analyzed for different values of k. The vertical cluster mean-filed theory is used to study the system behavior exactly in strong coupling conditions and approximately in intermediate coupling conditions. Additionally, the consequences of particular dynamics such as totally asymmetric simple exclusion process (TASEP), partially asymmetric simple exclusion process (PASEP) and symmetric simple exclusion process (SSEP) in either one or both channels are investigated. It is found that the transition rates have a significant influence on both the qualitative and quantitative nature of the phase diagrams. The mathematical computation shows how the number of phases varies from 3 via 6 to 7 under different environments. Interestingly, in fully asymmetric coupling case, the results are found to be independent of the magnitude of non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte-Carlo simulation results.
Journal of Physics A: Mathematical and General, 2004
Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains ... more Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase diagram are calculated exactly by mapping the system into an effective one-channel totally asymmetric exclusion model. For intermediate couplings, a simple approximate theory, that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters, is developed. It is found that, similarly to the case of one-channel totally asymmetric simple exclusion processes, there are three stationary state phases, although the phase boundaries and stationary properties strongly depend on inter-channel coupling. Extensive computer Monte Carlo simulations fully support the theoretical predictions.
This work is devoted to the development of a novel theoretical approach, named hybrid approach, t... more This work is devoted to the development of a novel theoretical approach, named hybrid approach, to handle a localized bottleneck in a symmetrically coupled two-channel totally asymmetric simple exclusion process with Langmuir kinetics. The hybrid approach is combined with singular perturbation technique to get steady-state phase diagrams and density profiles. We have thoroughly examined the role played by the strength of bottleneck, binding constant and lane-changing rate in the system dynamics. The appearances of bottleneck-induced shock, a bottleneck phase and Meissner phase are explained. Further, the critical values of bottleneck rate are identified, which signify the changes in the topology of phase diagram. It is also found that increase in lane-changing rate as well as unequal attachment, detachment rates weaken the bottleneck effect. Our theoretical arguments are in good agreement with extensively performed Monte Carlo simulations.
International Journal of Modern Physics C, May 6, 2022
In intracellular transport, the motor proteins may jump between the filaments due to structural d... more In intracellular transport, the motor proteins may jump between the filaments due to structural deformity where the motion is hindered by presence of bound proteins. This motivates us to study a system of two parallel disordered exclusion processes with Langmuir kinetics under symmetric and asymmetric coupling conditions. Theoretically, continuum mean-field approximation is employed to obtain steady-state equations which are further solved numerically. The steady-state system dynamics are examined for different values of coupling constant [Formula: see text], which indicates ratio of lane-changing rates. The effect of binding constant [Formula: see text] and defect parameters is also explored. Under the symmetric coupling case, the topological structure of phase diagram turns out to be similar to that in single-lane model, which differs significantly under fully asymmetric coupling. The asymmetric coupling increases magnitude of difference between densities in two lanes. At a very large attachment/detachment rate, the LK dynamics dominate the effect of asymmetric coupling in the lanes. The defect parameters are found to reduce particle flux in the steady state. The numerical results are validated through extensive Monte Carlo simulation.
Being inspired by the biological process of gene transcription, we investigate the phenomenology ... more Being inspired by the biological process of gene transcription, we investigate the phenomenology of transport on two-channel TASEP in the presence of dynamical defects under symmetric coupling conditions. The continuum mean-field equations are derived and then solved numerically to obtain steady-state phase diagrams. The role of various parameters namely defect (un-)binding constants, lane-changing rates has been thoroughly examined. The defect (un-)binding rates are found to affect the phase boundaries in the phase plane. The effect of system size on the steady-state dynamics of the system has also been analyzed. The theoretical results are validated by performing extensive Monte Carlo simulations.
In intracellular transport, the motor proteins may jump between the filaments due to structural d... more In intracellular transport, the motor proteins may jump between the filaments due to structural deformity where the motion is hindered by presence of bound proteins. This motivates us to study a system of two parallel disordered exclusion processes with Langmuir kinetics under symmetric and asymmetric coupling conditions. Theoretically, continuum mean-field approximation is employed to obtain steady-state equations which are further solved numerically. The steady-state system dynamics are examined for different values of coupling constant [Formula: see text], which indicates ratio of lane-changing rates. The effect of binding constant [Formula: see text] and defect parameters is also explored. Under the symmetric coupling case, the topological structure of phase diagram turns out to be similar to that in single-lane model, which differs significantly under fully asymmetric coupling. The asymmetric coupling increases magnitude of difference between densities in two lanes. At a very l...
