Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

Growth of 1-Periodic Graphs

A new class of graphs is introduced: 1-periodic graphs. A problem on the form of the growth of these graphs is stated. For certain classes of graphs, a self-similar growth in the form of a polygon is proved. Certain general conjectures on the form of the growth are stated. Bibliography: 1 title.     

Fixed points in the family of convex representations of a maximal monotone operator

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exists a convex representation of the operator which is a fixed point of this conjugation.

     

The role of As2O3 on the stability and some physical properties of PbO-Sb2O3 glasses

PbO-Sb₂O₃ glasses added with different concentrations of As₂O₃ (10-55 mol%) were prepared to understand their IR spectra, elastic properties (Young's modulus E, Shear modulus G, microhardness H), optical absorption and dielectric properties (constant ε, loss tan δ, ac conductivity σ_ac over a moderately wide range of frequency and temperature and breakdown strength in air medium at room temperature). Results have indicated that the structure of the PbO-Sb₂O₃-As₂O₃ glass is more rigid when the concentration of As₂O₃ is around 40 mol%.     

Deformed Quantum Calogero-Moser Problems and Lie Superalgebras

The deformed quantum Calogero-Moser-Sutherland problems related to the root systems of the contragredient Lie superalgebras are introduced. The construction is based on the notion of the generalized root systems suggested by V. Serganova. For the classical series a recurrent formula for the quantum integrals is found, which implies the integrability of these problems. The corresponding algebras of the quantum integrals are investigated, the explicit formulas for their Poincare series for generic values of the deformation parameter are presented.     

Collisional parameters of H2O lines: effects of vibration

A complex semiclassical model for the calculation of line widths and shifts of H₂O broadened by N₂, derived from the Robert and Bonamy approach, is tested by comparisons with measurements for selected transitions in various vibrational bands. The lines retained, which involve rotational states with Kc=J or J−1 have been chosen for two reasons. The first is that they show large variations of the widths with J and thus enable a severe test of the model. The second is that, as explained in this paper, they are well-suited for the study of the effects of vibration on the collisional parameters. The measured values have been extracted from an updated version of a database built years ago (JQSRT 52 (1994) 481) that contains all available measurements. Comparisons between experimental and calculated widths and shifts at room temperature illustrate the quality of the model and clearly demonstrate, for the first time, that there is a vibrational dependence of the broadening. Values of collisional parameters are first studied in fundamental bands. This shows that the theoretical approach accounts for most of the dependence of broadening and shifting on rotational quantum numbers: the variations of γ, which reach a factor of nearly 20 from low to high J values, are correctly accounted for by the model as are some specific features of the shifts δ. Analysis confirms that the bending and stretching vibrations have significantly different effects on δ, due to the vibrational dependence of the intermolecular potential. On the other hand, differences on the widths are rather small with slightly smaller broadening for lines of the bending band. Calculations show that there is a spectroscopic effect, due to the larger rotational constant A in the v₂=1 state. Calculations made for overtone bands involving numerous quanta of the stretching vibration are then presented. They predict that a significant dependence of the width should be observed for high J lines due to the effect of vibration on the interaction potential. This is confirmed by comparisons with measurements for lines involving a change of three and four quanta of stretching vibration.     

Fourier-Feynman transform, convolution and first variation

We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral. This revised version was published online in June 2006 with corrections to the Cover Date.     

Methods for implementing the stream boundary condition in DSMC computations

In the direct simulation Monte‐Carlo (DSMC) method for simulating rarefied gas flows, the velocities of simulator particles that cross a simulation boundary and enter the simulation space are typically generated using the acceptance–rejection procedure that samples the velocities from a truncated theoretical velocity distribution that excludes low and high velocities. This paper analyses an alternative technique, where the velocities of entering particles are obtained by extending the simulation procedures to a region adjacent to the simulation space, and considering the movement of particles generated within that region during the simulation time step. The alternative method may be considered as a form of acceptance–rejection procedure, and permits the generation of all possible velocities, although the population of high velocities is depleted with respect to the theoretical distribution. Nevertheless, this is an improvement over the standard acceptance–rejection method. Previous implementations of the alternative method gave a number flux lower than the theoretical number required. Two methods for obtaining the correct number flux are presented. For upstream boundaries in high‐speed flows, the alternative method is more computationally efficient than the acceptance–rejection method. However, for downstream boundaries, the alternative method is extremely inefficient. The alternative method, with the correct theoretical number flux, should therefore be used in DSMC computations in favour of the acceptance–rejection method for upstream boundaries in high‐speed flows. Copyright © 2003 John Wiley & Sons, Ltd.     

Computing Zeta Functions of Kummer Curves via Multiplicative Characters

We present a practical polynomial-time algorithm for computing the zeta function of a Kummer curve over a finite field of small characteristic. Such algorithms have recently been obtained using a method of Kedlaya based upon Monsky–Washnitzer cohomology, and are of interest in cryptography. We take a different approach. The problem is reduced to that of computing the L-function of a multiplicative character sum. This latter task is achieved via a cohomological formula based upon the work of Dwork and Reich. We show, however, that our method and that of Kedlaya are very closely related.Dedicated to the memory of Gian-Carlo Rota