Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Cryopreservation of winter-dormant apple buds: 1 - variation in recovery with cultivar and winter conditions

The widely-adopted protocol for the cryopreservation of winter buds of fruit trees, such as Malus and Pyrus, was developed in a region with a continental climate, that provides relatively hard winters with a consequent effect on adaptive plant hardiness. In this study the protocol was evaluated in a typical maritime climate (eastern Denmark) where milder winters can be expected. The survival over two winters was evaluated, looking at variation between seasons and cultivars together with the progressive reduction in survival due to individual steps in the protocol. The study confirms that under such conditions significant variation in survival can be expected and that an extended period of imposed dehydration at -4oC is critical for bud survival. The occurrence of freezing events during this treatment suggests that cryodehydration may be involved, as well as evaporative water loss. To optimize the protocol for maritime environments, further investigation into the water status of the explants during cryopreservation is proposed. Keywords: Malus x domestica, cryopreservation, dormant bud, survival, grafting