The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities

In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting $x,t$-independent higher order symmetries and conserved densities. Using a recursive relation, we explicitly generate infinitely many higher order conserved densities dependent on arbitrary parameters. We find three Nijenhuis recursion operators resulting from Hamiltonian pairs, of which two are new. They generate three hierarchies of commuting local symmetries. Finally, we give a local recursion operator depending on an arbitrary parameter. As a by-product, we classify all anti-symmetric operators of a definite form that are compatible with the Hamiltonian operator $D_x^{-1}$

A census of massive stars in NGC 346. Stellar parameters and rotational velocities

Spectroscopy for 247 stars towards the young cluster NGC 346 in the Small Magellanic Cloud has been combined with that for 116 targets from the VLT-FLAMES Survey of Massive Stars. Spectral classification yields a sample of 47 O-type and 287 B-type spectra, while radial-velocity variations and/or spectral multiplicity have been used to identify 45 candidate single-lined systems, 17 double-lined systems, and one triple-lined system. Atmospheric parameters (T$_eff$ and log$g$) and projected rotational velocities ($v_e$sin$i$) have been estimated using TLUSTY model atmospheres; independent estimates of $v_e$sin$i$ were also obtained using a Fourier Transform method. Luminosities have been inferred from stellar apparent magnitudes and used in conjunction with the T$_eff$ and $v_e$sin$i$ estimates to constrain stellar masses and ages using the BONNSAI package. We find that targets towards the inner region of NGC 346 have higher median masses and projected rotational velocities, together with smaller median ages than the rest of the sample. There appears to be a population of very young targets with ages of less than 2 Myr, which have presumably all formed within the cluster. The more massive targets are found to have lower $v_e$sin$i$ consistent with previous studies. No significant evidence is found for differences with metallicity in the stellar rotational velocities of early-type stars, although the targets in the SMC may rotate faster than those in young Galactic clusters. The rotational velocity distribution for single non-supergiant B-type stars is inferred and implies that a significant number have low rotational velocity ($\simeq$10\% with $v_e$<40 km/s), together with a peak in the probability distribution at $v_e \simeq$300 km/s. Larger projected rotational velocity estimates have been found for our Be-type sample and imply that most have rotational velocities between 200-450 km/s.Comment: Accepted by A&

The VLT-FLAMES survey of massive stars: Nitrogen abundances for Be-type stars in the Magellanic Clouds

Aims. We compare the predictions of evolutionary models for early-type stars with atmospheric parameters, projected rotational velocities and nitrogen abundances estimated for a sample of Be-type stars. Our targets are located in 4 fields centred on the Large Magellanic Cloud cluster: NGC 2004 and the N 11 region as well as the Small Magellanic Cloud clusters: NGC 330 and NGC 346. Methods. Atmospheric parameters and photospheric abundances have been determined using the non-LTE atmosphere code tlusty. Effective temperature estimates were deduced using three different methodologies depending on the spectral features observed; in general they were found to yield consistent estimates. Gravities were deduced from Balmer line profiles and microturbulences from the Si iii spectrum. Additionally the contributions of continuum emission from circumstellar discs were estimated. Given its importance in constraining stellar evolutionary models, nitrogen abundances (or upper limits) were deduced for all the stars analysed. Results. Our nitrogen abundances are inconsistent with those predicted for targets spending most of their main sequence life rotating near to the critical velocity. This is consistent with the results we obtain from modelling the inferred rotational velocity distribution of our sample and of other investigators. We consider a number of possibilities to explain the nitrogen abundances and rotational velocities of our Be-type sample.Comment: 14 pages, 9 figures, submitted to A&

Diurnal and seasonal changes in nitrate reductase activity and nitrogen content of grapevines: Effect of canopy management

Diurnal and seasonal in viva nitrate reductase activity (NRA) and nitrogen (N) contents in leaves, berries, and roots and the effect of canopy management were investigated in Vitis vinifera L. cv. Cabernet Sauvignon/99 Richter grapevines. Peak NRA in leaves occurred from mid-morning to mid-day. Young leaves had almost the same NRA as mature leaves before berries reached pea size stage, but subsequent to that displayed higher activity. Leaf NRA increased during the post-harvest period. Differences in NRA patterns between leaves conformed with classic source:sink behaviour. Canopy management stimulated nitrate reduction in basal source leaves, most likely through its favourable effect on canopy Light microclimate and photosynthetic activity. The NRA in the berries generally increased towards ripeness; treatments affected NRA only slightly. Peak root NRA corresponded to seasonal root growth patterns. In contrast to leaves and berries, NRA in roots increased from the morning to the afternoon. Effect of treatment on root NRA was minor. Leaf and berry N contents declined during the season, whereas reasonably stable concentrations were maintained in the roots. An involvement of NR in the N assimilation and in the energy supply pathways of the grapevine was substantiated. NRA proved to be a good indicator of fluctuations in N assimilation during growth, suggesting its determination to be instrumental in defining the N status and fertilization needs of the grapevine

