Design and use of an electronic speckle pattern interferometer for testing of turbine parts

The construction and use of an electronic speckle pattern interferometer for vibration testing of critical gas turbine parts in the factory, is described.     

Rubber networks containing unattached macromolecules. III. Nonlinear stress relaxation in the system ethylene–propylene terpolymer with ethylene–propylene copolymer and behavior of extracted networks

Further stress relaxation experiments, mostly at 50°C, are reported on mixtures of crosslinkable ethylene–propylene terpolymer with saturated ethylene–propylene copolymer (molecular weights 3.6 and 45 × 10⁴) containing up to 50% by weight of copolymer, crosslinked by sulfur to leave the saturated copolymer unattached and free to reptate in the copolymer network. Stress relaxation was measured in small simple elongations (stretch ratio about 1.15) on samples which had been extracted to remove a large part of the unattached copolymer and dried. The relative increase in modulus at long times (10⁴ sec) increased with the proportion extracted; at short times (1 sec), extraction of the lower molecular weight copolymer increased the modulus to about the same extent but extraction of the higher molecular weight copolymer affected it very little. The relaxation modulus of the copolymer extracted from sample 50H (50% copolymer of high molecular weight), obtained by difference, agreed with that for the total copolymer except for a small difference probably attributable to molecular weight selectivity in the extraction. Stress relaxation was measured on sample 50H at six higher elongations up to a stretch ratio of 3. The dependence of stress on time and strain was consistent with an analysis based on the following assumptions: (a) linear additivity of the network and unattached copolymer contributions, (b) strain–time factorization of the stress contributions from the individual components, (c) a strain dependence for the unattached component corresponding to the presence of a Mooney–Rivlin C₂ term only, (d) a strain dependence for the network component which does not follow the Mooney–Rivlin equation but is dominated by a simple neo-Hookean term.     

Angular focusing of acoustoelectrically active phonons in ZnO and CdS at 300K

The energy focusing of a uniform angular distribution of quasi-transverse acoustic phonons has been investigated. It is found that the energy enhancement above the average value in certain crystallographic directions depends strongly on the normalized phonon frequency, v/?_m.     

Performance improvement of direct detection systems using local and/or long-distance pumped fiber amplifiers

Erbium-doped fiber amplifiers (EDFAs) in eight different system configurations are investigated, using a full-scale model, and the midline placement of the amplifier is shown to be optimal. A distributed amplifier compared to the remote pumping scheme shows no system improvement. Use of a booster (next to the transmitter), a midline remote-pumped amplifier, and a preamplifier (next to the receiver) allows up to 180 km of extra transmission fiber to be added.     

Kinetic theory and rheology of dilute polymer solutions

Summary A summary is given of some recent attempts to relate the results of the kinetic theory of rigid and flexible macromolecules to continuum mechanics results.With 1 table     

Positivity preserving transformations for -binomial coefficients

Several new transformations for -binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving transformations, as well as their connection with the Bailey lemma, many new summation and transformation formulas for basic hypergeometric series are found. The new -binomial transformations are also applied to obtain multisum Rogers-Ramanujan identities, to find new representations for the Rogers-Szegö polynomials, and to make some progress on Bressoud's generalized Borwein conjecture. For the original Borwein conjecture we formulate a refinement based on new triple sum representations of the Borwein polynomials.

     

<Emphasis Type="Italic">q</Emphasis>-Selberg Integrals and Macdonald Polynomials

Using the theory of Macdonald polynomials, a number of q-integrals of Selberg type are proved. 2000 Mathematics Subject Classification: Primary—33D05, 33D52, 33D60     

Existence proof for orthogonal dynamics and the Mori-Zwanzig formalism

We study the existence of solutions to the orthogonal dynamics equation, which arises in the Mori-Zwanzig formalism in irreversible statistical mechanics. This equation generates the random noise associated with a reduction in the number of variables. IfL is the Liouvillian, or Lie derivative associated with a Hamiltonian system, andP an orthogonal projection onto a closed subspace ofL ², then the orthogonal dynamics is generated by the operator (I −P)L. We prove the existence of classical solutions for the case whereP has finite-dimensional range. In the general case, we prove the existence of weak solutions.