We show for the first time that only one similarity solution describes break-up of viscous liquid threads is linearly stable, while other solutions are unstable. Complex eigenvalues lead to presence oscillations close break-up.

Nonlinear dynamical systems described by a class of higher index differential-algebraic equations (DAE) are considered. A quantitative and qualitative analysis of their nature and of the stability properties of their solution is presented. Using tools from geometric control theory, higher index differential-algebraic systems are shown to be inherently unstable about their solution manifold. A q...

Recently a number of adaptive learning algorithms have been proposed for blind source separation. Although the underlying principles and approaches are di erent, most of them have very similar forms. Two important issues have remained to be elucidated further: the statistical e ciency and the stability of learning algorithms. The present letter analyzes a general form of statistically e cient a...

The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbati...

Existence and uniqueness theorems for unstable manifolds are well-known. Here we prove certain refinements. Let f : (C, 0) → C be a germ of an analytic diffeomorphism, whose derivative Df(0) has eigenvalues λ1, . . . , λn such that |λ1| ≥ · · · ≥ |λk| > |λk+1| ≥ · · · ≥ |λn|, with |λk| > 1. Then there is a unique k-dimensional invariant submanifold whose tangent space is spanned by the generali...

Knowledge of the relaxation spectrum is important because (I) it provides an intrinsic characterization of the mechanical properties for linearly viscoelastic materials and (.%‘) it offers a rational way to derive the coefficients for a Prony or Dirichlet series representation of the relaxation modulus of importance to some engineering analyses. A numerical solution based on Simpson quadrature ...

We consider the elliptic equation −∆u = f(u) in the whole R , where f is of bistable type. It is known that there exists a saddleshaped solution in R. This is a solution which changes sign in R and vanishes only on the Simons cone C = {(x, x) ∈ R×R : |x| = |x|}. It is also known that these solutions are unstable in dimensions 2 and 4. In this article we establish that when 2m = 6 every saddle-s...