Low-Cost Experiments with Everyday Objects for Homework Assignments

We describe four classical undergraduate physics experiments that were done with everyday objects and low-cost sensors: mechanical oscillations, transmittance of light through a slab of matter, beam deformation under load, and thermal relaxation due to heat loss. We used these experiments to train students for experimental homework projects but they could be used and expanded in a variety of contexts: lecture demonstrations, low cost students' labs, science projects, distance learning courses...Comment: details on students where added : a section dedicated to the student difficulties and general feedback on this teaching unit. Minor typos were fixed. Published in Physics Educatio

Dynamical stability for the gravitational evolution of a homogeneous polytrope

URL: http://www-spht.cea.fr/articles/s00/008 Stabilité dynamique de l'évolution gravitationnelle d'un polytrope homogèneThe dynamic stability of the spherical gravitational evolution (collapse or expansion) for a homogeneous polytropic gas with any exponent $\gamma ,$ is studied using the lagrangian formalism. We obtain the analytical expression for density perturbations at the first order. In the case $\gamma =~4/3,$ the Jeans'criterion is easily generalized to a self-similar expanding background. The collapsing case is found to be always unstable. The stability of density modes obtained for $\gamma \not = 4/3$ does not introduce any conditions on the wavelength perturbation, but only a criterion on the polytropic index. As a result, stability is obtained for an expanding gas provided $\gamma 5/3.

Specific heat of single crystal MgB_2: a two-band superconductor with two different anisotropies

Heat-capacity measurements of a 39 microgramm MgB_2 single crystal in fields up to 14 T and below 3 K allow the determination of the low-temperature linear term of the specific heat, its field dependence and its anisotropy. Our results are compatible with two-band superconductivity, the band carrying the small gap being isotropic, that carrying the large gap having an anisotropy of ~ 5. Three different upper critical fields are thus needed to describe the superconducting state of MgB2.Comment: 4 pages, 4 figures - V2: Bibliography updated and some typo corrected. One reference added - V3: version accepted for publication in PRL, changes made in the tex

A subset of precise UML for Model-based Testing

This paper presents an original model-based testing approach that takes a UML behavioural view of the system under test and automatically generates test cases and executable test scripts according to model coverage criteria. This approach is embedded in the LEIRIOS Test Designer tool and is currently deployed in domains such as Enterprise IT and electronic transaction applications. This model-based testing approach makes it possible to automatically produce the traceability matrix from requirements to test cases as part of the test generation process. This paper defines the subset of UML used for model-based testing and illustrates it using a small example

Similarity Properties and Scaling Laws of Radiation Hydrodynamic Flows in Laboratory Astrophysics

The spectacular recent development of modern high-energy density laboratory facilities which concentrate more and more energy in millimetric volumes allows the astrophysical community to reproduce and to explore, in millimeter-scale targets and during very short times, astrophysical phenomena where radiation and matter are strongly coupled. The astrophysical relevance of these experiments can be checked from the similarity properties and especially scaling laws establishment, which constitutes the keystone of laboratory astrophysics. From the radiating optically thin regime to the so-called optically thick radiative pressure regime, we present in this paper, for the first time, a complete analysis of the main radiating regimes that we encountered in laboratory astrophysics with the same formalism based on the Lie-group theory. The use of the Lie group method appears as systematic which allows to construct easily and orderly the scaling laws of a given problem. This powerful tool permits to unify the recent major advances on scaling laws and to identify new similarity concepts that we discuss in this paper and which opens important applications for the present and the future laboratory astrophysics experiments. All these results enable to demonstrate theoretically that astrophysical phenomena in such radiating regimes can be explored experimentally thanks to powerful facilities. Consequently the results presented here are a fundamental tool for the high-energy density laboratory astrophysics community in order to quantify the astrophysics relevance and justify laser experiments. Moreover, relying on the Lie-group theory, this paper constitutes the starting point of any analysis of the self-similar dynamics of radiating fluids.Comment: Astrophys. J. accepte

Effect of density of state on isotope effect exponent of two-band superconductors

