Related papers: Dynamics in Systems with Modulated Symmetries
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
Modulated symmetries are internal symmetries which do not commute with spatial symmetries; dipolar symmetries are a prime example. We give a general recipe for constructing topological phases protected by modulated symmetries via a defect…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
We study a driven-dissipative model of spins one-half (qubits) on a lattice with nearest-neighbor interactions. Focusing on the role of spatially extended spin-spin correlations in determining the phases of the system, we characterize the…
Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
We study spontaneous symmetry breaking in a one-dimensional driven two-species stochastic cellular automaton with parallel sublattice update and open boundaries. The dynamics are symmetric with respect to interchange of particles. Starting…
In complex systems, groups of interacting objects may form prevalent and persistent spatiotemporal patterns, which we refer to as motifs. These motifs can exhibit features that reveal how individual objects interact with one another.…
The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…
Soliton dynamics in a large variety of longitudinally modulated lattices are studied in terms of phase space analysis for an effective particle approach and direct numerical simulations. Complex soliton dynamics are shown to depend strongly…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
From the perfect radial symmetries of radiolarian mineral skeletons to the broken symmetry of homochirality, the logic of Nature's regularities has fascinated scientists for centuries. Some of Nature's symmetries are clearly visible in…
This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…
We show that spatial variation and correlation of superconductivity fluctuations in a two-band model are scaled by two characteristic lengths. This results in substantially more complicated picture compared to one-band systems. In…
We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…