Stability analysis of homogeneous shear flow : the linear and nonlinear theories and a Hamiltonian formulation

The stability of steady-state solutions of the equations governing two-dimensional, homogeneous, incompressible fluid flow are analyzed in the context of shear-flow in a channel. Both the linear and nonlinear theories are reviewed and compared. In proving nonlinear stability of an equilibrium, emphasis is placed on using the stability algorithm developed in Holm et al. (1985). It is shown that for certain types of equilibria the linear theory is inconclusive, although nonlinear stability can be proven. Establishing nonlinear stability is dependent on the definition of a norm on the space of perturbations. McIntyre and Shepherd (1987) specifically define five norms, two for corresponding to one flow state and three to a different flow state, and suggest that still others are possible. Here, the norms given by McIntyre and Shepherd (1987) are shown to induce the same topology (for the corresponding flow states), establishing their equivalence as norms, and hence their equivalence as measures of stability. Summaries of the different types of stability and their mathematical definitions are presented. Additionally, a summary of conditions on shear-flow equilibria under which the various types of stability have been proven is presented. The Hamiltonian structure of the two-dimensional Euler equations is outlined following Olver (1986). A coordinate-free approach is adopted emphasizing the role of the Poisson bracket structure. Direct calculations are given to show that the Casimir invariants, or distinguished functionals, are time-independent and therefore are conserved quantities in the usual sense

Existence of a solution to a variational data assimilation method in two-dimensional hydrodynamics

The main result of this paper is a proof of the existence of a solution generated by a method for the variational assimilation of observational data into the two-dimensional, incompressible Euler equations. The data are assumed to be given by linear (measurement) functionals acting on the space of functions representing vorticity. From a practical point of view, the data are considered to be sparse and available on a fixed space-time domain. The objective of the variational assimilation is to obtain an estimate of the vorticity which minimizes a cost functional. The cost functional is the sum of a generalized mean squared error in the dynamics, a generalized mean squared error in the initial condition, and a weighted squared error in the misfit to the observed data. These generalized mean squared errors are computed over the fixed space-time domain containing the data. The estimate then provides a best (generalized) least squares fit between the model, the initial condition, and the data. A necessary condition for the estimate of vorticity to minimize the cost functional is that it must satisfy the corresponding system of Euler-Lagrange equations, which consist of a nonlinear, coupled system of partial differential equations with an initial condition, a final condition, and boundary conditions. Construction of a solution to the Euler-Lagrange equations is possible provided they are linearized through an iterative scheme. Analysis of one such scheme motivates a reformulation of the variational problem in terms of an iterated linearization of the dynamics. This second method results in a slightly different iterated system of Euler-Lagrange equations. The sequence of solutions generated is shown to be bounded in the Sobolev space W[superscrit k,p] (in space-time). It follows from a Sobolev imbedding theorem that the sequence contains a convergent subsequence, the limit of which is a classical solution of the nonlinear, forced Euler equation corresponding to the forward problem of the Euler-Lagrange system. The two schemes mentioned above are compared based on formal applications of Newton's method to the operators defining the systems. We conclude that the two formulations of the assimilation problem are in fact different and provide some intuitive reasons for preferring the second method, beyond the fact that the existence proof is established

The CH3SH molecule deposited on Cu(111) and deprotonation

We demonstrate for the first time that when a methanethiol adsorbed on the regular Cu(111) surface, the dissociative structure is thermodynamically more stable than the intact one. The computational results show that at low temperature the methanethiol adsorbate prefers the atop site of the regular Cu(111) surface. As the temperature is increased, the S-H bond is broken and the methylthiolate favors the hollow sites. On the defected Cu(111) surface, the dissociative configuration is still thermodynamically more stable than the nondissociative one. The calculation indicates that the hydrogen initially attached to the sulfur would like to form a bond with the copper surface rather than desorb from it. Even though both copper and gold are the noble metal, the stability of the methanethiol adsorption on the Cu(111) substrate is almost the reverse of that on the Au(111).Comment: 13 pages, 7 figures, submitted to Phys. Rev.

Observations of gas flows inside a protoplanetary gap

Gaseous giant planet formation is thought to occur in the first few million years following stellar birth. Models predict that giant planet formation carves a deep gap in the dust component (shallower in the gas). Infrared observations of the disk around the young star HD142527, at ~140pc, found an inner disk ~10AU in radius, surrounded by a particularly large gap, with a disrupted outer disk beyond 140AU, indicative of a perturbing planetary-mass body at ~90 AU. From radio observations, the bulk mass is molecular and lies in the outer disk, whose continuum emission has a horseshoe morphology. The vigorous stellar accretion rate would deplete the inner disk in less than a year, so in order to sustain the observed accretion, matter must flow from the outer-disk into the cavity and cross the gap. In dynamical models, the putative protoplanets channel outer-disk material into gap-crossing bridges that feed stellar accretion through the inner disk. Here we report observations with the Atacama Large Millimetre Array (ALMA) that reveal diffuse CO gas inside the gap, with denser HCO+ gas along gap-crossing filaments, and that confirm the horseshoe morphology of the outer disk. The estimated flow rate of the gas is in the range 7E-9 to 2E-7 Msun/yr, which is sufficient to maintain accretion onto the star at the present rate

Predicting protein decomposition: the case of aspartic-acid racemization kinetics