We study a single-channel dynamically disordered totally asymmetric simple exclusion process with... more We study a single-channel dynamically disordered totally asymmetric simple exclusion process with bulk particle attachment and detachment. The continuum mean-field equations are derived and solved numerically to obtain steady-state phase diagrams and density profiles. The effects of various parameters, namely particle attachment rate, defect binding and unbinding rates, and binding constant, have been investigated. An increase in the attachment rate of particles reduces the number of steady-state phases, whereas a variation in defect binding and unbinding rates shifts the phase boundaries. One of the important consequences of introducing particle nonconserving dynamics is the appearance of shock in the steady state. The shock dynamics have been thoroughly examined and the defect strength is found to have a significant effect on the shock position. The mean-field solutions are validated using extensive Monte Carlo simulations.
In order to understand the complexity of real world processes, one need to model these processes ... more In order to understand the complexity of real world processes, one need to model these processes mathematically. In this thesis, we review a epidemic compartmental models and their classifications. The aim of our approach is to develop an intuitive understanding of epidemic models and adapt a new technique Monte Carlo simulations for the validation of various epidemic model. A new model SEIQR has been introduced and results are validated using Runge Kutta method and Monte Carlo simulations
The steady-state dynamics of a two-channel TASEP coupled with Langmuir kinetics in the presence o... more The steady-state dynamics of a two-channel TASEP coupled with Langmuir kinetics in the presence of a localized bottleneck are investigated under a fully asymmetric lane-changing rule. A hybrid mean-field approach is adopted to generate the density profiles as well as phase diagrams. The effect of lane-changing rate and strength of bottleneck on the stationary dynamics of the system has also been investigated. It is observed that an increase in lane-changing rate weakens the effect of bottleneck. As a part of studying the shock dynamics, we have identified and analyzed turning effect in the movement of shock with respect to lane-changing rate. Our theoretical arguments are in good agreement with extensively performed Monte-Carlo simulations.
We analyze the origin and characteristics of the bottleneck-induced shock in a two-channel totall... more We analyze the origin and characteristics of the bottleneck-induced shock in a two-channel totally asymmetric simple exclusion process with Langmuir kinetics under symmetric coupling conditions. The variation in height of the spike, which has been found to be a precursor to the bottleneck-induced shock, is analyzed with respect to lane-changing rate and bottleneck rate q. The critical value of q(q c), below which the effect of bottleneck turns from local to global, has been identified. A non-monotonic variation of q c with respect to is observed. The bottleneck-induced shock exhibits turning effect with respect to an increase in .
This letter studies a fully asymmetrically coupled three-lane totally asymmetric simple exclusion... more This letter studies a fully asymmetrically coupled three-lane totally asymmetric simple exclusion process with Langmuir kinetics under open boundary conditions. Phase diagrams and density profiles for different kinetic rates are obtained using a mean-field analysis along with a singular perturbation technique and are found to be in good agreement with Monte Carlo simulation results. Some mixed phases are observed in the middle lane resulting into bulk-induced phase transitions. We have found that a number of steady-state phases firstly increases then decreases with respect to an increase in lane changing rate. Critical values of the lane changing rate are identified at which the appearance or disappearance of certain phases is observed. We have identified the jumping effect in the position of shock in the middle lane with respect to an increase in the lane changing rate.
We analyze an open system comprised of two parallel totally asymmetric simple exclusion processes... more We analyze an open system comprised of two parallel totally asymmetric simple exclusion processes with particle attachment and detachment in the bulk under partially asymmetric coupling conditions. The phase diagrams are obtained using boundary layer analysis of continuum mean-field equations and characterized for different values of lane-changing rates. The structure of the phase diagram remains qualitatively the same as the one in fully asymmetric coupling conditions up to a certain critical order of lane-changing rates, after which significant changes are found in the phase diagram. The effect of system size on the steady-state dynamics has also been examined. To validate theoretical findings, extensive Monte Carlo simulations are carried out.
