Related papers: Field Patterns: A New Mathematical Object
In this work we develop a theory of interaction of randomly patterned surfaces as a generic prototype model of protein-protein interactions. The theory predicts that pairs of randomly superimposed identical (homodimeric) random patterns…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
A phase separation in a spatially heterogeneous environment is closely related to intracellular science and material science. For the phase separation, initial heterogeneous perturbations play an important role in pattern formations. In…
In this paper we study the time evolution of a class of two-level systems driven by periodic fields in terms of new convergent perturbative expansions for the associated propagator U(t). The main virtue of these expansions is that they do…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
The influence of a periodic spatial forcing on the pattern formation in a generalized Cahn-Hilliard model is studied in order to describe the pattern formation in Langmuir-Blodgett transfer onto prestructured substrates. The occurring…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…
Dynamical coherent structure (pattern) formation in the Klein-Gordon lattice excited by periodic external field near the optical resonance is studied. It is shown that besides spatial patterns discovered recently (V.M.Burlakov,…
When can complex ecological interactions drive an entire ecosystem into a persistent non-equilibrium state, where species abundances keep fluctuating without going to extinction? We show that high-diversity spatially-extended systems, in…
We investigate the conformal and superconformal properties of a non-relativistic spinning particle propagating in a curved background coupled to a magnetic field and with a scalar potential. We derive the conditions on the couplings for a…
Developmental trajectories are known to be canalized, or robust to both environmental and genetic perturbations. However, even when these trajectories are decanalized by an environmental perturbation outside of the range of conditions to…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
We imitate the spectrum character of one-dimensional disorder system with our new rain model. It has been shown that the transmission spectrum can be approximately characterized by the model, which include some coupled lorentzian…
We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…
We investigate active particles that exhibit long-range interactions only restricted by a field of view, which is characterized by an angle $\beta$. We show that constraining attractive interactions to a field of view leads to the emergence…
We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…
The emergence of collective motion, also known as flocking or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that is manifested at multiple spatial…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
The response of dynamical systems to varying conditions and disturbances is a fundamental aspect of their analysis. In spatially extended systems, particularly in pattern-forming systems, there are many possible responses, including…