Time-periodic flows play important roles in many practical problems, with a wide range of examples occurring in engineering, physiology and ocean dynamics, among others fields. While the stability of spatially developing fluid flows is a relatively well-studied topic of research, there is a relative paucity of corresponding results that discuss purely time-periodic flows. Here we examine the stability of the classical plane Stokes layer: this is the flow generated in a layer of fluid that lies above a bounding plate that oscillates harmonically in its own plane. It has proved surprisingly difficult to understand the linear stability of this type of fluid flow, and here we trace the steps that have been taken to achieve this goal. There is a significant difference between the theoretical description of the stability of a Stokes layer and the corresponding practical measurements. We discuss possible reasons for this discrepancy and its possible implications for more general time-periodic motions.

Calculation of the flux through a two-dimensional channel with one sinusoidal wall is presented using a perturbation expansion. This gives a series for the flux up to $\mathcal {O}(\epsilon ^{160})$, where $\epsilon $ is the amplitude of the wall undulation, ranging from 0 (flat wall) to 2 (channel pinched off). The series appears to diverge near $\epsilon =0.95$, but is continued through the use of Padé approximants. The divergence is investigated and found to be caused by pole singularities lying at $\epsilon \approx \pm 0.977i$ on the imaginary axis. The continued series is validated against a purely numerical solution with excellent agreement for all values of the undulation amplitude.

This research was initiated to investigate the dynamic behaviour of Len Lye’s Kinetic Sculpture Trilogy. Safety concerns and reliability issues have led to the call for a redesign of the original mechanism. Numerical methods including FEA are used to model the artworks dynamic behaviour. Vibratory mode shapes and natural resonance frequencies of the artwork are found. Motion Capturing (MOCAP) is employed to experimentally analyse and record the dynamic behaviour of the artwork. Whirling behaviour in the form of mode shapes was recorded equally below and above the resonance frequencies.

A global spectral method is presented for unsteady incompressible fluid flow in smoothly varying channels. Recombined Chebyshev bases are implemented with numerical conformal mapping, ensuring boundary conditions are met for both straight walls and smoothly varying walls. The pressure calculation reduces to matrix operations that comprise 8% of runtime, while maintaining spectral accuracy and mass continuity. The method is demonstrated for Reynolds numbers from $Re=1$ up to $Re=10^5$. The method is verified by comparison with known results for a straight-walled channel, and with lubrication theory and linearization estimates for a channel with a periodic wavy lower wall. Some simple wall shapes are modelled at low Reynolds number. Long term stability is demonstrated for high Reynolds number flow, with an analysis of convergence against grid spacing.

The Gaia collaboration announced the discovery of a massive black hole (BH) with a low-mass giant star companion, Gaia BH3, located in the ED-2 stellar stream. The properties of Gaia BH3 bridge the gap between known Milky Way BHs and extragalactic BHs found with gravitational waves (GWs). We aim to determine the most likely formation scenario for Gaia BH3 in the progenitor cluster of the ED-2 stream. We perform N-body simulations of that progenitor cluster and find that, most likely, Gaia BH3 formed from a stellar binary that formed during cluster formation, which then underwent multiple dynamical interactions that significantly altered its properties, including exchanging the companion star. We highlight the importance of cluster dynamics and discard a formation scenario where it evolved in quasi-isolation.

“From Nbody1 to Nbody6 : The Growth of an Industry” is the title of a 1999 invited review by Sverre Aarseth, for Publications of the Astronomical Society of the Pacific (PASP). I took this as an inspiration for the title of this paper; it describes how Sverre’s Nbody Industry has further grown since 90s of the previous century, and how it is further flourishing and hopefully developing, in his spirit, even after the sad news of his passing away reached us. My contact and friendship with Sverre started a few decades ago being sent to Cambridge to learn Nbody5, counting input parameters, and learning about the fact that even a sophisticated code (which had already at that time quite a history) requires permanent maintenance and bug fixes. Managed by Sverre, who relentlessly ran his code and responded to the widely spread crowd of “customer” colleagues. There has been a phase of massive and fast development and improvements due to vectorization, parallelization, GRAPE and GPU acceleration, and Sverre has been always on top of it if not ahead, but also fully adopting ideas of collaborators, once they tested well. Nbody6++GPU and Nbody7 entered the scene, and also recent new competitors, such as PeTar or BiFrost. We all have learnt a lot from Sverre, and strive to continue in his open-minded spirit, for open source and exchange. A striking evidence for the further growth of the “industry” is the number of papers here (and two of them follow in this session, but also in other sessions) using and further developing the aforementioned codes, as well as the occurrence of new and competing codes, which keep the field alive.

