Graphoidal Tree d - Cover

Acharya and Sampathkumar defined a graphoidal cover as a partition of edges into internally disjoint (not necessarily open) paths. If we consider only open paths in the above definition then we call it as a graphoidal path cover

Spatial control of irreversible protein aggregation

Liquid cellular compartments spatially segregate from the cytoplasm and can regulate aberrant protein aggregation, a process linked to several medical conditions, including Alzheimer's and Parkinson's diseases. Yet the mechanisms by which these droplet-like compartments affect protein aggregation remain unknown. Here, we combine kinetic theory of protein aggregation and liquid-liquid phase separation to study the spatial control of irreversible protein aggregation in the presence of liquid compartments. We find that, even for weak interactions between the compartment constituents and the aggregating monomers, aggregates are strongly enriched inside the liquid compartment relative to the surrounding cytoplasm. We show that this enrichment is caused by a positive feedback mechanism of aggregate nucleation and growth which is mediated by a flux maintaining the phase equilibrium between the compartment and the cytoplasm. Our model predicts that the compartment volume that maximizes aggregate enrichment in the compartment is determined by the reaction orders of aggregate nucleation. The underlying mechanism of aggregate enrichment could be used to confine cytotoxic protein aggregates inside droplet-like compartments suggesting potential new avenues against aberrant protein aggregation. Our findings could also represent a common mechanism for the spatial control of irreversible chemical reactions in general

Transitions to Nematic states in homogeneous suspensions of high aspect ratio magnetic rods

Isotropic-Nematic and Nematic-Nematic transitions from a homogeneous base state of a suspension of high aspect ratio, rod-like magnetic particles are studied for both Maier-Saupe and the Onsager excluded volume potentials. A combination of classical linear stability and asymptotic analyses provides insight into possible nematic states emanating from both the isotropic and nematic non-polarized equilibrium states. Local analytical results close to critical points in conjunction with global numerical results (Bhandar, 2002) yields a unified picture of the bifurcation diagram and provides a convenient base state to study effects of external orienting fields.Comment: 3 Figure

Electronic Structure of Sr_2FeMoO_6

We have analysed the unusual electronic structure of Sr_2FeMoO_6 combining ab-initio and model Hamiltonian approaches. Our results indicate that there are strong enhancements of the intraatomic exchange strength at the Mo site as well as the antiferromagnetic coupling strength between Fe and Mo sites. We discuss the possibility of a negative effective Coulomb correlation strength (U_{eff}) at the Mo site due to these renormalised interaction strengths.Comment: To appear in Phys. Rev. Let

The predictability of large-scale wind-driven flows

International audienceThe singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving examples of wind-driven, double-gyre circulations in different flow regimes are explored. By changing the Reynolds number in simple quasi-geostrophic models of the wind-driven circulation, steady, weakly aperiodic and chaotic states may be examined. The singular vectors of the steady state reveal some of the physical mechanisms responsible for optimally growing perturbations. In time-dependent cases, the dominant singular values show significant variability in time, indicating strong variations in the predictability of the flow. When the underlying flow is weakly aperiodic, the dominant singular values co-vary with integral measures of the large-scale flow, such as the basin-integrated upper ocean kinetic energy and the transport in the western boundary current extension. Furthermore, in a reduced gravity quasi-geostrophic model of a weakly aperiodic, double-gyre flow, the behaviour of the dominant singular values may be used to predict a change in the large-scale flow, a feature not shared by an analogous two-layer model. When the circulation is in a strongly aperiodic state, the dominant singular values no longer vary coherently with integral measures of the flow. Instead, they fluctuate in a very aperiodic fashion on mesoscale time scales. The dominant singular vectors then depend strongly on the arrangement of mesoscale features in the flow and the evolved forms of the associated singular vectors have relatively short spatial scales. These results have several implications. In weakly aperiodic, periodic, and stationary regimes, the mesoscale energy content is usually relatively low and the predictability of the wind-driven circulation is determined by the large-scale structure of the flow. In the more realistic, strongly chaotic regime, in which energetic mesoscale eddies are produced by the meandering of the separated western boundary current extension, the predictability of the flow locally tends to be a stronger function of the local mesoscale eddy structure than of the larger scale structure of the circulation. This has a broader implication for the effectiveness of different approaches to forecasting the ocean with models which sequentially assimilate new observations