The increase in proportion of the non-biological (D-) isomer of aspartic acid (Asp) relative to the L- isomer has been widely used in archaeology and geochemistry as a tool for dating. The method has proved controversial, particularly when used for bones. The non-linear kinetics of Asp racemization have prompted a number of suggestions as to the underlying mechanism(s) and have led to the use of mathe- matical transformations which linearize the increase in D-Asp with respect to time. Using one example, a suggestion that the initial rapid phase of Asp racemization is due to a contribution from asparagine (Asn), we demonstrate how a simple model of the degradation and racemization of Asn can be used to predict the observed kinetics. A more complex model of peptide bound Asx (Asn+Asp) racemization, which occurs via the formation of a cyclic succinimide (Asu), can be used to correctly predict Asx racemi- zation kinetics in proteins at high temperatures (95-140 °C). The model fails to predict racemization kinetics in dentine collagen at 37 °C. The reason for this is that Asu formation is highly conformation dependent and is predicted to occur extremely slowly in triple helical collagen. As conformation strongly in£uences the rate of Asu formation and hence Asx racemization, the use of extrapolation from high temperatures to estimate racemization kinetics of Asx in proteins below their denaturation temperature is called into question. In the case of archaeological bone, we argue that the D:L ratio of Asx re£ects the proportion of non- helical to helical collagen, overlain by the e¡ects of leaching of more soluble (and conformationally unconstrained) peptides. Thus, racemization kinetics in bone are potentially unpredictable, and the proposed use of Asx racemization to estimate the extent of DNA depurination in archaeological bones is challenged

VIBES: VIsual Binary Exoplanet survey with SPHERE Upper limits on wide S-planet and S-BD frequencies, triple system discovery, and astrometric confirmation of 20 stellar binaries and three triple systems

Recent surveys indicate that planets in binary systems are more abundant than previously thought, which is in agreement with theoretical work on disc dynamics and planet formation in binaries. In order to measure the abundance and physical characteristics of wide-orbit giant exoplanets in binary systems, we have designed the 'VIsual Binary Exoplanet survey with Sphere' (VIBES) to search for planets in visual binaries. It uses the SPHERE instrument at VLT to search for planets in 23 visual binary and four visual triple systems with ages of <145 Myr and distances of <150 pc. We used the IRDIS dual-band imager on SPHERE to acquire high-contrast images of the sample targets. For each binary, the two components were observed at the same time with a coronagraph masking only the primary star. For the triple star, the tight components were treated as a single star for data reduction. This enabled us to effectively search for companions around 50 individual stars in binaries and four binaries in triples. We derived upper limits of $<$13.7\% for the frequency of sub-stellar companions around primaries in visual binaries, $<$26.5\% for the fraction of sub-stellar companions around secondaries in visual binaries, and an occurrence rate of $<$9.0\% for giant planets and brown dwarfs around either component of visual binaries. We have combined our observations with literature measurements to astrometrically confirm, for the first time, that 20 binaries and two triple systems, which were previously known, are indeed physically bound. Finally, we discovered a third component of the binary HD~121336. The upper limits we derived are compatible with planet formation through the core accretion and the gravitational instability processes in binaries. These limits are also in line with limits found for single star and circumbinary planet search surveys.Comment: Accepted for publication in Astronomy & Astrophysics on 18.09.2020 21 pages, 11 figure

Exploring dust around HD142527 down to 0.025" / 4au using SPHERE/ZIMPOL

We have observed the protoplanetary disk of the well-known young Herbig star HD 142527 using ZIMPOL Polarimetric Differential Imaging with the VBB (Very Broad Band, ~600-900nm) filter. We obtained two datasets in May 2015 and March 2016. Our data allow us to explore dust scattering around the star down to a radius of ~0.025" (~4au). The well-known outer disk is clearly detected, at higher resolution than before, and shows previously unknown sub-structures, including spirals going inwards into the cavity. Close to the star, dust scattering is detected at high signal-to-noise ratio, but it is unclear whether the signal represents the inner disk, which has been linked to the two prominent local minima in the scattering of the outer disk, interpreted as shadows. An interpretation of an inclined inner disk combined with a dust halo is compatible with both our and previous observations, but other arrangements of the dust cannot be ruled out. Dust scattering is also present within the large gap between ~30 and ~140au. The comparison of the two datasets suggests rapid evolution of the inner regions of the disk, potentially driven by the interaction with the close-in M-dwarf companion, around which no polarimetric signal is detected.Comment: 11 pages, 7 figures, accepted for publication in A

Dynamic response of berea sandstone shock-loaded under dry, wet and water-pressurized conditions

A single-stage light-gas gun was used to perform shock-recovery experiments on Berea sandstone under dry, wet and hydrostatically water-pressurized conditions. The samples were impacted by flyer-plates to achieve stress levels in the range 1.3 to 9.8 GPa. The microstructure of the shocked samples was analyzed using scanning electron microscopy (SEM), laser particle analysis and X-ray computed microtomography (XCMT). The dry samples show strongly fragmented and irregularly fractured quartz grains with a considerably reduced porosity, whereas the wet and water-pressurized specimens show less grain damage and less porosity reduction. During shock compression the water in the pores distributes the stresses and therefore the contact force between the grains is reduced. The interaction between the grains during the shock process was modeled by explicitly treating the grain-pore structure using Smooth Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM)