Characterisation of the Etching Quality in Micro-Electro-Mechanical Systems by Thermal Transient Methodology

Our paper presents a non-destructive thermal transient measurement method that is able to reveal differences even in the micron size range of MEMS structures. Devices of the same design can have differences in their sacrificial layers as consequence of the differences in their manufacturing processes e.g. different etching times. We have made simulations examining how the etching quality reflects in the thermal behaviour of devices. These simulations predicted change in the thermal behaviour of MEMS structures having differences in their sacrificial layers. The theory was tested with measurements of similar MEMS devices prepared with different etching times. In the measurements we used the T3Ster thermal transient tester equipment. The results show that deviations in the devices, as consequence of the different etching times, result in different temperature elevations and manifest also as shift in time in the relevant temperature transient curves.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models

The effect of quantization on the FCIQMC sign problem

The sign problem in Full Configuration Interaction Quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.Comment: 4 pages w/ 2 page appendix, 2 figures, 1 tabl

Consistent Vector-valued Regression on Probability Measures

I will focus on the distribution regression problem (DRP): our goal is to regress from probability measures to vector-valued outputs, in the two-stage sampled setup when only samples from the distributions are available. The studied DRP framework incorporates several important machine learning and statistical tasks, including multi-instance learning or point estimation problems without analytical solution (such as hyperparameter estimation). Obtaining theoretical guarantees, bounds on the generalization error of the estimated predictor is pretty challenging due to the two-stage sampled characteristic of the task. To the best of our knowledge, among the vast number of heuristic approaches in the literature, the only theoretically justified technique tackling the DRP problem requires that the domain of the distributions be compact Euclidean, and uses density estimation (which often performs poorly in practice). We present a simple, analytically tractable alternative: we embed the probability measures to a reproducing kernel Hilbert space, and perform ridge regression from the embedded distributions to the outputs. We prove that this method is consistent under mild conditions, on separable topological domains endowed with kernels. Specifically, we establish the consistency of the traditional set kernel in regression, which was a 15-year-old open question. We demonstrate the efficiency of our method in supervised entropy learning and aerosol prediction based on multispectral satellite images

Three-electron anisotropic quantum dots in variable magnetic fields: exact results for excitation spectra, spin structures, and entanglement

Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection S_z=1/2 are similar to the representative class of strongly entangled states referred to as W-states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy.Comment: To appear in Physical Review B. REVTEX4. 13 pages with 16 color figures. To download a copy with higher-quality figures, go to publication #78 in http://www.prism.gatech.edu/~ph274cy

Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems

This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition. The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods