Importance of an Astrophysical Perspective for Textbook Relativity

The importance of a teaching a clear definition of the ``observer'' in special relativity is highlighted using a simple astrophysical example from the exciting current research area of ``Gamma-Ray Burst'' astrophysics. The example shows that a source moving relativistically toward a single observer at rest exhibits a time ``contraction'' rather than a ``dilation'' because the light travel time between the source and observer decreases with time. Astrophysical applications of special relativity complement idealized examples with real applications and very effectively exemplify the role of a finite light travel time.Comment: 5 pages TeX, European Journal of Physics, in pres

Stability analysis of surface ion traps

Motivated by recent developments in ion trap design and fabrication, we investigate the stability of ion motion in asymmetrical, planar versions of the classic Paul trap. The equations of motion of an ion in such a trap are generally coupled due to a nonzero relative angle $\theta$ between the principal axes of RF and DC fields, invalidating the assumptions behind the standard stability analysis for symmetric Paul traps. We obtain stability diagrams for the coupled system for various values of $\theta$, generalizing the standard $q$-$a$ stability diagrams. We use multi-scale perturbation theory to obtain approximate formulas for the boundaries of the primary stability region and obtain some of the stability boundaries independently by using the method of infinite determinants. We cross-check the consistency of the results of these methods. Our results show that while the primary stability region is quite robust to changes in $\theta$, a secondary stability region is highly variable, joining the primary stability region at the special case of $\theta=45^{\circ}$, which results in a significantly enlarged stability region for this particular angle. We conclude that while the stability diagrams for classical, symmetric Paul traps are not entirely accurate for asymmetric surface traps (or for other types of traps with a relative angle between the RF and DC axes), they are safe in the sense that operating conditions deemed stable according to standard stability plots are in fact stable for asymmetric traps, as well. By ignoring the coupling in the equations, one only underestimates the size of the primary stability region

Nonlinear analysis of spacecraft thermal models

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.Comment: 29 pages, 4 figure

Generation of directional, coherent matter beams through dynamical instabilities in Bose-Einstein condensates

We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with non-equal scattering lengths, and show that dynamical instabilities can be excited. We demonstrate that these instabilities are exponentially amplified resulting in highly-directional, oppositely-propagating, coherent matter beams at specific momenta. To accomplish this we prove that the mean field of our system is periodic, and extend the standard Bogoliubov approach to consider a time-dependent, but cyclic, background. This allows us to use Floquet's theorem to gain analytic insight into such systems, rather than employing the usual Bogoliubov-de Gennes approach, which is usually limited to numerical solutions. We apply our theory to the metastable Helium atom laser experiment of Dall et al. [Phys. Rev. A 79, 011601(R) (2009)] and show it explains the anomalous beam profiles they observed. Finally we demonstrate the paired particle beams will be EPR-entangled on formation.Comment: Corrected reference

Mechanical detection of carbon nanotube resonator vibrations

Bending-mode vibrations of carbon nanotube resonator devices were mechanically detected in air at atmospheric pressure by means of a novel scanning force microscopy method. The fundamental and higher order bending eigenmodes were imaged at up to 3.1GHz with sub-nanometer resolution in vibration amplitude. The resonance frequency and the eigenmode shape of multi-wall nanotubes are consistent with the elastic beam theory for a doubly clamped beam. For single-wall nanotubes, however, resonance frequencies are significantly shifted, which is attributed to fabrication generating, for example, slack. The effect of slack is studied by pulling down the tube with the tip, which drastically reduces the resonance frequency

One-dimensional dynamics of nearly unstable axisymmetric liquid bridges

A general one-dimensional model is considered that describes the dynamics of slender, axisymmetric, noncylindrical liquid bridges between two equal disks. Such model depends on two adjustable parameters and includes as particular cases the standard Lee and Cosserat models. For slender liquid bridges, the model provides sufficiently accurate results and involves much easier and faster calculations than the full three-dimensional model. In particular, viscous effects are easily accounted for. The one-dimensional model is used to derive a simple weakly nonlinear description of the dynamics near the instability limit. Small perturbations of marginal instability conditions are also considered that account for volume perturbations, nonequality of the supporting disks, and axial gravity. The analysis shows that the dynamics breaks the reflection symmetry on the midplane between the supporting disks. The weakly nonlinear evolution of the amplitude of the perturbation is given by a Duffing equation, whose coefficients are calculated in terms of the slenderness as a part of the analysis and exhibit a weak dependence on the adjustable parameters of the one-dimensional model. The amplitude equation is used to make quantitative predictions of both the (first stage of) breakage for unstable configurations and the (slow) dynamics for stable configurations

Dynamics of a linear oscillator connected to a small strongly non-linear hysteretic absorber

The present investigation deals with the dynamics of a two-degrees-of-freedom system which consists of a main linear oscillator and a strongly nonlinear absorber with small mass. The nonlinear oscillator has a softening hysteretic characteristic represented by a Bouc-Wen model. The periodic solutions of this system are studied and their calcu- lation is performed through an averaging procedure. The study of nonlinear modes and their stability shows, under specific conditions, the existence of localization which is responsible for a passive irreversible energy transfer from the linear oscillator to the nonlinear one. The dissipative effect of the nonlinearity appears to play an important role in the energy transfer phenomenon and some design criteria can be drawn regarding this parameter among others to optimize this energy transfer. The free transient response is investigated and it is shown that the energy transfer appears when the energy input is sufficient in accordance with the predictions from the nonlinear modes. Finally, the steady-state forced response of the system is investigated. When the input of energy is sufficient, the resonant response (close to nonlinear modes) experiences localization of the vibrations in the nonlinear absorber and jump phenomena

Dimension dependent energy thresholds for discrete breathers

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. We study the existence of energy thresholds for discrete breathers, i.e., the question whether, in a certain system, discrete breathers of arbitrarily low energy exist, or a threshold has to be overcome in order to excite a discrete breather. Breather energies are found to have a positive lower bound if the lattice dimension d is greater than or equal to a certain critical value d_c, whereas no energy threshold is observed for d<d_c. The critical dimension d_c is system dependent and can be computed explicitly, taking on values between zero and infinity. Three classes of Hamiltonian systems are distinguished, being characterized by different mechanisms effecting the existence (or non-existence) of an energy threshold.Comment: 20 pages, 5 figure

Audio mixing in a tri-port nano-electro-mechanical device

We report on experiments performed on a cantilever-based tri-port nano-electro-mechanical (NEMS) device. Two ports are used for actuation and detection through the magnetomotive scheme, while the third port is a capacitively coupled gate electrode. By applying a low frequency voltage signal on the gate, we demonstrate mixing in the mechanical response of the device, even for {\it low magnetomotive drives, without resorting to conduction measurements through the NEMS}. The technique can thus be used in particular in the linear regime, as an alternative to nonlinear mixing, for normal conducting devices. An analytic theory is presented reproducing the data without free parameter

A piecewise-linear reduced-order model of squeeze-film damping for deformable structures including large displacement effects

This paper presents a reduced-order model for the Reynolds equation for deformable structure and large displacements. It is based on the model established in [11] which is piece-wise linearized using two different methods. The advantages and drawbacks of each method are pointed out. The pull-in time of a microswitch is determined and compared to experimental and other simulation data.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838