Hierarchical Models for Independence Structures of Networks

We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erd\"os-R\'enyi and beta-models to create hierarchical Erd\"os-R\'enyi and beta-models. We describe various methods for parameter estimation as well as simulation studies for models with sparse dependency graphs.Comment: 19 pages, 7 figure

Contaminant Interferences with SIMS Analyses of Microparticle Impactor Residues on LDEF Surfaces

Elemental analyses of impactor residues on high purity surface exposed to the low earth orbit (LEO) environment for 5.8 years on Long Duration Exposure Facility (LDEF) has revealed several probable sources for microparticles at this altitude, including natural micrometeorites and manmade debris ranging from paint pigments to bits of stainless steel. A myriad of contamination interferences were identified and their effects on impactor debris identification mitigated during the course of this study. These interferences included pre-, post-, and in-flight deposited particulate surface contaminants, as well as indigenous heterogeneous material contaminants. Non-flight contaminants traced to human origins, including spittle and skin oils, contributed significant levels of alkali-rich carbonaceous interferences. A ubiquitous layer of in-flight deposited silicaceous contamination varied in thickness with location on LDEF and proximity to active electrical fields. In-flight deposited (low velocity) contaminants included urine droplets and bits of metal film from eroded thermal blankets

Ion microprobe elemental analyses of impact features on interplanetary dust experiment sensor surfaces

Hypervelocity impact features from very small particles (less than 3 microns in diameter) on several of the electro-active dust sensors used in the Interplanetary Dust Experiment (IDE) were subjected to elemental analysis using an ion microscope. The same analytical techniques were applied to impact and containment features on a set of ultra-pure, highly polished single crystal germanium wafer witness plates that were mounted on tray B12. Very little unambiguously identifiable impactor debris was found in the central craters or shatter zones of small impacts in this crystalline surface. The surface contamination, ubiquitous on the surface of the Long Duration Exposure Facility, has greatly complicated data collection and interpretation from microparticle impacts on all surfaces

Electrophoretic Properties of Highly Charged Colloids: A Hybrid MD/LB Simulation Study

Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e. macroion and electrolyte), propagated via molecular dynamics (MD), are coupled to a Lattice Boltzmann (LB) fluid. In a recent experiment it was shown that, for multivalent salt ions, the mobility $\mu$ initially increases with charge density $\sigma$, reaches a maximum and then decreases with further increase of $\sigma$. The aim of the present work is to elucidate the behaviour of $\mu$ at high values of $\sigma$. Even for the case of monovalent microions, we find a decrease of $\mu$ with $\sigma$. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subject to an external electrical field. The number of counterions in the Stern layer, $q_0$, is a crucial parameter for the behavior of $\mu$ at high values of $\sigma$. In this case, the mobility $\mu$ depends primarily on the ratio $q_0/Q$ (with $Q$ the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing $\sigma$ leads to the lowering of $\mu$ does not hold for high $\sigma$. In fact, we show that the deformation of the EDL decreases with increase of $\sigma$. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of $\sigma$ the phenomenon of charge inversion is found.Comment: accepted in J. Chem Phys., 10 pages, 9 figure

Phase Separation in Charge-Stabilized Colloidal Suspensions: Influence of Nonlinear Screening

The phase behavior of charge-stabilized colloidal suspensions is modeled by a combination of response theory for electrostatic interparticle interactions and variational theory for free energies. Integrating out degrees of freedom of the microions (counterions, salt ions), the macroion-microion mixture is mapped onto a one-component system governed by effective macroion interactions. Linear response of microions to the electrostatic potential of the macroions results in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume energy, while nonlinear response modifies the effective interactions [A. R. Denton, \PR E {\bf 70}, 031404 (2004)]. The volume energy and effective pair potential are taken as input to a variational free energy, based on thermodynamic perturbation theory. For both linear and first-order nonlinear effective interactions, a coexistence analysis applied to aqueous suspensions of highly charged macroions and monovalent microions yields bulk separation of macroion-rich and macroion-poor phases below a critical salt concentration, in qualitative agreement with predictions of related linearized theories [R. van Roij, M. Dijkstra, and J.-P. Hansen, \PR E {\bf 59}, 2010 (1999); P. B. Warren, \JCP {\bf 112}, 4683 (2000)]. It is concluded that nonlinear screening can modify phase behavior but does not necessarily suppress bulk phase separation of deionized suspensions.Comment: 14 pages of text + 9 figure