| Research

SELF-ORGANIZED SYSTEMS AND MODELS

Complex, unpredictable behavior emerges out of simple, local interactions in self-organized systems. We use mathematical tools in characterizing the complex signatures of natural hazards such as landslides and earthquakes, and laboratory and computational models.

Space and Time Characterization of Natural Hazards

Earthquakes in the Philippines,
1973-2016

Earthquakes are self-organized systems characterized by very long periods of energy accumulation driven by the slow rates of crustal motion, and the sudden energy release during a series of correlated earthquake sequences. Additionally, many other natural hazards, such as rain/drought events, landslides, snow avalanches, etc., can be understood from the framework of self-organized criticality, hinting at similar underlying mechanisms governing their complex signatures. We investigate the patterns that can be recovered from the space and time occurrences of these events to understand the underlying processes involved in their generation.

FEATURED RESEARCH

Visualizing the dual spatio-temporal regimes of earthquakes using simple inter-event statistics

R. C. Batac and H. Kantz, Observing spatio-temporal clustering and separation using interevent distributions of regional earthquakes, Nonlinear Processes in Geophysics 21, 735-744, https://doi.org/10.5194/npg-21-735-2014 (2014).

Earthquakes are rarely solitary events. When the ground shakes, it often sets off a chain reaction of smaller tremors, creating a complex web of seismic activity that stretches across time and space. In a 2014 study published in Nonlinear Processes in Geophysics, researchers Rene C. Batac and Holger Kantz delved into this complexity by analyzing interevent separations in time and distance between consecutive earthquakes to uncover the hidden patterns that govern how our planet releases its pent-up energy.

A sandpile model of earthquake occurrences

R.C. Batac, Clustering regimes in a sandpile with targeted triggering, EPL (Europhysics Letters) 135, 19003, https://doi.org/10.1209/0295-5075/135/19003 (2021).

R.C. Batac, A.A. Paguirigan Jr., A.B. Tarun, and A.G. Longjas, Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes, Nonlinear Processes in Geophysics 24(2), 179-187, https://doi.org/10.5194/npg-24-179-2017 (2017).

The theory of self-organized criticality (SOC), in which a system drives itself towards a critical behavior without a need for fine-tuning of external parameters, is one of the mechanisms to explain the occurrence of earthquakes. Earthquakes are generated when the crust stores energy driven via the very slow mechanism of tectonic motion, and release the energy in rapid succession through a sequence of correlated events. Despite the differences in the rates and mechanisms of crustal motion, all earthquake occurrences follow the Gutenberg-Richter law, a power-law distribution of energy released. This nearly universal energy distribution is deemed to be a consequence of SOC.

Sandpiles and Other Discrete Models of Complexity

Avalanche propagation in a
sandpile grid wih sinks

The sandpile model is a discrete cellular automata model that illustrates how small, local disturbances can propagate to produce fat-tailed avalanche size distribution. The sandpile model is self-organized, and has been used to replicate the statistical distributions of natural hazard occurrences. The group investigates the spatial and temporal properties of the sandpile model and its variants to make them more apt for simulating the occurrences of bursty events in many physical systems. We use the sandpile model as a simple representative system for probing the fundamental characteristics of self-organized systems.

FEATURED RESEARCH

A sandpile model of earthquake occurrences

R.C. Batac, Clustering regimes in a sandpile with targeted triggering, EPL (Europhysics Letters) 135, 19003, https://doi.org/10.1209/0295-5075/135/19003 (2021).

R.C. Batac, A.A. Paguirigan Jr., A.B. Tarun, and A.G. Longjas, Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes, Nonlinear Processes in Geophysics 24(2), 179-187, https://doi.org/10.5194/npg-24-179-2017 (2017).

The theory of self-organized criticality (SOC), in which a system drives itself towards a critical behavior without a need for fine-tuning of external parameters, is one of the mechanisms to explain the occurrence of earthquakes. Earthquakes are generated when the crust stores energy driven via the very slow mechanism of tectonic motion, and release the energy in rapid succession through a sequence of correlated events. Despite the differences in the rates and mechanisms of crustal motion, all earthquake occurrences follow the Gutenberg-Richter law, a power-law distribution of energy released. This nearly universal energy distribution is deemed to be a consequence of SOC.

Can self-organized criticality be controlled?
Insights from a sandpile with targeted intervention

P.B. Sy and R.C. Batac, The role of intervention mechanisms on a self-organized system: Dynamics of a sandpile with site reinforcement, Journal of Physics: Complexity 5, 15012, https://doi.org/10.1088/2632-072X/ad28ff (2024).

In the world of complex systems, from power grids to neural networks, disaster often arrives in the form of an avalanches, wherein locally interconnected portions of the system experience cascaded failure that propagates, even affecting the entire system. For years, scientists have used models that are similar to the sandpile, an externally-driven grid that produces local redistribution rules to form avalanches. These models help scientists study how these systems naturally reach a tipping point where a tiny change triggers a massive collapse.

A model of a growing network via Hebbian learning, simulating the brain connectome

Brain modeling

The brain is deemed to be operating at a critical state, optimizing its information transmission, processing, and computation capabilities. In coming up with a better description for the critical brain, insights from experiments, theoretical analyses, and computational modeling have to be accounted for. With the availability of detailed experimental data probing the brain structure and dynamics, models of critical behavior can be used to complement and explain these observations.

FEATURED RESEARCH

Capturing brain structure using the sandpile model of criticality

M.T. Cirunay, R.C. Batac, and G. Ódor, Learning and criticality in a self-organizing model of connectome growth, Scientific Reports 15, 31890, https://doi.org/10.1038/s41598-025-16377-8 (2025).

For decades, neuroscientists have observed that the brain operates at a critical state, where information states and propagation are optimized in the form of neural avalanches. A great deal of this behavior is made possible because of the connectivity of the individual neurons in the brain, in a structure called the connectome. Recently, there have been great strides in deepening our understanding of the individual neuronal connections that form various connectomes of different species.