Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSynchronization Patterns in Geometrically Frustrated Turing Rings
269
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that leads to a canard explosion in a single Brusselator. In this highly nonlinear regime it is numerically found that rings of coupled Brusselators do not follow the predictions from Turning analysis. We find that the behavior can be explained using a piecewise linear approximation.
rate research
Read More
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or asymmetries in small networks. We also analyze consistency, defined as the persistence of coexistent synchronization patterns regardless of the initial conditions. Our results show that complex weighted networks display richer consistency than regular networks, suggesting why certain functional network topologies are often constructed when experimental data are analyzed.
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities for a spatially heterogeneous reaction-diffusion system, and derive conditions for instability which are loc
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop a modelling framework for bi-layer reaction-diffusion systems and relate it to a range of existing models. We derive conditions for diffusion-driven instability of a spatially homogeneous equilibrium analogous to the classical conditions for a Turing instability in the simplest nontrivial setting where one domain has a standard reaction-diffusion system, and the other permits only diffusion. Due to the transverse coupling between these two regions, standard techniques for computing eigenfunctions of the Laplacian cannot be applied, and so we propose an alternative method to compute the dispersion relation directly. We compare instability conditions with full numerical simulations to demonstrate impacts of the geometry and coupling parameters on patterning, and explore various experimentally-relevant asymptotic regimes. In the regime where the first domain is suitably thin, we recover a simple modulation of the standard Turing conditions, and find that often the broad impact of the diffusion-only domain is to reduce the ability of the system to form patterns. We also demonstrate complex impacts of this coupling on pattern formation. For instance, we exhibit non-monotonicity of pattern-forming instabilities with respect to geometric and coupling parameters, and highlight an instability from a nontrivial interaction between kinetics in one domain and diffusion in the other. These results are valuable for informing design choices in applications such as synthetic engineering of Turing patterns, but also for understanding the role of stratified media in modulating pattern-forming processes in developmental biology and beyond.
The layered FeTe2O5Cl compound was studied by specific-heat, muon spin relaxation, nuclear magnetic resonance, dielectric, as well as neutron and synchrotron x-ray diffraction measurements, and the results were compared to isostructural FeTe2O5Br. We find that the low-temperature ordered state, similarly as in FeTe2O5Br, is multiferroic - the elliptical amplitude-modulated magnetic cycloid and the electric polarization simultaneously develop below 11 K. However, compared to FeTe2O5Br, the magnetic elliptical envelop rotates by 75(4) deg and the orientation of the electric polarization is much more sensitive to the applied electric field. We propose that the observed differences between the two isostructural compounds arise from geometric frustration, which enhances the effects of otherwise subtle Fe3+ (S = 5/2) magnetic anisotropies. Finally, x-ray diffraction results imply that, on the microscopic scale, the magnetoelectric coupling is driven by shifts of the O1 atoms, as a response to the polarization of the Te4+ lone-pair electrons involved in the Fe-O-Te-O-Fe exchange bridges.
The nature of the low temperature ground state of the pyrochlore compound Tb2Ti2O7 remains a puzzling issue. Dynamic fluctuations and short-range correlations persist down to 50 mK, as evidenced by microscopic probes. In parallel, magnetization measurements show irreversibilities and glassy behavior below 200 mK. We have performed magnetization and AC susceptibility measurements on four single crystals down to 57 mK. We did not observe a clear plateau in the magnetization as a function of field along the [111] direction, as suggested by the quantum spin ice model. In addition to a freezing around 200 mK, slow dynamics are observed in the AC susceptibility up to 4 K. The overall frequency dependence cannot be described by a canonical spin-glass behavior.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
