A tentative approach to the direct simulation of drag reduction by polymers

An efficient technique for drag reduction uses dilute solutions of a few p.p.m. of polymers. A possible reduction in drag of up to 80% is achieved. Several experimental observations have been made which tend to indicate that the polymers modify the turbulence structures within the buffer layer. Flow visualisations have shown that the changes consist of a weakening of the strength of the streamwise vortices. Existing literature reveals no attempts of numerical simulation of this phenomenon. In this paper an approach is pursued by using a constitutive equation which relates the elongation viscosity to the local properties of the flow. According to this model this viscosity is large in zones where the amount of strain rate is greater than the amount of vorticity, and is zero when the vorticity exceeds the strain rate. Simulations have been performed in a “minimal channel” to give good resolution with a limited number of grid points. The accuracy of the method is tested by comparison with the results of other techniques. For simulations with polymers, quantitative comparisons cannot be made, but the results reproduce the qualitative outputs of the experiments. The mean streamwise velocity is modified in the buffer layer; the peak of the streamwise turbulent intensity, in wall units, increases and its maximum moves far from the wall; and the vertical turbulent intensity is largely reduced in the wall region. An interesting outcome from both the simulation and the experiments is that the strength of the longitudinal vortices is reduced when the polymers are present.     

Damage spreading in a single-component irreversible reaction process: Dependence of the system's immunity on the Euclidean dimension

The spreading of a globally distributed damage, created in the stationary regime, is studied in a single-component irreversible reaction process, i.e., the BK model [Browne and Kleban,Phys. Rev. A 40, 1615 (1989)]. The BK model describes one variant of the A+AA₂ reaction process on a lattice in contact with a reservoir of A species. The BK model has a single parameter, namely the rate of arrival of A species to the lattice (Y). The model, exhibits an irreversible phase transition between a stationary reactive state with production of A₂ species and a poisoned state with the lattice fully covered by A species. The transition takes place at critical points (Y _C ) which solely depend on the Euclidean dimensiond. It is found that the system is immune ford=1 andd=2, in the sense that even 100% of initial damage is healed within a finite healing period (T _H ). Within the reactive regime,T _H diverges when approachingY _C according toT _H (Y _C –Y)^–, with 1.62 and 1.08 ford=1 andd=2, respectively. Ford=3 a frozen-chaotic transition is found close toY _s 0.4125, i.e., well inside the reactive regime 0YY _C 0.4985. Just atY _S the damageD(t) heals according toD(t) t ^–, with 0.71. For the frozen-chaotic transition atd=3 the order parameter critical exponent 0.997 is determined.     

Homotopy types for tamely approximable Sobolev maps between manifolds

We define a class ^p (M,N) of Sobolev maps from a manifoldM into a manifoldN, in such a way that each mapu ^p (M, N) has a well defined [p]-homotopy type, providedN satisfies a topological hypothesis. Using this, we prove the existence of minimizers in [p]-homotopy classes for some polyconvex variational problems.     

Vortex rings interacting with a wall

Accurate numerical simulations of vortex rings impinging on flat boundaries have revealed the same features observed in the experiment of Walkeret al. (1987). They observed atRe _v >1250 the formation of azimuthal instabilities in the secondary ring during its compression within the primary ring. In the present numerical simulation the number of waves agrees very well with those observed in the experiment. The distributions of the vorticities together with the distribution of each term in the vorticity equations give insights on the formation of azimuthal instabilities.     

Interfaces and typical Gibbs configurations for one-dimensional Kac potentials

Summary We consider a one dimensional Ising spin system with a ferromagnetic Kac potential J(|r|),J having compact support. We study the system in the limit, »0, below the Lebowitz-Penrose critical temperature, where there are two distinct thermodynamic phases with different magnetizations. We prove that the empirical spin average in blocks of size ^–1 (for any positive ) converges, as »0, to one of the two thermodynamic magnetizations, uniformly in the intervals of size ^–p , for any given positivep1. We then show that the intervals where the magnetization is approximately constant have lengths of the order of exp(c ^–1),c>0, and that, when normalized, they converge to independent variables with exponential distribution. We show this by proving large deviation estimates and applying the Ventsel and Friedlin methods to Gibbs random fields. Finally, if the temperature is low enough, we characterize the interface, namely the typical magnetization pattern in the region connecting the two phases.The research has been partially supported by CNR, GNFM, GNSM and by grant SC1CT91-0695 of the Commission of European Communities     

Vibronic intensity borrowing. Deuterium effect and emission—absorption asymmetry of the S1---S0 transition in pyrene

The intensities of the vibrationally induced bands in the S₁---S₀ emission and absorption spectra of pyrene-h₁₀ and -d₁₀ are measured and analysed. Several new expressions are reported which relate the deuterium effect and emission—absorption asymmetry of induced spectra to the vibronic coupling mechanism.     

