My scientific contribution is summarised in the application of theoretical and computational techniques to investigate spatial systems in nature. Searching for the stable analytical solutions of differential equations in systems with scalar fields, I proved that topological defects could be found by solving the first order differential equations in the Bogolmon´yi limit. Applying domain wall, cosmic string and magnetic monopole networks to structure formation of the universe, I showed that topological defects play a role in the spatial-time variation of the fundamental constants. Performing very accurate numerics, I show that the domain walls may have contributed to the recent accelerated expansion of the universe, dominated by dark energy. The same stochastic and deterministic simulations when applied to population dynamics, has proved to be a powerful tool to study the spatial interactions among species. Comparing the evolution of two and three-dimensional networks evolving in cosmology and population dynamics, I used evolutionary game theory to describe spiral waves and defect networks in biology. Using the same framework and numerical analysis, I performed spatial simulations to investigate cry wolf plants and disease mediated coexistence among weak and strong competitors. I am also currently engaged in applying the same spatial computational techniques to study cancer tumour growth.
Citations on Scholar Google
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Junctions and spiral patterns in Rock-Paper-Scissors type modelsWe investigate the population dynamics in generalized Rock-Paper-Scissors models with an arbitrary number of species N. We show, for the first time, that spiral patterns with N-arms may develop both for odd and even N, in particular in models where a bidirectional predation interaction of equal strength between all species is modified to include one N-cyclic predator-prey rule. We explicitly demonstrate the connection between interface junctions and spiral patterns in these models and compute the corresponding scaling laws. This work significantly extends the results of previous studies of population dynamics and could have profound implications for the understanding of biological complexity in systems with a large number of species.
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Von-Neumann's and related scaling laws in Rock-Paper-Scissors type modelsWe introduce a family of Rock-Paper-Scissors type models with ZN symmetry (N is the number of species) and we show that it has a very rich structure with many completely different phases. We study realizations which lead to the formation of domains, where individuals of one or more species coexist, separated by interfaces whose (average) dynamics is curvature driven. This type of behavior, which might be relevant for the development of biological complexity, leads to an interface network evolution and pattern formation similar to the ones of several other nonlinear systems in condensed matter and cosmology.
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Defect Junctions and Domain Wall DynamicsWe study a number of domain wall forming models where various types of defect junctions can exist. We focus on the issue of whether or not cosmological frustrated domain wall networks can exist at all, but our results are also relevant for the dynamics of cosmic (super)strings, where junctions are expected to be ubiquitous. We carry out a number of numerical simulations of the evolution of these networks, analyse and contrast their results, and discuss their implications for our no-frustration conjecture.
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Dynamics of domain wall networks with junctionsWe use a combination of analytic tools and an extensive set of the largest and most accurate three-dimensional field theory numerical simulations to study the dynamics of domain wall networks with junctions. We build upon our previous work and consider a class of models which, in the limit of large number N of coupled scalar fields, approaches the so-called `ideal' model. We find compelling evidence for a gradual approach to scaling, strongly supporting our no-frustration conjecture. We also discuss the various possible types of junctions and their roles in the dynamics of the network.
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We investigate the presence of defects in systems described by real scalar field in (D,1) spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D=1.
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