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Patterns on broken surfaces are well-known from everyday experience, but surprisingly, how and why they form are very much open questions. Well-defined facets are commonly observed1-4 along fracture surfaces which are created by slow…
The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms through which extinction of infection propagation comes about. We here report on a…
Standard evolutionary theories of aging and mortality, implicitly based on assumptions of spatial averaging, hold that natural selection cannot favor shorter lifespan without direct compensating benefit to individual reproductive success.…
We study a dynamical system motivated by our earlier work on the statistical physics of social balance on graphs that can be viewed as a generalization of annihilating walks along two directions: first, the interaction topology is a…
The frequent outbreak of severe foodborne diseases warns of a potential threat that the global trade networks could spread fatal pathogens. The global trade network is a typical overlay network, which compounds multiple standalone trade…
Wildfires pose a significant threat to the safe and reliable operations of the electric grid. To mitigate wildfire risk, system operators resort to public safety power shutoffs, or PSPS, that shed load for a subset of customers. As wildfire…
Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular ($A/L \times L)$ landscape and, once reached, they…
The survival probability of immobile targets, annihilated by a population of random walkers on inhomogeneous discrete structures, such as disordered solids, glasses, fractals, polymer networks and gels, is analytically investigated. It is…
The spreading of an epidemic is determined by the connectiviy patterns which underlie the population. While it has been noted that a virus spreads more easily on a network in which global distances are small, it remains a great challenge to…
The firefighter problem is a monotone dynamic process in graphs that can be viewed as modeling the use of a limited supply of vaccinations to stop the spread of an epidemic. In more detail, a fire spreads through a graph, from burning…
We consider branching particle processes on discrete structures like the hypercube in a random fitness landscape (i.e., random branching/killing rates). The main question is about the location where the main part of the population sits at a…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We…
Identifying the regions responsible for plastic flow in amorphous solids remains an open problem, since structural disorder seems to prevent the direct application of concepts such as dislocations, topological defects that successfully…
In tropical regions, fires propagate readily in grasslands but typically consume only edges of forest patches. Thus forest patches grow due to tree propagation and shrink by fires in surrounding grasslands. The interplay between these…
This paper investigates the dynamics of stocks in the S&P500 index for the last 30 years. Using a stochastic geometry technique, we investigate the evolution of the market space and define a new measure for that purpose, which is a robust…
Street networks allow people and goods to move through cities, but they are vulnerable to disasters like floods, earthquakes, and terrorist attacks. Well-planned network design can make a city more resilient and robust to such disruptions,…
Topological surgery occurs in natural phenomena where two points are selected and attracting or repelling forces are applied. The two points are connected via an invisible `thread'. In order to model topologically such phenomena we…