Flow injection analysis: Rayleigh light scattering technique for total protein determination

A novel flow injection analysis (FIA) method with Rayleigh light scattering (RLS) detection was developed for the determination of total protein concentrations. This method is based on the weak intensity of RLS of bromothymol blue (BB) (3',3"-dibromothymolsulfonephthalein) which can be enhanced by the addition of protein in weakly acidic solution. A common spectrofluorimeter was used as a detector. It was proved that the application of this method to quantify the total proteins in real samples by using bovine serum albumin was possible. The RLS signal was detected at lambda(ex)= lambda(em)=572 nm. The linear range was 7.0-70.0 microg mL(-1), the detection limit was 3.75 microg mL(-1), the reproducibility was 5.5% (n=7), and the sample throughput was 26 h(-1).     

A theoretical study of the lowest electronic states of azobenzene: the role of torsion coordinate in the cis–trans photoisomerization

In the present paper we report the results of a multiconfigurational computational study on potential-energy curves of azobenzene along the NN twisting to clarify the role of this coordinate in the decay of the S₂(*) and S₁(n*) states. We have found that there is a singlet state, S₃ at the trans geometry, on the basis of the doubly excited configuration n²*², that has a deep minimum at about 90° of twisting, where it is the lowest excited singlet state. The existence of this state provides an explanation for the short lifetime of S₂(*) and for the wavelength-dependence of azobenzene photochemistry. We have characterized the S₁(n*) state by calculating its vibrational frequencies, which are found to correspond to the recently observed transient Raman spectrum. We have also computed the potential-energy curve for the triplet T₁(n*) at the density functional theory B3LYP level, which indicates that in this state the isomerization occurs along the twisting coordinate.Acknowledgement The financial support from MIUR (project Modellistica delle proprietà spettroscopiche di sistemi molecolari complessi funds ex 60% and project Dinamiche molecolari in sistemi di interesse chimico funds ex 40%), from the University of Bologna (Funds for Selected Research Topics) is gratefully acknowledged.Contribution to the Jacopo Tomasi Honorary Issue     

NEMCA effect: why are the work function changes of the gas exposed catalyst-electrode surface one-to-one related to the changes in the catalyst working electrode potential?

In the present work, an important point concerning the NEMCA effect is addressed. We analyse the reasons why the changes in the work function of the gas exposed catalyst-electrode surface are one to one related to the changes in the catalyst working electrode potential E with respect to a reference electrode. It is concluded that this is due to the unique properties of the catalyst/solid electrolyte interface: the structure of the double layer in this region is very different from that in liquid electrolytes, being the potential difference at this interface mainly determined by the specific adsorption of the mobile species in the solid electrolyte.

Complex Tellurium Salts with Supramolecular Bidimensional Lattices: Synthesis and X‐ray Characterization of (2‐Br‐C5NH5)2[TeX6] (X = Cl,Br)

The reaction of tellurium(IV) tetrahalides with hydrochloric and hydrobromic acid leads to the formation of (H₃O)₂[TeX₆], which reacts subsequently with (2‐Br‐C₅NH₅)⁺X^‐ to afford (2‐Br‐C₅NH₅)₂[TeCl₆] ( 1 ) and (2‐Br‐C₅NH₅)₂[TeBr₆] ( 2 ). The structure of the complex salts were analysed by X‐ray diffractometry affording the centrosymmetric space groups P2₁/n (monoclinic, 1 ) and P1¯ (triclinic, 2 ). Interionic hydrogen bondings hold their lattices in bidimensional supramolecular arrays not yet described in the literature. The lone electron pair of the AX₆E‐system of the hexahalotellurates [TeX₆]^2‐ (X = Cl, Br) seems to be fully delocalized since only small octahedral deviations were observed for the anionic species. The structures of the title compounds were refined with the Te atoms occupying sites with full point symmetry, approximately m3¯m. In both cases the Te atoms enclose centers of inversion and the octahedrally dynamic structures are enforced and stabilized along the supramolecular lattices by the crystal field of the 2‐Br‐pyridinium cations.