Numerical evaluation of the viscoelastic and viscoplastic behavior of composites

This paper is concerned with the development of homogenization methods in order to obtain the effective material parameters of viscoelastic and viscoplastic composites. In the case of a viscoelastic behavior, the constitutive laws at the heterogeneous scale are transposed into a LAPLACE-CARSON domain where the equations become similar to those of linear elasticity and classical homogenization procedures can be applied. Afterward, the results have to be converted by an inverse transformation. Mostly, this procedure is combined with analytical or semi-analytical models such as the self-consistent or Mori-Tanaka model. Since the application of this approach is limited to simple structured composites it is not suitable for materials with a complex internal architecture. In order to avoid this limitation, this paper is focused on the development of a homogenization procedure which is based on the LAPLACE-CARSON transformation and a numerical solution of the field problem. For heterogeneous material with viscoplastic or nonlinear viscoelastic properties, an additional linearization step is required. A new algorithm is proposed in order to combine this affine formulation with the numerical homogenization method. Finally, these procedures are used to estimate the effective material behavior of different types of composites. With that, the accuracy of the results and efficiency of the methodologies is assessed

Gravitational Decoherence and the Possibility of Its Interferometric Detection

We present a general master equation describing the quantum dynamics of a scalar bosonic field interacting with an external weak and stochastic gravitational field. The dynamics predicts decoherence both in position and in energy momentum. We show how the master equation reproduces, thus generalizing, the previous results in the literature by taking appropriate limits. We estimate the effect of gravitational decoherence in atom interferometers, providing also a straightforward way to assess the magnitude of the effect

Testing Dissipative Collapse Models with a Levitated Micromagnet

We present experimental tests of dissipative extensions of spontaneous wave function collapse models based on a levitated micromagnet with ultralow dissipation. The spherical micromagnet, with radius $R=27$ $\mu$m, is levitated by Meissner effect in a lead trap at $4.2$ K and its motion is detected by a SQUID. We perform accurate ringdown measurements on the vertical translational mode with frequency $57$ Hz, and infer the residual damping at vanishing pressure $\gamma/2\pi<9$ $\mu$Hz. From this upper limit we derive improved bounds on the dissipative versions of the CSL (continuous spontaneous localization) and the DP (Di\'{o}si-Penrose) models with proper choices of the reference mass. In particular, dissipative models give rise to an intrinsic damping of an isolated system with the effect parameterized by a temperature constant; the dissipative CSL model with temperatures below 1 nK is ruled out, while the dissipative DP model is excluded for temperatures below $10^{-13}$ K. Furthermore, we present the first bounds on dissipative effects in a more recent model, which relates the wave function collapse to fluctuations of a generalized complex-valued spacetime metric.Comment: 10 pages, 7 figure

Phase Space Tomography of Matter-Wave Diffraction in the Talbot Regime

We report on the theoretical investigation of Wigner distribution function (WDF) reconstruction of the motional quantum state of large molecules in de Broglie interference. De Broglie interference of fullerenes and as the like already proves the wavelike behaviour of these heavy particles, while we aim to extract more quantitative information about the superposition quantum state in motion. We simulate the reconstruction of the WDF numerically based on an analytic probability distribution and investigate its properties by variation of parameters, which are relevant for the experiment. Even though the WDF described in the near-field experiment cannot be reconstructed completely, we observe negativity even in the partially reconstructed WDF. We further consider incoherent factors to simulate the experimental situation such as a finite number of slits, collimation, and particle-slit van der Waals interaction. From this we find experimental conditions to reconstruct the WDF from Talbot interference fringes in molecule Talbot-Lau interferometry.Comment: 16 pages, 9 figures, accepted at New Journal of Physic

Monte Carlo Transmission Line Modeling of Multilayer Optical Coatings for Performance Sensitivity of a Dichroic Filter for the ARIEL Space Telescope

Dichroic beamsplitters, or dichroics, are filters that rely on the optical interference that occurs within thin layers to ensure the transmission and reflection of selective wavelengths of an incident beam of light. These optical components consist of a substrate coated on one or both surfaces with multiple layers of thin films, the spectral design and construction of which determine the isolation of particular wavebands. Discrepancies between the measured and expected spectral performance of optical elements with such coatings can largely be attributed to depositions errors and uncertainties in the refractive indices of the materials. Our model uses two-dimensional transmission line modeling to evaluate the transmittance of light through multilayer coatings deposited on a substrate material for given materials, angle of incidence and polarisation. This model allows us to perform Monte Carlo simulations to obtain statistical information about the tolerance of the coating performance to systematic and random uncertainties from the manufacturing process, as well as from environmental changes in space. With the aid of accurate manufacturing recipes and uncertainty amplitudes from commercial manufacturers, this tool can predict variations in the optical performance that result from the propagation of each of these uncertainties for various hypothetical scenarios. One particular application of this study are the dichroics of the ARIEL space telescope. We compare the predicted optical performance with transmission measurements at cryogenic temperatures for one of the ARIEL dichroics, which show the specification compliance of this prototype after many thermal cycles

A Mechanical Mass Sensor with Yoctogram Resolution

Nanoelectromechanical systems (NEMS) have generated considerable interest as inertial mass sensors. NEMS resonators have been used to weigh cells, biomolecules, and gas molecules, creating many new possibilities for biological and chemical analysis [1-4]. Recently, NEMS-based mass sensors have been employed as a new tool in surface science in order to study e.g. the phase transitions or the diffusion of adsorbed atoms on nanoscale objects [5-7]. A key point in all these experiments is the ability to resolve small masses. Here we report on mass sensing experiments with a resolution of 1.7 yg (1 yg = 10^-24 g), which corresponds to the mass of one proton, or one hydrogen atom. The resonator is made of a ~150 nm long carbon nanotube resonator vibrating at nearly 2 GHz. The unprecedented level of sensitivity allows us to detect adsorption events of naphthalene molecules (C10H8) and to measure the binding energy of a Xe atom on the nanotube surface (131 meV). These ultrasensitive nanotube resonators offer new opportunities for mass spectrometry, magnetometry, and adsorption experiments.Comment: submitted version of the manuscrip