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Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g. boundary layer flows. The dynamical…
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…
The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes…
We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…
In this paper we consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be…
This paper illustrates a further application of topological data analysis to the study of self-organising models for chemical and biological systems. In particular, we investigate whether topological summaries can capture the parameter…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Presented in this paper is a derivation of a 2D catalytic reaction-based model to solve combinatorial optimization problems (COPs). The simulated catalytic reactions, a computational metaphor, occurs in an artificial chemical reactor that…
The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically-arrested on experimental timescales so the…
The concept of (auto)catalytic systems has become a cornerstone in understanding evolutionary processes in various fields. The common ground is the observation that for the production of new species/goods/ideas/elements etc. the…
Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1/2$ defects in…
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…
To capture the global structure of a dynamical system we reformulate dynamics in terms of appropriately constructed topologies, which we call flow topologies; we call this process topologization. This yields a description of a semi-flow in…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of…