Slowly modulated oscillations in nonlinear diffusion processes

It is shown here that certain systems of nonlinear (parabolic) reaction-diffusion equations have solutions which are approximated by oscillatory functions in the form R(ξ - cτ)P(t^*) where P(t^*) represents a sinusoidal oscillation on a fast time scale t* and R(ξ - cτ) represents a slowly-varying modulating amplitude on slow space (ξ) and slow time (τ) scales. Such solutions describe phenomena in chemical reactors, chemical and biological reactions, and in other media where a stable oscillation at each point (or site) undergoes a slow amplitude change due to diffusion

Phase Behavior of Colloidal Superballs: Shape Interpolation from Spheres to Cubes

The phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box. A superball's interior is defined by the inequality $|x|^{2q} + |y|^{2q} + |z|^{2q} \leq 1$, which provides a versatile family of convex particles ($q \geq 0.5$) with cube-like and octahedron-like shapes as well as concave particles ($q < 0.5$) with octahedron-like shapes. Here, we consider the convex case with a deformation parameter q between the sphere point (q = 1) and the cube (q = 1). We find that the asphericity plays a significant role in the extent of cubatic ordering of both the liquid and crystal phases. Calculation of the first few virial coefficients shows that superballs that are visually similar to cubes can have low-density equations of state closer to spheres than to cubes. Dense liquids of superballs display cubatic orientational order that extends over several particle lengths only for large q. Along the ordered, high-density equation of state, superballs with 1 < q < 3 exhibit clear evidence of a phase transition from a crystal state to a state with reduced long-ranged orientational order upon the reduction of density. For $q \geq 3$, long-ranged orientational order persists until the melting transition. The width of coexistence region between the liquid and ordered, high-density phase decreases with q up to q = 4.0. The structures of the high-density phases are examined using certain order parameters, distribution functions, and orientational correlation functions. We also find that a fixed simulation cell induces artificial phase transitions that are out of equilibrium. Current fabrication techniques allow for the synthesis of colloidal superballs, and thus the phase behavior of such systems can be investigated experimentally.Comment: 33 pages, 14 figure

MicroR159 regulation of most conserved targets in Arabidopsis has negligible phenotypic effects

BACKGROUND A current challenge of microRNA (miRNA) research is the identification of biologically relevant miRNA:target gene relationships. In plants, high miRNA:target gene complementarity has enabled accurate target predictions, and slicing of target mRNAs has facilitated target validation through rapid amplification of 5' cDNA ends (5'-RACE) analysis. Together, these approaches have identified more than 20 targets potentially regulated by the deeply conserved miR159 family in Arabidopsis, including eight MYB genes with highly conserved miR159 target sites. However, genetic analysis has revealed the functional specificity of the major family members, miR159a and miR159b is limited to only two targets, MYB33 and MYB65. Here, we examine the functional role of miR159 regulation for the other potential MYB target genes. RESULTS For these target genes, functional analysis failed to identify miR159 regulation that resulted in any major phenotypic impact, either at the morphological or molecular level. This appears to be mainly due to the quiescent nature of the remaining family member, MIR159c. Although its expression overlaps in a temporal and spatial cell-specific manner with a subset of these targets in anthers, the abundance of miR159c is extremely low and concomitantly a mir159c mutant displays no anther defects. Examination of potential miR159c targets with conserved miR159 binding sites found neither their spatial or temporal expression domains appeared miR159 regulated, despite the detection of miR159-guided cleavage products by 5'-RACE. Moreover, expression of a miR159-resistant target (mMYB101) resulted predominantly in plants that are indistinguishable from wild type. Plants that displayed altered morphological phenotypes were found to be ectopically expressing the mMYB101 transgene, and hence were misrepresentative of the in vivo functional role of miR159. CONCLUSIONS This study presents a novel explanation for a paradox common to plant and animal miRNA systems, where among many potential miRNA-target relationships usually only a few appear physiologically relevant. The identification of a quiescent miR159c:target gene regulatory module in anthers provides a likely rationale for the presence of conserved miR159 binding sites in many targets for which miR159 regulation has no obvious functional role. Remnants from the demise of such modules may lead to an overestimation of miRNA regulatory complexity when investigated using bioinformatic, 5'-RACE or transgenic approaches.RSA was funded by an ANU postgraduate scholarship and by a CSIRO Emerging Science Initiative. JL is the recipient of an ANU international student postgraduate scholarship. This research was supported by an Australian Research Council grant DP0773270

