相关论文: Connectivity of Turing structures

Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…

The configurational and melting properties of large two-dimensional clusters of charged classical particles interacting with each other via the Coulomb potential are investigated through the Monte Carlo simulation technique. The particles…

Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…

Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…

We examine the various linkings in space-time of ``ball-like'' and ``ring-like'' topological solitons in certain nonlinear sigma models in 2+1 and 3+1 dimensions. By going to theories where soliton overlaps are forbidden, these linkings…

Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot…

In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…

In social networks, the balance theory has been studied by considering either the triple interactions between the links (structural balance) or the triple interaction of nodes and links (coevolutionary balance). In the structural balance…

We examine phase transitions between the easy, hard, and the unsolvable phases when attempting to identify structure in large complex networks (community detection) in the presence of disorder induced by network noise (spurious links that…

The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…

We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…

The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…

The combined effect of disorder and symmetry-breaking fields on the two-dimensional XY model is examined. The study includes disorder in the interaction among spins in the form of random phase shifts as well as disorder in the local…

Strongly interacting binary mixtures of superparamagnetic colloidal particles confined to a two-dimensional water-air interface are examined by theory, computer simulation and experiment. The mixture exhibits a partial clustering in…

Tunneling in a quantum coherent structure is not restricted to only nearest neighbours. Hopping between distant sites is possible via the virtual occupation of otherwise avoided intermediate states. Here we report the observation of long…

Periodic boundary conditions are a common theoretical and computational tool used to emulate effectively infinite domains. However, two-dimensional periodic domains are topologically distinct from the infinite plane, eliciting the question:…

We examine the geometrical and topological properties of surfaces surrounding clusters in the 3--$d$ Ising model. For geometrical clusters at the percolation temperature and Fortuin--Kasteleyn clusters at $T_c$, the number of surfaces of…

Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from regular patterns of dryland vegetation to complex structures of bacterial colonies. Many of these patterns can be explained in the…

Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…

We demonstrate the possibility of using time-space crystalline structures to simulate eight-dimensional systems based on only two physical dimensions. A suitable choice of system parameters allows us to obtain a gapped energy spectrum,…