Low-dimensional representations of early transition in rotating fluid flow

Low-dimensional representations of the axisymmetric Navier-Stokes equations are generated by a Galerkin projection. Proper orthogonal decomposition (POD) techniques based on snapshots generated from a finite-difference algorithm are used. The Reynolds number range is extended by adding displacement vectors to the Galerkin basis. For the fluid flow enclosed in a cylindrical vessel with rotating end cover, the first transition from steady to oscillatory motion is detected as a supercritical Hopf bifurcation. Comparison with the full numerical solution of the Navier-Stokes equations as well as experimental results show excellent agreement.One of the authors (EAC) acknowledges financial support from the Danish Research Academy (Grant S910171), the Danish Technical Research Council (Grant 16-4967-2 OS), the Louis Dreyer Myhrwold's Fund, and the Fisker & Nielsens Fund.     

Engineering competing nonlinearities

Weak modulation of a quasi-phase-matching (QPM) grating opens possibilities for engineering both the average quadratic nonlinearity and the incoherent average cubic nonlinearity induced by QPM. The relative strength of the average quadratic and effective (intrinsic plus induced) cubic nonlinearity is studied for LiNbO(3) . We show how the induced average cubic nonlinearity can be engineered to dominate the intrinsic material cubic nonlinearity and how doing so will allow the intensity at which the quadratic and cubic nonlinearities balance and thus compete to be decreased to a few gigawatts per square centimeter.     

The Moment Problem Associated with the q -Laguerre Polynomials

Abstract. We consider the indeterminate Stieltjes moment problem associated with the q -Laguerre polynomials. A transformation of the set of solutions, which has all the classical solutions as fixed points, is established and we present a method to construct, for instance, continuous singular solutions. The connection with the moment problem associated with the Stieltjes—Wigert polynomials is studied; we show how to come from q -Laguerre solutions to Stieltjes—Wigert solutions by letting the parameter α —> ∞ , and we explain how to lift a Stieltjes—Wigert solution to a q -Laguerre solution at the level of Pick functions. Based on two generating functions, expressions for the four entire functions from the Nevanlinna parametrization are obtained.     

On the collapse solution in limit analysis

The existence and regularity of collapse solutions in limit analysis of a plastic continuum is examined. Collapse fields for stresses and velocity exist as a saddle point for the duality between the static and kinematic formulations. The velocity field is defined as a pair u = (u , u ^T), where u is of bounded deformation in , while u^T is the velocity of the surface. A generalized Green's formula for the collapse fields is proved under certain regularity conditions.     

Color singlet strangelets

When considering strangelets at finite temperature it is important to obey the constraint that any observed state must be color singlet. This constraint results in an increase in strangelet masses as calculated at fixed entropy per baryon. We use the color singlet partition function for an MIT bag, derived using the group theoretical projection method, to calculate strangelet masses. Mean shell effects are included in a liquid drop model, by using a density of states obtained from the multiple reflection expansion. Another important effect of the color singlet restriction, namely many orders of magnitude suppression of thermal nucleation of quark-gluon plasma in collisions, will also briefly be described.     

Response theory for vibrational wave functions

A formalism for deriving and implementing response functions for vibrational wave functions is described. The formalism utilizes a recently developed second-quantization formulation of many-mode dynamics to define nonredundant parameterizations for different types of approximate vibrational wave functions. The derived response functions cover the cases of an exact state, a vibrational self-consistent field state, and a vibrational configuration interaction state. Sample calculations are presented for the linear-response function and response excitation energies for a two-mode model system and for formaldehyde employing a quartic force field. The advantages and disadvantages of the response theoretical approach for describing excitation energies using different parameterizations are discussed.     

Measurements of spatial cyclotron damping in a uniform magnetic field

The dispersion and damping of whistler waves has been measured in an essentially collisionless plasma at frequencies up to 0.92ω_c, the electron cyclotron frequency. The experimental results agree to within ± 10% of the plane wave hot plasma dispersion relation.     

Reflection of fluxons on a Josephson line cavity

A single fluxon on a semi-infinite Josephson line is reflected at a passive or an active termination. By numerical computation we find a single reflected fluxon, an antifluxon, absorption of the incident fluxon, or fission into an arbitrary number of fluxons depending on the boundary condition. For the passive termination an analytical approximation based on energy analysis is developed.     

Uniformly distributed sums of bernoulli variables

Sums of independent, identically distributed (iid) binomial variates have binomial distributions; yet it is possible to construct a sequence of binomial distributions over {0, 1} for variatesX ₁,X ₂, ... such that all partial sumsY _i =X ₁ + ... +X _i have uniform distributions. The price to pay is to give up the iid condition. Requiring the property of only one sum does not alleviate the situation much.It is also possible to generate on a computerm × n-matrices, of 0–1 binomial variates with uniformly distributed row and column sums of all major submatrices, but only for smallm andn. Even a three-dimensional 2 × 2 × 2 array can have a similar property.Other target distributions than the rectangular are possible, but cumbersome. An example with smaller variance is given.The results were needed for simulating the performance of some Operations Research algorithms.Dedicated to Peter Naur on the occasion of his 60th birthday     

A dual finite element complex on the barycentric refinement

A simplicial mesh on an oriented two-dimensional surface gives rise to a complex $X^{?}$ of finite element spaces centered on divergence conforming Raviart–Thomas vector fields and naturally isomorphic to the simplicial cochain complex. On the barycentric refinement of such a mesh, we construct finite element spaces forming a complex $Y^{?}$, centered around curl conforming vector fields, naturally isomorphic to the simplicial chain complex on the original mesh and such that $Y^{2?i}$ is in ${\mathrm{L}}^2$ duality with $X^i$. In terms of differential forms this provides a finite element analogue of Hodge duality. To cite this article: A. Buffa, S.H. Christiansen, C. R. Acad. Sci. Paris, Ser. I 340 (2005).