Driven oscillations of a curved object under a laminar jet of water

By putting a ball on a flat surface under a jet of water, one may observe spontaneous oscillations of the ball of well-defined amplitude and frequency. As a simpler conformation, the study of a cylinder shows that the mere effect of the jet is sufficient to observe an oscillation for a certain range of parameters such as the curvature of the object and the characteristics of the jet. An empirical model of the forces strengthened by direct measurements of the forces and torque allowed us to predict a theoretical period of 0.64 s when the experimental one was 0.80 s. Further, the origin of the oscillation was determined to be a dynamic hysteresis of the torque as it is deflected on one side of the can even when the jet hits its center. This phenomenon results in a gain of energy that counterbalances the losses by friction and leads to oscillations. Domain of oscillation is also shortly addressed while improvements of the theoretical model and other experiments are suggested as well.

The Gauss pendulum

Recently, the Gauss rifle has gained attention as an interesting problem for physics and engineering education. In this manuscript we propose and analyze a novel problem that, while being related to the Gauss rifle, is rather simpler: the Gauss pendulum, which yields more consistent results and allows further agreement between model, simulation and experimental data. The Gauss pendulum, unlike the rifle, does not involve rotational movement of balls and the difference between the initial and final energy state of the system can be easily accessed by measuring the final height of the swinging projected ball. An extensive assessment of a Gauss pendulum has been developed using free software and accessible laboratory equipment. Focusing on the validation of the magnetic potential well model to understand the gain in kinetic energy, it was possible to obtain a remarkable agreement between the experimental and theoretically simulated data.

Two types of fog shapes above a cold evaporating liquid

When liquid nitrogen is poured into a mug, a mist forms above. This article explores the influence of air humidity on the cloud and the formation of these boundaries in a controlled environment. We have identified that both homogeneous and heterogeneous nucleations occur during their formation. We highlight two types of ice clouds that differ only in the level of air humidity. Indeed, there is a critical humidity level at which one goes from a banded cloud to another without lower limit, extending to the cold liquid. We argue that this critical humidity level is related to the nitrogen flux.

Digital micromirror device for holographic and Fourier optics applications

The electromagnetic wavefront diffracted by an object carries information about the shape of the object from which the wave was emitted. Being able to record the phase and intensity of such a wave thus allows to reconstruct the object from the information carried by the wave, even if the object is no longer present. Among the reconstruction techniques, holography plays a big part. However the waves may experience a great variety of distortions on their way from the object to the measurement apparatus. Thus being able to shape the wavefront at will is key in holography. Micromirror light modulators are powerful tools for that matter and are well known for holographic applications. This paper explores the fundamental principles for digitally reconstructing a precise image of an object, but also for digitally correcting an imperfectly shaped wavefront, by exploiting the diffraction properties of light on a reflective surface. The methods presented here have been implemented as part of practical work for 2nd year students at the Ecole Polytechnique (last year of undergraduate program).

Bimetallic ammeter: a novel method of current measurement

An electric current flowing through a bimetallic coil heats it up, and due to thermal expansion, the coil either unwinds or winds depending on the direction of net heat transfer and the specific heat capacities of the metals used. This means that by relating a certain measure of its mechanical displacement with current, the bimetallic coil can be used as an ammeter. Thus, a mathematical model relating the current to the time taken by the bimetallic coil to unwind a fixed displacement was developed and verified through experiments, which show a good agreement between theoretical and experimental values.

String Shooter’s overall shape in ambient air

In this article, we study the behaviour of a looped string launched in ambient air using motorised wheels. We show that the loop, once it reaches its stationary state, is either in the pulley or the air-lifted state. The transition between these two distinct states occurs at the so-called takeoff speed. We prove that this speed differs from one string to another based on its characteristics. However, it is independent from the loop’s length and its initial launch angle. This speed indeed corresponds to the threshold where air drag starts compensating for the weight of the string.

Origami launcher

The article studies the elastic and locomotive properties of Miura-ori-type paper origami. The mechanics of a single paper crease is studied experimentally, and its non-elastic properties turn out to be crucial. The entire origami construction is then described as a collection of individual creases, its capability to launch small objects is evaluated, and the equation of motion is found. Thus, the height of the launched ball is studied theoretically and experimentally as a function of governing parameters.

L∞-algebras and their cohomology

We give an overview of different characterisations of L∞-structures in terms of symmetric brackets and (co)differentials on the symmetric (co)algebra. We then do the same for their representations (up to homotopy) and approach L∞-algebra cohomology using the commutator bracket on the space of coderivations of the symmetric coalgebra. This leads to abelian extensions of L∞-algebras by 2-cocycles.

Sound of a nut rolling inside an elastic rubber balloon

This article studies the sound produced by nuts of different shapes swirling in an elastic rubber balloon. First, the sound is studied experimentally, both in terms of frequency and amplitude. Regarding the frequency components of the sound, we show that they can be divided into two main contributions – one due to the oscillations of the elastic membrane, the other due to the hits of the nut against the balloon – and present models to describe the frequency’s dependence on the main parameters of the system. We analysed the influence of several parameters such as the balloon’s geometry, the nut’s geometry and its mass.

From the microstructure of steels to the explosion of sparks

Sparks ejected by the grinding of steel can be observed to split in mid-flight. In this paper, we investigate the link between steel microstructure and the splitting behavior using two different steels: hypoeutectoid (containing less than 0:8% carbon) and hypereutectoid (>0:8% carbon). We used a high-speed camera filming at 1000 fps to observe the sparks, and a Scanning Electron Microscope to image the microstructures. For the hypoeutectoid steel, we also quantified the splitting behavior of the sparks by measuring the statistical distribution of the linear distance they travel before splitting occurs. We find that our results are coherent with the common explanation of the splitting phenomenon, stating that sparks split because their microstructures allow the formation of pockets of CO2 by oxidation of Fe3C, producing an internal pressure and leading to explosion.