Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational radiation by prescribing data for the incoming fields of the Weyl tensor. High-frequency perturbations about any given spacetime (including a shift vector with subluminal normal component) are analyzed using the Fourier-Laplace technique. We show that the system is boundary-stable. In addition, we develop a criterion that can be used to detect weak instabilities with polynomial time dependence, and we show that our system does not suffer from such instabilities. A numerical robust stability test supports our claim that the initial-boundary value problem is most likely to be well-posed even if nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added, several minor amendments; version accepted for publication in Class. Quantum Gra

Response of an artificially blown clarinet to different blowing pressure profiles

Using an artificial mouth with an accurate pressure control, the onset of the pressure oscillations inside the mouthpiece of a simplified clarinet is studied experimentally. Two time profiles are used for the blowing pressure: in a first set of experiments the pressure is increased at constant rates, then decreased at the same rate. In a second set of experiments the pressure rises at a constant rate and is then kept constant for an arbitrary period of time. In both cases the experiments are repeated for different increase rates. Numerical simulations using a simplified clarinet model blown with a constantly increasing mouth pressure are compared to the oscillating pressure obtained inside the mouthpiece. Both show that the beginning of the oscillations appears at a higher pressure values than the theoretical static threshold pressure, a manifestation of bifurcation delay. Experiments performed using an interrupted increase in mouth pressure show that the beginning of the oscillation occurs close to the stop in the increase of the pressure. Experimental results also highlight that the speed of the onset transient of the sound is roughly the same, independently of the duration of the increase phase of the blowing pressure.Comment: 14 page

High-order implicit time integration scheme based on Pad\'e expansions

A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It is constructed from the Pad\'e expansions of the matrix exponential solution of a system of first-order ordinary differential equations formulated in the state-space. A computationally efficient scheme is developed exploiting the techniques of polynomial factorization and partial fractions of rational functions, and by decoupling the solution for the displacement and velocity vectors. An important feature of the novel algorithm is that no direct inversion of the mass matrix is required. From the diagonal Pad\'e expansion of order $M$ a time-stepping scheme of order $2M$ is developed. Here, each elevation of the accuracy by two orders results in an additional system of real or complex sparse equations to be solved. These systems are comparable in complexity to the standard Newmark method, i.e., the effective system matrix is a linear combination of the static stiffness, damping, and mass matrices. It is shown that the second-order scheme is equivalent to Newmark's constant average acceleration method, often also referred to as trapezoidal rule. The proposed time integrator has been implemented in MATLAB using the built-in direct linear equation solvers. In this article, numerical examples featuring nearly one million degrees of freedom are presented. High-accuracy and efficiency in comparison with common second-order time integration schemes are observed. The MATLAB-implementation is available from the authors upon request or from the GitHub repository (to be added).Comment: 43 pages, 19 figure

A shape memory alloy adaptive tuned vibration absorber: design and implementation

In this paper a tuned vibration absorber (TVA) is realized using shape memory alloy (SMA) elements. The elastic modulus of SMA changes with temperature and this effect is exploited to develop a continuously tunable device.A TVA with beam elements is described, a simple two-degree-of-freedom model developed and the TVA characterized experimentally. The behaviour during continuous heating and cooling is examined and the TVA is seen to be continuously tunable. A change in the tuned frequency of 21.4% is observed between the cold, martensite, and hot, austenite, states. This corresponds to a change in the elastic modulus of about 47.5%, somewhat less than expected.The response time of the SMA TVA is long because of its thermal inertia. However, it is mechanically simple and has a reasonably good performance, despite the tuning parameters depending on the current in a strongly nonlinear way

CfA Plasma Talks

Notes from a series of 13 one hour (or more) lectures on Plasma Physics given to Ramesh Narayan' research group at the Harvard-Smithsonian Center for Astrophysics, between January and July 2012. Lectures 1 to 5 cover various key Plasma Physics themes. Lectures 6 to 12 mainly go over the Review Paper on "Multidimensional electron beam-plasma instabilities in the relativistic regime" [\emph{Physics of Plasmas} \textbf{17}, 120501 (2010)]. Lectures 13 talks about the so-called Biermann battery and its ability to generate magnetic fields from scratch.Comment: 58 pages, 21 figure

Chaotic saddles in nonlinear modulational interactions in a plasma

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres

Modulational stability of nonlinear saturated gravity waves

Stationary gravity waves, such as mountain lee waves, are effectively described by Grimshaw's dissipative modulation equations even in high altitudes where they become nonlinear due to their large amplitudes. In this theoretical study, a wave-Reynolds number is introduced to characterize general solutions to these modulation equations. This non-dimensional number relates the vertical linear group velocity with wavenumber, pressure scale height and kinematic molecular/eddy viscosity. It is demonstrated by analytic and numerical methods that Lindzen-type waves in the saturation region, i.e. where the wave-Reynolds number is of order unity, destabilize by transient perturbations. It is proposed that this mechanism may be a generator for secondary waves due to direct wave-mean-flow interaction. By assumption the primary waves are exactly such that altitudinal amplitude growth and viscous damping are balanced and by that the amplitude is maximized. Implications of these results on the relation between mean-flow acceleration and wave breaking heights are discussed