A Gas-Kinetic Scheme for Turbulent Flow

RANS simulations may not provide accurate results for all flow conditions. The interaction between a shock wave and a turbulent boundary layer is an example which may still be difficult to simulate accurately. Beside the inability to reproduce physical phenomena such as shock unsteadiness, the argument is put forward that the conventional numerical schemes, based on the Navier-Stokes equations, may be unable to generate a physically consistent turbulent stress tensor in the presence of large unresolved scales of motion. A large ratio between unresolved and resolved scales of motion, a sort of Knudsen number based on turbulent fluctuations, might introduce inaccuracies for which the turbulence model is not accountable. In order to improve the accuracy of RANS simulations, researchers have suggested various ad-hoc modifications to standard turbulence models which limit eddy viscosity or the turbulent stress tensor in the presence of strong gradients. Gas-kinetic schemes might be able to improve RANS predictions in shocklayers by removing or limiting the errors caused by the large scales ratio. These schemes are a class of their own; in the framework of a finite-volume or finite-elements discretizations, they model the numerical fluxes on the basis of the Boltzmann equation instead of the Navier-Stokes equations as is conventionally done. In practical terms, these schemes provide a higher accuracy and, more importantly, an in-built “multiscalar” mechanism, i.e. the ability to adjust to the size of unresolved scales of motion. This property makes them suitable for shock-capturing and rarefied flow. Gas-kinetic scheme may be coupled to a conventional RANS turbulence model; it is shown that the turbulent stress tensor is naturally adjusted as a function of the unresolved-to-resolved scales ratios and achieves a higher physical consistency than conventional schemes. The simulations shown - well-known benchmark cases with strong shock-boundary layer interactions - have been obtained with a standard two-equation turbulence model (k- ω). It is shown that the gas-kinetic scheme provides good quality predictions, where conventional schemes with the same turbulence model are known to fail.     

Canonical Drude Weight for Non-integrable Quantum Spin Chains

The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably, the proofs work for both integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.     

NMR Characterization of Ethylene/Propylene Copolymers and Propylene Impact Copolymers from MgCl2/TiCl4/ID+AlR3/ED Catalytic Systems

Summary: The aim of this work was to study the comonomer distribution and the chemical composition distribution generated by different Ziegler-Natta (ZN) systems (different internal donors, ID, dicyclopentadienyl-dimethoxy silane, D donor, as the external donor) and to define the potentialities of different IDs to produce improved heterophasic copolymers (HECO). A methodology to quantify the amount of ethylene-propylene copolymer (EP) portion in ZN-HECO and ethylene content of the EP portion by ¹³C-NMR was established. By using this method, it was possible to analyze the composition of ZN-HECO obtaining results comparable to those obtained with a more complex fractionation technique.     

Continuous Dependence on Initial Data in Fluid–Structure Motions

We prove a continuous dependence theorem for weak solutions of equations governing a fluid–structure interaction problem in two spatial dimensions. The proof is based on a priori estimates which, in particular, convey uniqueness of weak solutions. The estimates are obtained using Eulerian coordinates, without remapping the problem into a fixed domain.     

Numerical calculation of FSS/RSS transition in highly overexpanded rocket nozzle flows

Turbulent flow separation in over-expanded rocket nozzles is investigated numerically in a sub-scale parabolic nozzle fed with cold nitrogen. Depending upon the feeding to ambient pressure ratio either a free shock separation or a restricted shock separation is computed, with a significant hysteresis between these two flow regimes. This hysteresis was also found in experimental tests with the same nozzle geometry. The present study is mainly focused on the transition between the two shock separation patterns. The analysis of the numerical solutions aims to provide clues for the explanation of the hysteresis cycle.     

A Diene‐Containing Noncanonical Amino Acid Enables Dual Functionality in Proteins: Rapid Diels–Alder Reaction with Maleimide or Proximity‐Based Dimerization

Here, we describe a diene‐containing noncanonical amino acid (ncAA) capable of undergoing fast and selective normal electron‐demand Diels–Alder (DA) reactions following its incorporation into antibodies. A cyclopentadiene derivative of lysine (CpHK) served as the reactive handle for DA transformations and the substrate for genetic incorporation. CpHK incorporated into antibodies with high efficiency and was available for maleimide conjugation or self‐reaction depending on position in the amino acid sequence. CpHK at position K274 reacted with the maleimide drug‐linker AZ1508 at a rate of ≈79 m ^?1 s^?1 to produce functional antibody–drug conjugates (ADCs) in a one‐step process. Incorporation of CpHK at position S239 resulted in dimerization, which covalently linked antibody heavy chains together. The diene ncAA described here is capable of producing therapeutic protein conjugates with clinically validated and widely available maleimide compounds, while also enabling proximity‐based stapling through a DA dimerization reaction.     

2.1-microm lasers frequency stabilized against CO2 lines: comparison between fringe-side and frequency-modulation locking methods

A comparison between the use of the fringe-side and the frequency-modulation methods to frequency stabilize diode-pumped Tm-Ho:YAG lasers against linear absorption lines of CO2 near 2.1 microm is reported. Frequency stability was evaluated by monitoring of the beat signal between two independently stabilized Tm-Ho:YAG systems. Frequency instability levels of approximately 20 and approximately 400 kHz for 1-s integration time were achieved by the frequency-modulation and fringe-side methods, respectively.     

Gas chromatographic-tandem mass spectrometric identification of phenolic compounds in Sicilian olive oils

Phenolic compounds in Sicilian olive oils were analyzed by GC-MS and GC-MS/MS after extraction with methanol:water 80:20 and derivatization with bis(trimethylsilyl)trifluoracetamide and trimethylchlorosilane (BSTFA:TMCS 99:1). Numerous compounds were detected and 23 were identified. Tyrosol, hydroxytyrosol and the decarbomethoxy ligstroside and oleuropein aglycons in the dialdehydic forms were the most abundant compounds. 4-(Acetoxyethyl)-1-hydroxybenzene, 3,4-dihydroxyphenylacetaldehyde, syringaldehyde and the cis form of ferulic acid were identified: these compounds were not found in olive oils before. The presence of the dialdehydic form of elenolic acid (without carbomethoxy group) linked to 3-methoxy-4-hydroxyphenylethanol was hypothesized. There were quantitative differences in oils from the varieties Nocellara del Belice, Santagatese and Cerasuola; these differences could depend on the olive varieties and ripeness.     

Quasi static growth of brittle cracks in a linearly elastic flexural plate

In this paper we propose a variational model for the irreversible quasi static growth in brittle fractures for a linearly elastic homogeneous isotropic plate, subject to a time dependent vertical displacement on a part of its lateral surface. The model is based on the Griffith’s criterion for crack growth and is inspired to the model proposed in [11] by Francfort and Marigo in the case of 3-D elasticity. We give a precise mathematical formulation of the model and in this framework we prove an existence result. Mathematics Subject Classification (2000) 74K20, 35J35, 74G65, 35R35, 35A35, 74R10