On the entrainment assumption in Schatzmann’s integral plume model

The behaviour of stationary, non-passive plumes can be simulated in a reasonably simple and accurate way by integral models. One of the key requirements of these models, but also one of their less well-founded aspects, is the entrainment assumption, which parameterizes turbulent mixing between the plume and the environment. The entrainment assumption developed by Schatzmann and adjusted to a set of experimental results requires four constants and an ad hoc hypothesis to eliminate undesirable terms. With this assumption, Schatzmann’s model exhibits numerical instability for certain cases of plumes with small velocity excesses, due to very fast radius growth. The purpose of this paper is to present an alternative entrainment assumption based on a first-order turbulence closure, which only requires two adjustable constants and seems to solve this problem. The asymptotic behaviour of the new formulation is studied and compared to previous ones. The validation tests presented by Schatzmann are repeated and it is found that the new formulation not only eliminates numerical instability but also predicts more plausible growth rates for jets in co-flowing streams.     

Hitting, returning and the short correlation function

We consider a stochastic process with the weakest mixing condition: the so called α. For any fixed n-string we prove the following results. (1) The hitting time has approximately exponential law. (2) The return time has approximately a convex combination between a Dirac measure at the origin and an exponential law. In both cases the parameter of the exponential law is λ(A)ℙ(A) where ℙ(A) is the measure of the string and λ(A) is a certain autocorrelation function of the string. We show also that the weight of the convex combination is approximately λ(A). We describe the behavior of this autocorrelation function. Our results hold when the rate of mixing decays polinomially fast with power larger than the golden number.     

Flow birefringence studies of a concentrated polystyrene solution in a two-roll mill. I. Steady flow and start-up of steady flow

We have studied a 4.8 volume percent solution of a narrow distribution polystyrene with molecular weight 3.84 × 10⁶ in flows generated by a co-rotating two-roll mill. These flows have a stagnation point at the midpoint between the roller axes. Further, they are linear, two-dimensional, and the magnitudes of the strain-rates are greater than the vorticity. The overall objective of our studies is to explore the dynamics of concentrated polymer solutions which are in the highly deformed state that is generated in the two-roll mill. Birefringence data are presented for both steady flow and start-up of steady flow in the two-roll mill. The steady and transient data are used to analyze the linear and nonlinear viscoelastic regions of material behavior. In the nonlinear regime, the birefringence upon start-up shows an initial overshoot followed by a strong undershoot that is enhanced as the ratio of elongation to rotation is increased (i.e., the flow becomes increasingly extensional in character.) We attribute this undershoot, which does not seem to appear in simple shear flows, or flows close to simple shear flow, to polymer segment stretching following an initial period of segment reorientation. Model studies are currently underway to test this notion. © 1992 John Wiley & Sons, Inc.     

Acoustic voice analysis in patients with Parkinson''s disease treated with dopaminergic drugs

To quantify several acoustic features of the voice in patients withParkinson's disease (PD), 41 patients and 28 age and sex-matched controls were studied. PD severity was assessed with the Unified PD Rating Scale (UPDRS) and the Hoehn and Yahr staging. The Computerized Speech Lab 4300 program (Kay Elemetrics) was used. Two seconds of a sustained /a/ and a sentence were captured with a microphone and laryngograph equipment. Measures included fundamental frequency (FO), frequency perturbation (fitter), intensity perturbation (shimmer), and harmonic/noise ratio (H/N) of the vowel /a/, and frequency and intensity variability of a sentence, phonational range, dynamic range at the natural frequency, maximum phonational time and s/z ratio. All subjects underwent indirect laryngoscopy and/or laryngeal fibroscopy. When compared with controls, PD patients showed higher jitter, lower H/N ratio, lower frequency and intensity variability of the sentence, and lower phonational range and reported a higher frequency of the presence of low voice-intensity, monopitch, voice arrests, and struggle. These features seem to be unaffected by the duration and severity of the disease.     

Straightforward α-carbamoylation of NADH-like dihydropyridines and enol ethers

The protonation of NADH-like dihydropyridines and cyclic enol ethers generates reactive cationic intermediates, which interact with isocyanides to afford α-carbamoylated heterocycles after an aqueous quenching, in Ugi and Passerini-type reactions, thus broadening the scope of these multicomponent processes.     

Hybrid Modelling for Robust Solving

We study a balanced academic curriculum problem and an industrial steel mill slab design problem. These problems can be modelled in different ways, using both Integer Linear Programming (ILP) and Constraint Programming (CP) techniques. We consider the utility of each model. We also propose integrating the models to create hybrids that benefit from the complementary strengths of each model. Experimental results show that hybridization significantly increases the domain pruning and decreases the run-time on many instances. Furthermore, a CP/ILP hybrid model gives a more robust performance in the face of varying instance data.     

Functionalisation of unactivated methyl groups through cyclopalladation reactions

The transformation of the organopalladium compound (3) into the corresponding deuteriated, chlorinated, or oxidized derivatives (7), (8), or (9), (11), and (12) respectively. is described. The palladation of compound (9) takes place regioselectively leading to the palladated system (13), which is transformed into the difunctionalised oximes (15) and (16). The palladation of $\text{E}$-2,2-dimethyl and 2,2,6,6-tetramethyl-cyclohexanone oxime leads to the corresponding organopalladium compounds (17) and (27), which through deuteriation or oxidation affords the expected products (21) and (31), or (22), (23), (24), and (32), respectively. The second palladation of the compound (22) takes place on the remaining methyl group yielding the organopalladium derivative (26). Finally, $\text{E}$-lupanone oxime is palladated selectively in the 23-position leading to the organopalladium compound (38); the transformation of this compound into its 23-deuterio and 23-acetoxy- derivatives (41) and (42), respectively is also described. The stereochemistry in the palladatlon of lupanone oxime is deduced from NOE studies at 500 MHz.     

The relative deformation tensor for small displacements in general relativity

By means of the world-function, an approximate formula for the relative deformation tensor of an elastic continuum in a space-time opf finite curvature is obtained. The coordinate displacements are supposed to be small with respect to the characteristic measure of the geodesic joining an arbitrary point of that continuum and a fixed point of the space-time. The formula contains all the terms up to the third order of approximation with respect to this geodesic measure, which is the basis of the approximation.     

Fourth-order orbital equations in stationary weak gravitational fields

The equations of motion in fourth approximation for gravitational bodies are used to obtain orbital equations, first integrals, differential equations for the corresponding trajectories, and fourth-order contributions to the orbital motions in stationary weak gravitational fields.