Interactions of Self-organizing Systems in Nature

Nature essentially consists of complex systems. The paper presents a conceptual framework to understand how complex systems interact with each other in nature. All natural systems are thermodynamically open and physically adaptive. The process of adaptation and continual self-organization cause these systems to interact continuously with the environment and compete against such similar systems for limited resources

Statistical Analysis of Bus Networks in India

Through the past decade the field of network science has established itself as a common ground for the cross-fertilization of exciting inter-disciplinary studies which has motivated researchers to model almost every physical system as an interacting network consisting of nodes and links. Although public transport networks such as airline and railway networks have been extensively studied, the status of bus networks still remains in obscurity. In developing countries like India, where bus networks play an important role in day-to-day commutation, it is of significant interest to analyze its topological structure and answer some of the basic questions on its evolution, growth, robustness and resiliency. In this paper, we model the bus networks of major Indian cities as graphs in \textit{L}-space, and evaluate their various statistical properties using concepts from network science. Our analysis reveals a wide spectrum of network topology with the common underlying feature of small-world property. We observe that the networks although, robust and resilient to random attacks are particularly degree-sensitive. Unlike real-world networks, like Internet, WWW and airline, which are virtual, bus networks are physically constrained. The presence of various geographical and economic constraints allow these networks to evolve over time. Our findings therefore, throw light on the evolution of such geographically and socio-economically constrained networks which will help us in designing more efficient networks in the future.Comment: Submitted to PLOS ON

An Overview of Emergent Order in Far-from-equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh-B\'enard Convection

Soft-matter systems when driven out-of-equilibrium often give rise to structures that usually lie in-between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayleigh-B\'enard convection system which when driven out-of-equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-organize are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to find connections between these systems, and systems in general which give rise to emergent order when driven out-of-equilibrium.Comment: Submitted to Entrop