Linear oscillations of axisymmetric viscous liquid bridges

Small amplitude free oscillations of axisymmetric capillary bridges are considered for varying values of the capillary Reynolds number C-1 and the slenderness of the bridge Λ . A semi-analytical method is presented that provides cheap and accurate results for arbitrary values of C-1 and Λ ; several asymptotic limits (namely, C>> 1, C>>1, Λ >> 1 \ {and} \ |π -Λ |>> 1 ) are considered in some detail, and the associated approximate results are checked. A fairly complete picture of the (fairly complex) spectrum of the linear problem is obtained for varying values of C and Λ . Two kinds of normal modes, called capillary and hydrodynamic respectively, are almost always clearly identified, the former being associated with free surface deformation and the latter, only with the internal flow field; when C is small the damping rate associated with both kind of modes is comparable, and the hydrodynamic ones explain the appearance of secondary (steady or slowly-varying) streaming flow

A note on the effect of surface contamination in water wave damping

Asymptotic formulas are derived for the effect of contamination on surface wave damping in a brimful circular cylinder; viscosity is assumed to be small and contamination is modelled through Marangoni elasticity with insoluble surfactant. It is seen that an appropriately chosen finite Marangoni elasticity provides an explanation for a significant amount of the unexplained additional damping rate in a well-known experiment by Henderson & Miles (1994); discrepancies are within 15%, significantly lower than those encountered by Henderson & Miles (1994) under the assumption of inextensible film

Extended D=3D=3 Bargmann supergravity from a Lie algebra expansion

In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from $D=3$, $\mathcal{N}=2$ superPoincar\'e and its corresponding Chern-Simons supergravity.Comment: 17 page

Dynamics of nearly unstable axisymmetric liquid bridges

The dynamics of a noncylindrical, axisymmetric, marginally unstable liquid bridge between two equal disks is analyzed in the inviscid limit. The resulting model allows for the weakly nonlinear description of both the (first stage of) breakage for unstable configurations and the (slow) dynamics for stable configurations. The analysis is made for both slender and short liquid brides. In the former range, the dynamics breaks reflection symmetry on the midplane between the supporting disks and can be described by a standard Duffing equation, while for short bridges reflection symmetry is preserved and the equation is still Duffing-like but exhibiting a quadratic nonlinearity. The asymptotic results compare well with existing experiments

Efficient state reduction methods for PLA-based sequential circuits

Experiences with heuristics for the state reduction of finite-state machines are presented and two new heuristic algorithms described in detail. Results on machines from the literature and from the MCNC benchmark set are shown. The area of the PLA implementation of the combinational component and the design time are used as figures of merit. The comparison of such parameters, when the state reduction step is included in the design process and when it is not, suggests that fast state-reduction heuristics should be implemented within FSM automatic synthesis systems

Weakly nonlinear nonaxisymmetric oscillations of capillary bridges at small viscosity

Weakly nonlinear nonaxisymmetric oscillations of a capillary bridge are considered in the limit of small viscosity. The supporting disks of the liquid bridge are subjected to small amplitude mechanical vibrations with a frequency that is close to a natural frequency. A set of equations is derived for accounting the slow dynamics of the capillary bridge. These equations describe the coupled evolution of two counter-rotating capillary waves and an associated streaming flow. Our derivation shows that the effect of the streaming flow on the capillary waves cannot be a priori ignored because it arises at the same order as the leading (cubic) nonlinearity. The system obtained is simplified, then analyzed both analytically and numerically to provide qualitative predictions of both the relevant large time dynamics and the role of the streaming flow. The case of parametric forcing at a frequency near twice a natural frequency is also considere