Biomedical subjects

Lingfa Yang

Publications and source records attributed to Lingfa Yang.

10 recordsLinked to original sources

PubMed2006

Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability.

We describe a new type of solitary waves, which propagate in such a manner that the pulse periodically disappears from its original position and reemerges at a fixed distance. We find such jumping waves as solutions to a reaction-diffusion system with a subcritical short-wavelength instability. We demonstrate closely related solitary wave solutions in the quintic complex Ginzburg-Landau equation. We study the characteristics of and interactions between these solitary waves and the dynamics of related wave trains and standing waves.

Algorithms↗

PubMed2006

Turing patterns beyond hexagons and stripes.

The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive reaction-diffusion system. The superlattices develop from initial conditions created by illuminating the system through a mask consisting of a simple hexagonal or square lattice with a wavelength close to a multiple of the intrinsic Turing pattern's wavelength. We show that interaction of the photochemical periodic forcing with the Turing instability generates multiple spatial harmonics of the forcing patterns. The harmonics situated within the Turing instability band survive after the illumination is switched off and form superlattices. The square superlattices are the first examples of time-independent square Turing patterns. We also demonstrate that in a system where the Turing band is slightly below criticality, spatially uniform internal or external oscillations can create oscillating square patterns.

Computer Simulation↗

PubMed2005

Segmented waves from a spatiotemporal transverse wave instability.

We observe traveling waves emitted from Turing spots in the chlorine dioxide-iodine-malonic acid reaction. The newborn waves are continuous, but they break into segments as they propagate, and the propagation of these segments ultimately gives rise to spatiotemporal chaos. We model the wave-breaking process and the motion of the chaotic segments. We find stable segmented spirals as well. We attribute the segmentation to an interaction between front rippling via a transverse instability and front symmetry breaking by a fast-diffusing inhibitor far from the codimension-2 Hopf-Turing bifurcation, and the chaos to a secondary instability of the periodic segmentation.

Journal Article↗

PubMed2005

Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system.

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay.

Journal Article↗

PubMed2004

Turing pattern formation in a two-layer system: superposition and superlattice patterns.

Turing patterns in the chlorine dioxide-iodine-malonic acid reaction are studied in a system consisting of two coupled gel layers. Patterns with two wavelengths are observed. Changing the strength of the interlayer coupling causes a transition between a superposition of Turing patterns and a superlattice pattern. The effects of the reactant concentrations on the pattern wavelengths are delineated.

Journal Article↗

PubMed2004

Stable squares and other oscillatory turing patterns in a reaction-diffusion model.

We study the Brusselator reaction-diffusion model under conditions where the Hopf mode is supercritical and the Turing band is subcritical. Oscillating Turing patterns arise in the system when bulk oscillations lose their stability to spatial perturbations. Spatially uniform external periodic forcing can generate oscillating Turing patterns when both the Turing and Hopf modes are subcritical in the autonomous system. Most of the symmetric patterns show period doubling in both space and time. Patterns observed include squares, rhombi, stripes, and hexagons.

Journal Article↗

PubMed2004

Symmetric, asymmetric, and antiphase Turing patterns in a model system with two identical coupled layers.

We study Turing pattern formation in a model reaction-diffusion system with two coupled identical layers. The coupling creates a pitchfork bifurcation, which unfolds the symmetric steady state via primary Turing instability, into a pair of distinct, unstable, asymmetric steady states (a-SS). The a-SS gain stability at a reverse Turing bifurcation. The multiple stabilities created by the coupling generate a corresponding multiplicity of structures, including symmetric, asymmetric, antiphase, and localized Turing patterns. Coexistence and competition of the different types of Turing patterns are studied. A one-dimensional localized structure exhibits striking curvature effects.

Journal Article↗

PubMed2003

Superlattice Turing structures in a photosensitive reaction-diffusion system.

Families of complex superlattice structures, consisting of combinations of basic hexagonal or square patterns, are found in a photosensitive reaction-diffusion system. The structures are induced by simple illumination patterns whose wavelengths are appropriately related to that of the system's intrinsic Turing pattern. Computer simulations agree with the structures and their stability. The technique offers a general approach to generating superlattices for use in information storage and other applications.

Journal Article↗

PubMed2003

Oscillatory Turing patterns in reaction-diffusion systems with two coupled layers.

A model reaction-diffusion system with two coupled layers yields oscillatory Turing patterns when oscillation occurs in one layer and the other supports stationary Turing structures. Patterns include "twinkling eyes," where oscillating Turing spots are arranged as a hexagonal lattice, and localized spiral or concentric waves within spot-like or stripe-like Turing structures. A new approach to generating the short-wave instability is proposed.

Journal Article↗

PubMed2002

Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes.

Spatial resonances leading to superlattice hexagonal patterns, known as "black-eyes," and superposition patterns combining stripes and/or spots are studied in a reaction-diffusion model of two interacting Turing modes with different wavelengths. A three-phase oscillatory interlacing hexagonal lattice pattern is also found, and its appearance is attributed to resonance between a Turing mode and its subharmonic.

Diffusion↗