A digital oscilloscope setup for the measurement of a transistor's characteristics

The measure of the characteristics of a transistor is an important step in an introductory electronics course. We propose to use a digital oscilloscope with a USB connection to perform a measurement of the characteristic curves with no additional custom circuitry. The setup is presented alongside with code that allows the importation and analysis of the results with open-source software.Comment: 4 pages, 7 figures. Data files and program files available upon request, contact info at: http://homepages.ulb.ac.be/~pdebuyl

Self-propulsion through symmetry breaking

In addition to self-propulsion by phoretic mechanisms that arises from an asymmetric distribution of reactive species around a catalytic motor, spherical particles with a uniform distribution of catalytic activity may also propel themselves under suitable conditions. Reactive fluctuation-induced asymmetry can give rise to transient concentration gradients which may persist under certain conditions, giving rise to a bifurcation to self-propulsion. The nature of this phenomenon is analyzed in detail, and particle-level simulations are carried out to demonstrate its existence.Comment: 6 pages, 3 figures. Appeared in EPL (Europhysics Letters

Driving-induced stability with long-range effects

We give a sufficient condition under which an applied rotation on medium particles stabilizes a slow probe in the rotation center. The symmetric part of the stiffness matrix thus gets a positive Lamb shift with respect to equilibrium. For illustration we take diffusive medium particles with a self-potential in the shape of a Mexican hat, high around the origin. There is a short-range attraction between the medium particles and the heavier probe, all immersed in an equilibrium thermal bath. For no or small rotation force on the medium particles, the origin is an unstable fixed point for the probe and the precise shape of the self-potential at large distances from the origin is irrelevant for the statistical force there. Above a certain rotation threshold, while the medium particles are still repelled from the origin, the probe stabilizes there and more details of the medium-density at large distance start to matter. The effect is robust around the quasi-static limit with rotation threshold only weakly depending on the temperature but the stabilization gets stronger at lower temperatures.Comment: 6 pages, 4 figure

Self-consistent inhomogeneous steady states in Hamiltonian mean field dynamics

Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of $N$ globally coupled particles moving on a ring, the Hamiltonian Mean Field model (HMF), have shown that it diverges as $N^\gamma$ for large $N$, with $\gamma \simeq 1.7$ for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analysing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with $N$ with the exponent $\gamma \simeq 1$. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases it provides a good approximation for the correspondence between the initial condition and the final steady state.Comment: 5 pages, 4 figures, revised, accepted for publication on Phys. Rev.

On the effectiveness of mixing in violent relaxation

Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas and wave-particle systems. These systems, adequately described by the Vlasov equation, present quasi-stationary states (QSS), i.e. long lasting intermediate stages of the dynamics that occur after a short significant evolution called "violent relaxation". The nature of the relaxation, in the absence of collisions, is not yet fully understood. We demonstrate in this article the occurrence of stretching and folding behavior in numerical simulations of the Vlasov equation, providing a plausible relaxation mechanism that brings the system from its initial condition into the QSS regime. Area-preserving discrete-time maps with a mean-field coupling term are found to display a similar behaviour in phase space as the Vlasov system.Comment: 10 pages, 11 figure