On the use of Helmholtz resonators as sound attenuators

Summary In the present paper a nonlinear acoustic theory is proposed, to accurately describe the properties of a generalized type of Helmholtz resonators. The theory may be used as a layout tool to design sound attenuators for combustion facilities. The present investigation shows that, in addition to the nonlinear effects, the effects due to thermoacoustic boundary layers and the first frequency correction to the Helmholtz approximation should be taken into account, in order to predict the frequency-dependent attenuation properties of Helmholtz attenuators with the accuracy required by typical technical applications. A series of experiments is presented which is used to validate the theoretical predictions.

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Zusammenfassung In der vorliegenden Abhandlung wird eine nichtlineare akustische Theorie vorgeschlagen, mit der das Verhalten einer verallgemeinerten Art von Helmholtzresonatoren beschrieben werden kann. Die Theorie kann als Werkzeug zur Auslegung von Schalldämpfern für Verbrennungsanlagen benutzt werden. Die vorliegende Arbeit zeigt, dass neben den nichtlinearen Effekten auch die Einflüsse der thermoakustischen Grenzschichten und der ersten Frequenzkorrektur zur Helmholtzapproximation berücksichtigt werden müssen, damit die frequenzabhängigen Eigenschaften von Helmholtzdämpfern mit technisch ausreichender Genauigkeit beschrieben werden können. Mit einer Reihe von Experimenten werden die theoretischen Ergebnisse untermauert.

     

Exponential weak Bernoulli mixing for collet-eckmann maps

We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK] and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim , wherec is the unique critical point ofT.     

Local Borel summability of Euclidean 311-1311-1311-1a simple proof via differential flow equations

It is shown how the differential flow equation (or, equivalently, the continous renormalization group) method can be employed to give an astonishingly easy proof of the local Borel summability of the renormalized perturbative Euclidean massive ₄ ⁴ .Supported by NSF grant # DMS-9100383     

Shape-tunable polymer nodules grown from liposomes via ring-opening metathesis polymerization

A new inisurf (acting as surfactant and initiator) molecule for ring-opening metathesis polymerization (ROMP) was synthesized and used in aqueous solution in order to control the size and shape of polymer nodules grown from liposomes. Nodules were observed to grow in size with conversion of monomer, and depending on the monomer used, they adopted either a spherical or comet-like shape. Here, we investigate polymer production from a liposome surface. We use a hydrophobic derivative of the Grubbs catalyst positioned at the liposome surface to allow for ROMP of monomers dissolved in the aqueous outer phase. We obtain nodules of polymer that can grow up to tens of micrometers, unveiling new efficient possibilities of polymerization from a membrane in an aqueous solution.     

Structure and reactivity of xanthocorrinoids. Part V. Formation of trans-diol derivatives of 5,6-dihydrocobyrinic acid from xanthocorrinoids under acidic conditions

On treatment with H₂SO₄/MeOH, epimerization of hexamethyl cis-5,6-dihydroxycobyrinate c,8-lactam ( 3 ) takes place quantitatively at C(6), yielding the corresponding trans-diol 4 . The corresponding lactone 7 , whose structure has been established by X-ray analysis, is obtained from xanthocorrinoids 5 and 6 under similar conditions.     

Low frequency Raman spectroscopic study on lamellar polymer crystals

The recently observed very low-frequencyRaman bands in polyethylene open up the possibility of determining the straight-chain stem lengths within the crystal as opposed to the full periodicity constituted by crystal core plus amorphous surface layer given by lowangle X-ray diffraction. Past works (6–10) have established the correlation with lamellar thickness but leave doubts about the possibility of making the distinction just indicated. The first objective of the present work was to examine this point on crystals where the chains are inclined to different extents with respect to the lamellar surface. The samples include single-crystals grown from solution at different temperatures and oriented bulk polyethylenes. It is concluded that the low-frequencyRaman peaks correspond to the inclined chain length as opposed to the layer thickness, hence providing a measure of a chain as opposed to a platelet property. TheRaman based length figures are only slightly below those of the appropriately inclined straight traverses across the full lamellae, hence on the basis of existing understanding non-trans chain sequences are confined to a surface region which must be much narrower than required by the usually envisaged amorphous crystalline two-phase structure. Similar studies were carried out also on single crystals of the linear polyester poly(decamethylene sebacate). These demonstrate in the first place that polymers other than polyethylene can also be amenable to suchRaman studies and secondly that in this particular instance, changes in the relative thicknesses of crystal core and surface layer could be registered. The two studies in conjunction affirm the potential of the low-frequencyRaman technique for the study of polymer crystal morphology.