We present a novel multiscale mathematical model of espresso brewing. The model captures liquid infiltration and flow through a packed bed of ground coffee, as well as coffee solubles transport (both in the grains and in the liquid) and solubles dissolution. During infiltration, a sharp interface separates the dry and wet regions of the bed. A matched asymptotic analysis (based on fast dissolution rates) reveals that the bed can be described by four asymptotic regions: a dry region yet to be infiltrated by the liquid, a region in which the liquid is saturated with solubles and very little dissolution occurs, a slender region in which solubles are rapidly extracted from the smallest grains, and region in which slower extraction occurs from larger grains. The position and extent of each of these regions move with time (one being an intrinsic moving internal boundary layer) making the asymptotic analysis intriguing in its own right. The analysis yields a reduced model that elucidates the rate-limiting physical processes. Numerical solutions of the reduced model are compared to those to the full model, demonstrating that the reduced model is both accurate and significantly cheaper to solve.

This paper proposes a linear quadratic approximation approach to dynamic nonlinear rationally inattentive control problems with multiple states and multiple controls. An efficient toolbox to implement this approach is provided. Applying this toolbox to five economic examples demonstrates that rational inattention can help explain the comovement puzzle in the macroeconomics literature.

Designing vibrating systems is challenging due to component interaction. One approach to reduce the resulting complexity is top-down design where requirements on components are formulated such that the overall system achieves the design goal. Previous work showed how to derive quantitative and solution-neutral requirements on components of a vibrating system, expressed as permissible ranges of impedance. This work adapts the methodology to a practical use case and provides a concrete technical solution: A hammer drill that can cause white finger syndromes to users is equipped with an appropriate vibration absorber. The hammer drill is represented by a lumped mass model and validated using experimental data of a reference design. Solution-neutral and quantitative component requirements on the overall dynamics of the vibration absorber expressed by impedance are derived. They provide a clear target for the component design. A vibration absorber in form of a Tuned Mass Damper (TMD) is designed accordingly. The final design is validated experimentally and shown to reduce the vibration by 47%.

Fault-tolerant hardware architectures for autonomous vehicles can be implemented through redundancy, diversity, separation, self-diagnosis, and reconfiguration. These approaches can be coupled with majority redundancy through M-out-of-N independent system architectures. The development of fault- tolerant systems is of central importance in the launch of autonomous driving systems from level 4. The increasing complexity of electrical and electronic systems is challenging for the design of safety-critical systems. This work aims to develop a method to manage this complexity in product development and to use it to compare different types of architectures. The basis is a system consisting of sensors and microcontrollers. The reliability of all possible MooN configurations of the system is calculated automatically by numerically solving the master equation of the corresponding Markov chain. Subsequently, a software-based fault tree analysis enables more detailed modeling of the component structure. The results show that four-line architectures can provide suitable results and that the development effort for 2-ECU systems is higher than for 1-ECU systems with respect to the ISO 26262 target values.

Recent higher-order explicit Runge–Kutta methods are compared with the classic fourth-order (RK4) method in long-term integration of both energy-conserving and lossy systems. By comparing quantity of function evaluations against accuracy for systems with and without known solutions, optimal methods are proposed. For a conservative system, we consider positional accuracy for Newtonian systems of two or three bodies and total angular momentum for a simplified Solar System model, over moderate astronomical timescales (tens of millions of years). For a nonconservative system, we investigate a relativistic two-body problem with gravitational wave emission. We find that methods of tenth and twelfth order consistently outperform lower-order methods for the systems considered here.