Complex transport systems: modeling, analysis & simulation

Abstract

From microscopic to the macroscopic level, complexity has emerged as a unifying aspect of our environment. In the domain of complex systems, ranging from physical to biological processes, it is critical to improving our understanding and skills. Moving in this direction, one must give due attention to transportation, one of the key factors on which the complex systems heavily rely. Vehicular flow is one of the most evident processes which arises in our commute to work, stores, hospitals, schools, and universities, etc. Some not so visible yet important transportation processes happen inside our body at the intracellular level too. These include the movement of motor proteins on micro-tubules that transport the cargo within the cell. In the aforementioned phenomena, the movement of entities, namely, vehicles and motor proteins are powered by fuel and ATP, respectively, thereby categorizing them into a special class of non-equilibrium processes, known as the driven di↵usive systems. The characteristic feature of such systems is the existence of a non-zero current even when other properties are unchanging with time. Over the years, an exclusion model, particularly, Totally Asymmetric Simple Exclusion Process (TASEP) has emerged as one of the paradigms to study the driven di↵usive systems. This model is characterized by the unidirectional flow of particles representing the vehicles, motor proteins, etc., on a discrete lattice portraying their respective pathways with a constant rate. Relying on this framework, we contribute to a comprehensive understanding of the collective behavior of particles in variations of the single and multi-lane models. Motivated by the movement of motor proteins, we analyze the impact of an inhomogeneity in the system in the form of a stochastic blockage on a non-conserving TASEP model. We implore the non-trivial e↵ects of the defect dynamics, as well as the non-conserving kinetics in terms of density profiles, phase diagrams, etc. Moving forward, we explore the behavior of biological and physical systems where the total entities remains conserved. In this direction, we study ring-like lattice where the entities may move at the non-constant rate which can be a↵ected by two factors: the position on the lattice, as well as the neighboring entities. In the recent years, a modification of TASEP has emerged where both the ends of the discrete lattice is connected to a finite reservoir, thus reflecting the limited availability of resources in a real system. Instigated by these considerations, we work on a TASEP model where the entry and exit of particles from the inhomogeneous lattice are regulated by the occupancy of the reservoir. Moreover, this inhomogeneity in the lattice is introduced as an impact of the stochastic blockage. We investigate the collective e↵ect of these dynamics on the system properties. Furthermore, we analyze a TASEP model where the entities can attach to or detach from the entirety of the lattice under the constraint of available resources and the crowding of reservoir. Stepping forward, we also study a bidirectional TASEP model, where the particles move in opposite directions classifying them into two distinct species in a conserved environment where the reservoir modulates the entry-exit of entities. Finally, we examine a model having two lattices with strategically placed distinct reservoirs together forming a ring-like structure which opens up the domain of studying the interplay of these reservoirs. In brief, we utilized mathematical modeling to comprehend the previously unknown diculties that may arise in transport processes, which are also seen through simulations, making it critical to understand the collective dynamics of moving entities.