The exact formula of Tc's equation and the isotope effect exponent of two-band s-wave superconductors in weak-coupling limit are derived by considering the influence of two kinds of density of state : constant and van Hove singularity. The pairing interaction in each band consisted of 2 parts : the electron-phonon interaction and non-electron-phonon interaction are included in our model. We find that the interband interaction of electron-phonon show more effect on isotope exponent than the intraband interaction and the isotope effect exponent with constant density of state can fit to an experimental data,MgB2, and high-Tc superconductors, better than van Hove singularity density of state.Comment: 11 pages. accepted in Physica

Infrared properties of Mg1−x_{1-x}Alx(_x(B1−y_{1-y}Cy_{y})2_2 single crystals in the normal and superconducting state

The reflectivity $R (\omega)$ of $ab$-oriented Mg$_{1-x}$Al$_x$(B$_{1-y }$C$_y$)$_2$ single crystals has been measured by means of infrared microspectroscopy for $1300<\omega<17000$ cm$^{-1}$. An increase with doping of the scattering rates in the $\pi$ and $\sigma$ bands is observed, being more pronounced in the C doped crystals. The $\sigma$-band plasma frequency also changes with doping due to the electron doping, while the $\pi$-band one is almost unchanged. Moreover, a $\sigma\to\sigma$ interband excitation, predicted by theory, is observed at $\omega_{IB} \simeq 0.47$ eV in the undoped sample, and shifts to lower energies with doping. By performing theoretical calculation of the doping dependence $\omega_{IB}$, the experimental observations can be explained with the increase with electron doping of the Fermi energy of the holes in the $\sigma$-band. On the other hand, the $\sigma$ band density of states seems not to change substantially. This points towards a $T_c$ reduction driven mainly by disorder, at least for the doping level studied here. The superconducting state has been also probed by infrared synchrotron radiation for $30<\omega<150$ cm$^{-1}$ in one pure and one C-doped sample. In the undoped sample ($T_c$ = 38.5 K) a signature of the $\pi$-gap only is observed. At $y$ = 0.08 ($T_c$ = 31.9 K), the presence of the contribution of the $\sigma$-gap indicates dirty-limit superconductivity in both bands.Comment: 12 pages, 9 figure

Thermal properties of MgB2: the effect of disorder on gap amplitudes and relaxation times of p and s bands

We present thermal conductivity and specific heat measurements on MgB2 and Mg-AlB2 samples. Thermal properties have been analysed by using a two-gap model in order to estimate the gap amplitudes, D(0)p and D(0)s and the intra-band scattering rates, Gss and Gpp. As a function of Al doping and disorder D(0)s rapidly decreases, while D(0)p is rather constant. Gss and Gpp are increased by the disorder, being Gpp more affected than Gss.Comment: 2 pages, 3 figures, presented to the conference M2S-HTSC, 25-30 May 2003, Rio de Janeir

Modeling multidimensional effects in the propagation of radiative shocks

Radiative shocks (also called supercritical shocks) are high Mach number shock waves that photoionize the medium ahead of the shock front and give rise to a radiative precursor. They are generated in the laboratory using high-energy or high-power lasers and are frequently present in a wide range of astronomical objects. Their modelisation in one dimension has been the subject of numerous studies, but generalization to three dimensions is not straightforward. We calculate analyticaly the absorption of radiation in a grey uniform cylinder and show how it decreases with $\chi R$, the product of the opacity $\chi$ and of the cylinder radius $R$. Simple formulas, whose validity range increases when $\chi R$ diminishes, are derived for the radiation field on the axis of symmetry. Numerical calculations in three dimensions of the radiative energy density, flux and pressure created by a stationary shock wave show how the radiation decreases whith $R$. Finally, the bidimensional structures of both the precursor and the radiation field are calculated with time-dependent radiation hydrodynamics numerical simulations and the influence of two-dimensional effects on the electron density, the temperature, the shock velocity and the shock geometry are exhibited. These simulations show how the radiative precursor shortens, cools and slows down when $R$ is decreased