A proposition of 3D inertial tolerancing to consider the statistical combination of the location and orientation deviations

Tolerancing of assembly mechanisms is a major interest in the product life cycle. One can distinguish several models with growing complexity, from 1-dimensional (1D) to 3-dimensional (3D) (including form deviations), and two main tolerancing assumptions, the worst case and the statistical hypothesis. This paper presents an approach to 3D statistical tolerancing using a new acceptance criterion. Our approach is based on the 1D inertial acceptance criterion that is extended to 3D and form acceptance. The modal characterisation is used to describe the form deviation of a geometry as the combination of elementary deviations (location, orientation and form). The proposed 3D statistical tolerancing is applied on a simple mechanism with lever arm. It is also compared to the traditional worst-case tolerancing using a tolerance zone

Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems

We consider a finite chain of non-linear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationary state, we show rigorously that for arbitrary temperature differences and arbitrary couplings, such a system has a unique stationary state. (This extends our earlier results for small temperature differences.) In all these cases, any initial state will converge (at an unknown rate) to the stationary state. We show that this stationary state continually produces entropy. The rate of entropy production is strictly negative when the temperatures are unequal and is proportional to the mean energy flux through the system

Radiative and collisional processes in translationally cold samples of hydrogen Rydberg atoms studied in an electrostatic trap

Supersonic beams of hydrogen atoms, prepared selectively in Rydberg-Stark states of principal quantum number $n$ in the range between 25 and 35, have been deflected by 90$^\circ$, decelerated and loaded into off-axis electric traps at initial densities of $\approx 10^6$ atoms/cm$^{-3}$ and translational temperatures of 150 mK. The ability to confine the atoms spatially was exploited to study their decay by radiative and collisional processes. The evolution of the population of trapped atoms was measured for several milliseconds in dependence of the principal quantum number of the initially prepared states, the initial Rydberg-atom density in the trap, and the temperature of the environment of the trap, which could be varied between 7.5 K and 300 K using a cryorefrigerator. At room temperature, the population of trapped Rydberg atoms was found to decay faster than expected on the basis of their natural lifetimes, primarily because of absorption and emission stimulated by the thermal radiation field. At the lowest temperatures investigated experimentally, the decay was found to be multiexponential, with an initial rate scaling as $n^{-4}$ and corresponding closely to the natural lifetimes of the initially prepared Rydberg-Stark states. The decay rate was found to continually decrease over time and to reach an almost $n$-independent rate of more than (1 ms)$^{-1}$ after 3 ms. To analyze the experimentally observed decay of the populations of trapped atoms, numerical simulations were performed which included all radiative processes, i.e., spontaneous emission as well as absorption and emission stimulated by the thermal radiation. These simulations, however, systematically underestimated the population of trapped atoms observed after several milliseconds by almost two orders of magnitude, although they reliably predicted the decay rates of the remaining atoms in the trap. TheComment: 36 pages, 18 figure

Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures

We study the statistical mechanics of a finite-dimensional non-linear Hamiltonian system (a chain of anharmonic oscillators) coupled to two heat baths (described by wave equations). Assuming that the initial conditions of the heat baths are distributed according to the Gibbs measures at two different temperatures we study the dynamics of the oscillators. Under suitable assumptions on the potential and on the coupling between the chain and the heat baths, we prove the existence of an invariant measure for any temperature difference, i.e., we prove the existence of steady states. Furthermore, if the temperature difference is sufficiently small, we prove that the invariant measure is unique and mixing. In particular, we develop new techniques for proving the existence of invariant measures for random processes on a non-compact phase space. These techniques are based on an extension of the commutator method of H\"ormander used in the study of hypoelliptic differential operators.Comment: 43 page

Generating non-Gaussian states using collisions between Rydberg polaritons

We investigate theoretically the deterministic generation of quantum states with negative Wigner functions, by using giant non-linearities due to collisional interactions between Rydberg polaritons. The state resulting from the polariton interactions may be transferred with high fidelity into a photonic state, which can be analyzed using homodyne detection followed by quantum tomography. Besides generating highly non-classical states of the light, this method can also provide a very sensitive probe for the physics of the collisions involving Rydberg states.Comment: 5 pages, 3 figure

Electric-field induced dipole blockade with Rydberg atoms

High resolution laser Stark excitation of np (60 < n < 85) Rydberg states of ultra-cold cesium atoms shows an efficient blockade of the excitation attributed to long-range dipole-dipole interaction. The dipole blockade effect is observed as a quenching of the Rydberg excitation depending on the value of the dipole moment induced by the external electric field. Effects of eventual ions which could match the dipole blockade effect are discussed in detail but are ruled out for our experimental conditions. Analytic and Monte-Carlo simulations of the excitation of an ensemble of interacting Rydberg atoms agree with the experiments indicates a major role of the nearest neighboring Rydberg atom.Comment: 4 page

Zeta functions with Dirichlet and Neumann boundary conditions for exterior domains

International audienceWe generalize earlier studies on the Laplacian for a bounded open domain $\Omega\subset\mathbb R^2$ with connected complement and piecewise smooth boundary. We compare it with the quantum mechanical scattering operator for the exterior of this same domain. Using single layer and double layer potentials we can prove a number of new relations which hold when one chooses independently Dirichlet or Neumann boundary conditions for the interior and exterior problem. This relation is provided by a very simple set of $\zeta$-functions, which involve the single and double layer potentials. We also provide Krein spectral formulas for all the cases considered and give a numerical algorithm to compute the $\zeta$-function

Inside-Outside Duality for Planar Billiards -- A Numerical Study

This paper reports the results of extensive numerical studies related to spectral properties of the Laplacian and the scattering matrix for planar domains (called billiards). There is a close connection between eigenvalues of the billiard Laplacian and the scattering phases, basically that every energy at which a scattering phase is $2\pi$ corresponds to an eigenenergy of the Laplacian. Interesting phenomena appear when the shape of the domain does not allow an extension of the eigenfunction to the exterior. In this paper these phenomena are studied and illustrated from several points of view.Comment: uuencoded tar-compressed (using uufiles) postscript file, 15 page