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.     

An interactive system for the loading of cargo aircraft

The paper describes an interactice, computer based procedure for solving the variant of the vehicle loading problem encountered when loading containers and pallets into an aircraft. The procedure is heuristic and practical oriented; it is presently being implemented by Scandinavian Airlines.     

Electron spin polarization and conduction band structure of doped ferromagnetic semiconductors

The spin polarization of the conduction electrons of a doped semiconductor (e.g. EuO + x%Gd) is calculated using a moment method together with an alloy analogy. It is shown to be caused by a complicated temperature- and carrier concentration-dependence of the quasiparticle spectrum of the s-f model. Obtained polarization agrees very well with recent photoemission experimental data.     

The effect of the surface enhanced polariton field on the tunneling current of a STM

The influence of surface polaritons (SPs), excited on the external (fast mode) and internal (slow mode) surfaces of a gold film, on the tunneling current of a STM is investigated. The role of the surface polaritons is directly demonstrated by the angular excitation spectra of the induced tunneling current. Possible mechanisms which might give rise to the SP induced change in the tunneling current are discussed. An electromagnetic field of SPs within a tunneling gap is estimated to be surface enhanced in order to explain the value of the induced tunneling current. Images of the polariton induced signal distribution over the sample surface taken by means of different SP modes are compared in order to obtain information on the structure of the internal surface of the film.     

Ground state of the half-filled extended Hubbard model beyond the Hartree-Fock approximation

The local approach for the intraatomic correlation is applied to study the ground state phase diagram of the extended Hubbard model with a half-filled band. The long-range orders are not destroyed by the correlation effect in the limit of weak interaction, though the values of the order parameters are reduced from those of the Hartree-Fock approximation, especially for the antiferromagnetic-state. We find that the antiferromagnetic-charge order phase boundary is only slightly shifted towards the charge ordered state, while the phase boundary between the singlet superconducting and the charge ordered phases remains the same as that derived from the Hartree-Fock approximation.     

Error introduced into determination of pore size distribution by size exclusion chromatography

Simultaneous use of large standard molecules and small particles of the product examined gives rise to errors in pore size determination by size exclusion chromatography. This error is calculated for packings of spherical particles, thus making corrections possible.