Multivariate stochastic delay differential equations and CAR representations of CARMA processes

In this study we show how to represent a continuous time autoregressive moving average (CARMA) as a higher order stochastic delay differential equation, which may be thought of as a CAR($\infty$) representation. Furthermore, we show how the CAR($\infty$) representation gives rise to a prediction formula for CARMA processes. To be used in the above mentioned results we develop a general theory for multivariate stochastic delay differential equations, which will be of independent interest, and which will have particular focus on existence, uniqueness and representations.     

Tetraethylammonium chloride tetrahydrate,a ‘double channel’ host lattice constructed from (H2O)4Cl− tetrahedra linked between vertices

Crystals of (C₂H₅)₄NCl·4H₂O are orthorhombic, space groupCcca, witha=19.104(3),b=23.084(4),c=13.330(3) , andZ=16. The structure features an anionic host lattice constructed from the linkage of (H₂O)₄Cl^– tetrahedra by hydrogen bonds between vertices, generating two open linear channel systems which accommodate the ordered cations. FinalR _F =0.080 for 1516 observed MoK data measured at 22°C. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82035 (12 pages)Dedicated to Professor G. A. Jeffrey     

On the accuracy of two-dimensional photoelastic experiments in which uniform edge loading is obtained by the inflatable-tubing technique

Good agreement is reported between newly acquired numerical solutions and previously obtained photoelastic solutions for hollow hexagons under external pressure on three and six sides. A procedure is discussed for calibration of pressure by means of shear-stress measurements directly on the model being analyzed.     

Rheology of Polydisperse Star Polymer Melts: Extension of the Parameter‐Free Tube Model of Milner and McLeish to Arbitrary Arm‐Length Polydispersity

Summary: This paper considers the extension of the parameter‐free tube model of Milner and McLeish for stress relaxation in melts of monodisperse star polymers to star polymers whose arms have a continuous molecular weight distribution such as the Flory distribution in the case of star‐nylons and star‐polyesters. Exact expressions are derived for the relaxation spectrum and the relaxation modulus for star polymers having an arbitrary continuous arm‐length distribution. For a Flory distribution a comparison is made with results of dynamic measurements on a melt of 8‐arm poly(ε‐caprolactone) (PCL) stars. An excellent quantitative agreement over a large frequency range is found, however, only if one treats, in contrast with the original parameter‐free tube model approach, the entanglement molecular weight that determines the relaxation spectrum as a fitting parameter independent of the entanglement molecular weight of the linear PCL. This discrepancy is not in anyway related to the polydispersity in arm‐length, but a consequence of the thermorheological complexity of the PCL stars. A similar discrepancy has been observed for hydrogenated polybutadiene stars, as described by Levine and Milner.

Measured and calculated storage moduli G′ as a function of frequency ω.     

Experiments on the Flow Field and Acoustic Properties of a Mach number 0·75 Turbulent Air Jet at a Low Reynolds Number

In this paper we present the experimental results of a detailed investigation of the flow and acoustic properties of a turbulent jet with Mach number 0·75 and Reynolds number 3·5 10³. We describe the methods and experimental procedures followed during the measurements, and subsequently present the flow field and acoustic field. The experiment presented here is designed to provide accurate and reliable data for validation of Direct Numerical Simulations of the same flow. Mean Mach number surveys provide detailed information on the centreline mean Mach number distribution, radial development of the mean Mach number and the evolution of the jet mixing layer thickness both downstream and in the early stages of jet development. Exit conditions are documented by measuring the mean Mach number profile immediately above the nozzle exit. The fluctuating flow field is characterised by means of a hot-wire, which produced radial profiles of axial turbulence at several stations along the jet axis and the development of flow fluctuations through the jet mixing layer. The axial growth rate of the jet instabilities are determined as function of Strouhal number, and the axial development of several spectral components is documented. The directivity of the overall sound pressure level and several spectral components were investigated. The spectral content of the acoustic far field is shown to be compatible with findings of hot-wire experiments in the mixing layer of the jet. In addition, the measured acoustic spectra agree with Tam’s large-scale similarity and fine-scale similarity spectra (Tam et al., AIAA Pap 96, 1996).