We develop a heterogeneous continuum model based upon a car-following model for a nonlane-based s... more We develop a heterogeneous continuum model based upon a car-following model for a nonlane-based system taking lateral separation into account. The criterion for linear stability analysis and traveling wave solution of the homogeneous case is studied. The consideration of the lateral separation not only stabilizes the flow but also shrinks the critical region. For heterogeneous case, the fundamental diagram is examined for two different equilibrium speed-density functions and the effect of lane width is investigated for different compositions of heterogeneous traffic. The theoretical findings agree well with the results of numerical simulation which justifies the applicability of the model to a nonlane-based system.
The phase transitions are investigated in a continuum speed-gradient model with a static bottlene... more The phase transitions are investigated in a continuum speed-gradient model with a static bottleneck under open boundary conditions. The bottleneck situation has been studied using two different approaches-explicit and implicit. The phase diagrams showing different traffic states are presented. The effect of strength of bottleneck has been analyzed, and it is found that the strength parameter has no qualitative effect in the explicit case while has considerable effect in the implicit case. Furthermore, the results of both the approaches are compared, and the consistency between them is discussed.
We study an open system composed of two parallel totally asymmetric simple exclusion processes wi... more We study an open system composed of two parallel totally asymmetric simple exclusion processes with particle attachment and detachment in the bulk. The particles are allowed to change their lane from lane-A to lane-B, but not conversely. We investigate the steady-state behavior of the system using boundary layer analysis on continuum mean-field equations to provide the phase diagram. The structure of the phase diagram is quite complex and provides a complete insight about the steady-state dynamics. We examine two kinds of transitions in the phase plane: bulk transitions and surface transitions, qualitatively as well as quantitatively. The dynamics of shock formation, localization and their dependence on the system parameters and boundary rates have been investigated. We also justify the non-existence of downward shock in both the lanes using fixed point theory. Further, we examine the effect of increasing lane-changing rate on the steady-state dynamics and observe that the number of steady-state phases reduces with increase in lane-changing rate. Our theoretical results are supported with extensive Monte-Carlo simulation results.
Physica A: Statistical Mechanics and its Applications, 2013
ABSTRACT We study the dynamics of a coupled two-channel ASEP in which intra-channel transition ra... more ABSTRACT We study the dynamics of a coupled two-channel ASEP in which intra-channel transition rates are dependent on the configuration of neighboring channel. The binding constant k, which signifies the ratio of inter-channel transition rates, is introduced and the symmetric and asymmetric coupling conditions are analyzed for different values of k. The vertical cluster mean-filed theory is used to study the system behavior exactly in strong coupling conditions and approximately in intermediate coupling conditions. Additionally, the consequences of particular dynamics such as totally asymmetric simple exclusion process (TASEP), partially asymmetric simple exclusion process (PASEP) and symmetric simple exclusion process (SSEP) in either one or both channels are investigated. It is found that the transition rates have a significant influence on both the qualitative and quantitative nature of the phase diagrams. The mathematical computation shows how the number of phases varies from 3 via 6 to 7 under different environments. Interestingly, in fully asymmetric coupling case, the results are found to be independent of the magnitude of non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte-Carlo simulation results.
Journal of Physics A: Mathematical and General, 2004
Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains ... more Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase diagram are calculated exactly by mapping the system into an effective one-channel totally asymmetric exclusion model. For intermediate couplings, a simple approximate theory, that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters, is developed. It is found that, similarly to the case of one-channel totally asymmetric simple exclusion processes, there are three stationary state phases, although the phase boundaries and stationary properties strongly depend on inter-channel coupling. Extensive computer Monte Carlo simulations fully support the theoretical predictions.
This work is devoted to the development of a novel theoretical approach, named hybrid approach, t... more This work is devoted to the development of a novel theoretical approach, named hybrid approach, to handle a localized bottleneck in a symmetrically coupled two-channel totally asymmetric simple exclusion process with Langmuir kinetics. The hybrid approach is combined with singular perturbation technique to get steady-state phase diagrams and density profiles. We have thoroughly examined the role played by the strength of bottleneck, binding constant and lane-changing rate in the system dynamics. The appearances of bottleneck-induced shock, a bottleneck phase and Meissner phase are explained. Further, the critical values of bottleneck rate are identified, which signify the changes in the topology of phase diagram. It is also found that increase in lane-changing rate as well as unequal attachment, detachment rates weaken the bottleneck effect. Our theoretical arguments are in good agreement with extensively performed Monte Carlo simulations.
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