The First X-Ray Proper-Motion Measurements of the Forward Shock in the Northeastern Limb of SN 1006

We report on the first X-ray proper-motion measurements of the nonthermally-dominated forward shock in the northeastern limb of SN 1006, based on two Chandra observations taken in 2000 and 2008. We find that the proper motion of the forward shock is about 0.48 arcsec/yr and does not vary around the rim within the ~10% measurement uncertainties. The proper motion measured is consistent with that determined by the previous radio observations. The mean expansion index of the forward shock is calculated to be ~0.54 which matches the value expected based on an evolutionary model of a Type Ia supernova with either a power-law or an exponential ejecta density profile. Assuming pressure equilibrium around the periphery from the thermally-dominated northwestern rim to the nonthermally-dominated northeastern rim, we estimate the ambient density to the northeast of SN 1006 to be about 0.085/cm^3.Comment: Accepted for publication in The Astrophysical Journal Letter

Magnetic-Field Amplification in the Thin X-ray Rims of SN1006

Several young supernova remnants (SNRs), including SN1006, emit synchrotron X-rays in narrow filaments, hereafter thin rims, along their periphery. The widths of these rims imply 50 to 100 $\mu$G fields in the region immediately behind the shock, far larger than expected for the interstellar medium compressed by unmodified shocks, assuming electron radiative losses limit rim widths. However, magnetic-field damping could also produce thin rims. Here we review the literature on rim width calculations, summarizing the case for magnetic-field amplification. We extend these calculations to include an arbitrary power-law dependence of the diffusion coefficient on energy, $D \propto E^{\mu}$. Loss-limited rim widths should shrink with increasing photon energy, while magnetic-damping models predict widths almost independent of photon energy. We use these results to analyze Chandra observations of SN 1006, in particular the southwest limb. We parameterize the full widths at half maximum (FWHM) in terms of energy as FWHM $\propto E^{m_E}_{\gamma}$. Filament widths in SN1006 decrease with energy; $m_E \sim -0.3$ to $-0.8$, implying magnetic field amplification by factors of 10 to 50, above the factor of 4 expected in strong unmodified shocks. For SN 1006, the rapid shrinkage rules out magnetic damping models. It also favors short mean free paths (small diffusion coefficients) and strong dependence of $D$ on energy ($\mu \ge 1$).Comment: Accepted by ApJ, 49 pages, 10 figure

SPITZER observations of dust destruction in the Puppis A supernova remnant

The interaction of the Puppis A supernova remnant (SNR) with a neighboring molecular cloud provides a unique opportunity to measure the amount of grain destruction in an SNR shock. Spitzer Space Telescope MIPS imaging of the entire SNR at 24, 70, and 160 μm shows an extremely good correlation with X-ray emission, indicating that the SNR’s IR radiation is dominated by the thermal emission of swept-up interstellar dust, collisionally heated by the hot shocked gas. Spitzer IRS spectral observations targeted both the Bright Eastern Knot (BEK) of the SNR where a small cloud has been engulfed by the supernova blast wave and outlying portions of the associated molecular cloud that are yet to be hit by the shock front. Modeling the spectra from both regions reveals the composition and the grain size distribution of the interstellar dust, both in front of and behind the SNR shock front. The comparison shows that the ubiquitous polycyclic aromatic hydrocarbons of the interstellar medium are destroyed within the BEK, along with nearly 25% of the mass of graphite and silicate dust grains