Chimera states consisting of domains of coherently and incoherently oscillating identical oscillators with nonlocal coupling are studied. These states usually coexist with the fully synchronized state and have a small basin of attraction. We propose a nonlocal phase-coupled model in which chimera states develop from random initial conditions. Several classes of chimera states have been found: (a) stationary multicluster states with evenly distributed coherent clusters, (b) stationary multicluster states with unevenly distributed clusters, and (c) a single cluster state traveling with a constant speed across the system. Traveling coherent states are also identified. A self-consistent continuum description of these states is provided and their stability properties analyzed through a combination of linear stability analysis and numerical simulation.

Chimera states consisting of domains of coherently and incoherently oscillating oscillators in a two-dimensional periodic array of nonlocally coupled phase oscillators are studied. In addition to the one-dimensional chimera states familiar from one spatial dimension, two-dimensional structures termed twisted chimera states and spiral wave chimera states are identified in simulations. The properties of many of these states, including stability, are determined using an evolution equation for a complex order parameter and are found to be in agreement with the simulations.

We attempt to characterize the degree of skin thermal damage by using multiphoton microscopy to characterize dermal thermal damage. Our results show that dermal collagen and elastic fibers display different susceptibility to thermal injury. Morphologically, dermal collagen starts to denature at 60 degrees C while fracture and aggregation of elastic fibers do not occur until 65 degrees C. With increasing temperatures, the structures of both elastic and collagen fibers deteriorate. While second-harmonic-generation (SHG) imaging is helpful in identifying the denaturation temperature of collagen, autofluorescence (AF) imaging can help to identify the structural alternations of tissue at higher temperatures when SHG signals have decayed. We also employ a ratiometric approach based on the AF-to-SHG index of dermis (ASID) to characterize the degree of dermal thermal damage. Use of the ASID index can bypass the difficulty in analyzing inhomogeneous dermal fibers and show that dermal collagen starts to denature at 60 degrees C. Our results suggest that with additional developments, multiphoton microscopy has potential to be developed into an effective in vivo imaging technique to monitor and characterize dermal thermal damage.

Two-dimensional convection in a plane layer bounded by stress-free perfectly conducting horizontal boundaries and rotating uniformly about the vertical is considered. Time-independent spatially localized structures, called convectons, of even and odd parity are computed. The convectons are embedded within a self-generated shear layer with a compensating shear flow outside the structure. These states are organized within a bifurcation structure called slanted snaking and may be present even when periodic convection sets in supercritically. These interesting properties are traced to the presence of a conserved quantity and hence to the use of stress-free boundary conditions.

The transition from subcritical to supercritical stationary periodic patterns is described by the one-dimensional cubic-quintic Ginzburg-Landau equationwhere A(x, t) represents the pattern amplitude and the coefficients µ, a 1 , a 2 and b are real. The conditions for Eckhaus instability of periodic solutions are determined, and the resulting spatially modulated states are computed. Some of these evolve into spatially localized structures in the vicinity of a Maxwell point, while others resemble defect states. The results are used to shed light on the behavior of localized structures in systems exhibiting homoclinic snaking during the transition from subcriticality to supercriticality.