Synchronization and structure in an adaptive oscillator network

We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance their mutual synchronization. We show that the evolving network reaches a small-world structure. Its clustering coefficient attains a maximum for an intermediate intensity of the coupling between oscillators, where a rich diversity of synchronized oscillator groups is observed. In the stationary state, these synchronized groups are directly associated with network clusters.Comment: 6 pages, 7 figure

A two-component phenomenology for the evolution of MHD turbulence

Incompressible MHD turbulence with a mean magnetic field B₀ develops anisotropic spectral structure and can be simply described only by including at least two distinct fluctuation components. These are conveniently referred to as “waves,” for which propagation effects are important, and “quasi-2D” turbulence, for which nonlinear effects dominate over propagation ones. The quasi-2D component has wavevectors approximately perpendicular to B₀. These two idealized ingredients capture the essential physics of propagation (high frequency fluctuations) and strong turbulence (low frequency fluctuations.) Here we present a two-component energy-containing range phenomenology for the evolution of homogeneous MHD turbulence

The Evolution of Cholesterol-Rich Membrane in Oxygen Adaption: The Respiratory System as a Model.

The increase in atmospheric oxygen levels imposed significant environmental pressure on primitive organisms concerning intracellular oxygen concentration management. Evidence suggests the rise of cholesterol, a key molecule for cellular membrane organization, as a cellular strategy to restrain free oxygen diffusion under the new environmental conditions. During evolution and the increase in organismal complexity, cholesterol played a pivotal role in the establishment of novel and more complex functions associated with lipid membranes. Of these, caveolae, cholesterol-rich membrane domains, are signaling hubs that regulate important in situ functions. Evolution resulted in complex respiratory systems and molecular response mechanisms that ensure responses to critical events such as hypoxia facilitated oxygen diffusion and transport in complex organisms. Caveolae have been structurally and functionally associated with respiratory systems and oxygen diffusion control through their relationship with molecular response systems like hypoxia-inducible factors (HIF), and particularly as a membrane-localized oxygen sensor, controlling oxygen diffusion balanced with cellular physiological requirements. This review will focus on membrane adaptations that contribute to regulating oxygen in living systems

Current singularities at finitely compressible three-dimensional magnetic null points

The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed

Reduced magnetohydrodynamics and parallel spectral transfer

The self-consistency of the reduced magnetohydrodynamics (RMHD) model is explored by examining whether (parallel) spectral transfer might invalidate the assumptions employed in deriving it. Using direct numerical simulations we find that transfer of energy to structures with high parallel wavenumber is in fact limited by ongoing perpendicular transfer. Thus, the dynamics associated with RMHD models remains consistent with the underlying assumptions of RMHD. In particular, in well-resolved simulations it is neither necessary nor correct to introduce additional dissipation terms that (artificially) damp spectral transfer parallel to the mean magnetic field B0

A two-component phenomenology for homogeneous magnetohydrodynamic turbulence

A one-point closure model for energy decay in three-dimensional magnetohydrodynamic (MHD) turbulence is developed. The model allows for influence of a large-scale magnetic field that may be of strength sufficient to induce Alfvén wave propagation effects, and takes into account components of turbulence in which either the wave-like character is negligible or is dominant. This two-component model evolves energy and characteristic length scales, and may be useful as a simple description of homogeneous MHD turbulent decay. In concert with spatial transport models, it can form the basis for approximate treatment of low-frequency plasma turbulence in a variety of solar, space, and astrophysical contexts

Direct comparisons of compressible magnetohydrodynamics and reduced magnetohydrodynamics turbulence

Direct numerical simulations of low Mach number compressible three-dimensional magnetohydrodynamic (CMHD3D) turbulence in the presence of a strong mean magnetic field are compared with simulations of reduced magnetohydrodynamics (RMHD). Periodic boundary conditions in the three spatial coordinates are considered. Different sets of initial conditions are chosen to explore the applicability of RMHD and to study how close the solution remains to the full compressible MHD solution as both freely evolve in time. In a first set, the initial state is prepared to satisfy the conditions assumed in the derivation of RMHD, namely, a strong mean magnetic field and plane-polarized fluctuations, varying weakly along the mean magnetic field. In those circumstances, simulations show that RMHD and CMHD3D evolve almost indistinguishably from one another. When some of the conditions are relaxed the agreement worsens but RMHD remains fairly close to CMHD3D, especially when the mean magnetic field is large enough. Moreover, the well-known spectral anisotropy effect promotes the dynamical attainment of the conditions for RMHD applicability. Global quantities (mean energies, mean-square current, and vorticity) and energy spectra from the two solutions are compared and point-to-point separation estimations are computed. The specific results shown here give support to the use of RMHD as a valid approximation of compressible MHD with a mean magnetic field under certain but quite practical conditions

Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions

Burchnall's method to invert the Feldheim-Watson linearization formula for the Hermite polynomials is extended to all polynomial families in the Askey-scheme and its $q$-analogue. The resulting expansion formulas are made explicit for several families corresponding to measures with infinite support, including the Wilson and Askey-Wilson polynomials. An integrated version gives the possibility to give alternate expression for orthogonal polynomials with respect to a modified weight. This gives expansions for polynomials, such as Hermite, Laguerre, Meixner, Charlier, Meixner-Pollaczek and big $q$-Jacobi polynomials and big $q$-Laguerre polynomials. We show that one can find expansions for the orthogonal polynomials corresponding to the Toda-modification of the weight for the classical polynomials that correspond to known explicit solutions for the Toda lattice, i.e., for Hermite, Laguerre, Charlier, Meixner, Meixner-Pollaczek and Krawtchouk polynomials