Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

On the force potential of strategy texts: a critical discourse analysis of a strategic plan and its power effects in a city organization

Despite increasing interest in the discursive aspects of strategy, few studies have examined strategy texts and their power effects. We draw from Critical Discourse Analysis to better understand the power of strategic plans as a directive genre. In our empirical analysis, we examined the creation of the official strategic plan of the City of Lahti in Finland. As a result of our inductive analysis, we identified five central discursive features of this plan: self-authorization, special terminology, discursive innovation, forced consensus and deonticity. We argue that these features can, with due caution, be generalized and conceived as distinctive features of the strategy genre. We maintain that these discursive features are not trivial characteristics; they have important implications for the textual agency of strategic plans, their performative effects, impact on power relations and ideological implications.

Dual-trap optical tweezers with real-time force clamp control

Single molecule force clamp experiments are widely used to investigate how enzymes, molecular motors, and other molecular mechanisms work. We developed a dual-trap optical tweezers instrument with real-time (200 kHz update rate) force clamp control that can exert 0–100 pN forces on trapped beads. A model for force clamp experiments in the dumbbell-geometry is presented. We observe good agreement between predicted and observed power spectra of bead position and force fluctuations. The model can be used to predict and optimize the dynamics of real-time force clamp optical tweezers instruments. The results from a proof-of-principle experiment in which lambda exonuclease converts a double-stranded DNA tether, held at constant tension, into its single-stranded form, show that the developed instrument is suitable for experiments in single molecule biology.