SCL Online Seminar by Iva Bačić
You are cordially invited to the SCL online seminar of the Center for the Study of Complex Systems, which will be held on Thursday, 14 October 2021 at 14:00 on Zoom. The talk entitled
Onset of physicality in a random network growth model
will be given by Dr. Iva Bačić (Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade and Department of Network and Data Science, Central European University, Budapest, Hungary). Abstract of the talk:
Networks are abstract representations of complex systems in which any physicality of their constituents is disregarded. In a number of real networks, however, nodes and links are physical objects embedded in space that cannot intersect with each other. If the size of nodes and links is small compared to the available space, physicality likely has little effect on the network; however, if the volume of the network is comparable to volume of the available space, physicality will affect the structure, the evolution, and the function of the networks. Examples of such systems include neurons in the brain, the vascular system, mycelial networks, three-dimensional integrated circuits, and subways or other similar infrastructures. This observation prompts the question: when does physicality matter? In this talk we will propose a tractable random growth model of physical networks that provides insight into this question. The model describes linear physical networks, where links are non-overlapping straight cylinders. Network growth is achieved by sequentially adding nodes to randomly chosen points within the unit cube, and connecting to a randomly chosen accessible node from the existing network, with non-crossing conditions taken into account. We will identify two critical transitions: (i) the onset of the weakly physical regime, where the average link length becomes shorter, although the volume of the network is still negligible compared to the available volume, and (ii) the onset of the strongly physical regime, where the network occupies a finite fraction of the cube's volume. We will demonstrate the validity of the analytical arguments by extensive numerical simulations.
