Related papers: Complex Structures Defined on Dynamically Triangul…
When a thin sheet is crushed into a small three-dimensional volume, it invariably forms a structure with a low volume fraction but high resistance to further compression. Being a far-from-equilibrium process, forced crumpling is not…
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…
The ideas of dynamical complexity induced intermittent turbulence by sporadic localized interactions of coherent structures are discussed. In particular, we address the phenomenon of magnetic reconfiguration due to coarse-grained…
We construct field theories in $2+1$ dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to "subsystem scale invariances", borrowing the language often…
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
Two typical morphology of two-dimensional aggregates are considered: compact crystalline clusters and string-like non-compact conformations. Simulated trajectories of both types of aggregates are analysed with fine spatial resolution. While…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
A surface $\Sigma$ in a 4-manifold $M$ is called flexible if any mapping class of the surface arises as the restriction of a diffeomorphism $(M,\Sigma) \to (M,\Sigma)$. We construct flexible surfaces in $\mathbb{C}P^2$ and $S^2 \times S^2$…
3+1 dimensional Causal Dynamical Triangulations (CDT) describe a quantum theory of fluctuating geometries without the introduction of a background geometry. If the topology of space is constrained to be that of a three-dimensional torus we…
Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…