ELFT HÍRADÓ

[Kormányos Andor <andor.kormanyos AT ttk.elte.hu>]

ELTE TTK Fizikai Intézet / ELTE Institute of Physics


ORTVAY KOLLOKVIUM / ORTVAY COLLOQUIUM
(https://physics.elte.hu/ortvayseminar)


Thursday, 29th February  2024, 15:00h.

Pócza Jenő Classroom,  Physics Building 1.71

Pázmány Péter sétány 1/A, 1117 Budapest.


Márton Pósfai

Central European University

Modelling physical networks

Physical networks are spatially embedded complex networks composed of nodes 
and links that are physical objects which cannot overlap. Examples of 
physical networks range from neural networks and networks of bio-molecules to 
computer chips and disordered meta-materials. It is hypothesized that the 
unique features of physical networks, such as the non-trivial shape of nodes 
and links and volume exclusion affect their network structure and function. 
However, the traditional tool set of network science cannot capture these 
properties, calling for a suitable generalization of network theory. Here, I 
present recent efforts to understand the impact of physicality through two 
classes of analytically tractable models: (i) linear physical networks (LPN), 
which construct networks from straight cylinders [1,2], and (ii) a 
network-of-network model (NoN) that construct physical networks from random 
walk trajectories [3]. Using a variety of analytical tools, I characterize, 
for example, the onset of physical effects and the emergence of a jamming 
transition in LPNs, showing that physicality impacts the network structure 
even when the total volume of the links is negligible. I also show that in 
the NoN model physicality induces heterogeneity in both the physical and the 
network properties and that the two become strongly correlated. I study the 
dynamics on physical networks by characterizing the network’s Laplacian 
spectrum, and we show that the Laplacian of the combinatorial network $Q_G$ 
is not sufficient to describe the dynamics on physical networks and that the 
physical layout must be taken into account as $V^{−1/2} Q_G V^{−1/2}$ where 
$V$ is a diagonal matrix containing the volume of the nodes. Overall, our 
model demonstrates that in the presence of volume exclusion, traditional 
methods of network science are not sufficient to characterize the structure 
of physical networks and the dynamics on them.

[1] Pósfai, Márton, et al. "Impact of physicality on network structure." 
Nature Physics (2023): 1-8.
[2] Bonamassa, I., et al. "Bundling by volume exclusion in non-equilibrium 
spaghetti." arXiv preprint arXiv:2401.02579 (2024).
[3] Pete, Gábor, et al. "A network-of-networks model for physical networks." 
arXiv preprint arXiv:2306.01583 (2023).



Andor Kormányos
coordinator