Computational Multiscale Methods for Linear Poroelasticity with High Contrast

In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use of the idea of energy minimization with suitable constraints in order to generate efficient basis functions for the displacement and the pressure. These basis functions are constructed by solving a class of local auxiliary optimization problems based on eigenfunctions containing local information on the heterogeneity. Techniques of oversampling are adapted to enhance the computational performance. Convergence of first order is shown and illustrated by a number of numerical tests.Comment: 14 pages, 9 figure

Pressure-dependent optical investigations of α\alpha-(BEDT-TTF)2_2I3_3: tuning charge order and narrow gap towards a Dirac semimetal

Infrared optical investigations of $\alpha$-(BEDT-TTF)$_2$I$_3$ have been performed in the spectral range from 80 to 8000~cm$^{-1}$ down to temperatures as low as 10~K by applying hydrostatic pressure. In the metallic state, $T > 135$~K, we observe a 50\% increase in the Drude contribution as well as the mid-infrared band due to the growing intermolecular orbital overlap with pressure up to 11~kbar. In the ordered state, $T<T_{\rm CO}$, we extract how the electronic charge per molecule varies with temperature and pressure: Transport and optical studies demonstrate that charge order and metal-insulator transition coincide and consistently yield a linear decrease of the transition temperature $T_{\rm CO}$ by $8-9$~K/kbar. The charge disproportionation $\Delta\rho$ diminishes by $0.017~e$/kbar and the optical gap $\Delta$ between the bands decreases with pressure by -47~cm$^{-1}$/kbar. In our high-pressure and low-temperature experiments, we do observe contributions from the massive charge carriers as well as from massless Dirac electrons to the low-frequency optical conductivity, however, without being able to disentangle them unambiguously.Comment: 13 pages, 17 figures, submitted to Phys. Rev.

Characterization of the quasi-one-dimensional compounds δ-(EDT-TTF-CONMe2)2X, X=AsF6 and Br by vibrational spectroscopy and density functional theory calculations

We have investigated the infrared spectra of the quarter-filled charge-ordered insulators delta-(EDT-TTF-CONMe2)(2)X (X=AsF6, Br) along all three crystallographic directions in the temperature range from 300 to 10 K. DFT-assisted normal mode analysis of the neutral and ionic EDT-TTF-CONMe2 molecule allows us to assign the experimentally observed intramolecular modes and to obtain relevant information on the charge ordering and intramolecular interactions. From frequencies of charge-sensitive vibrations we deduce that the charge-ordered state is already present at room temperature and does not change on cooling, in agreement with previous NMR measurements. The spectra taken along the stacking direction clearly show features of vibrational overtones excited due to the anharmonic electronic molecule potential caused by the large charge disproportionation between the molecular sites. The shift of certain vibrational modes indicates the onset of the structural transition below 200 K. (C) 2014 AIP Publishing LLC

Anisotropic charge dynamics in the quantum spin-liquid candidate κ\kappa-(BEDT-TTF)2_2Cu2_2(CN)3_3

We have in detail characterized the anisotropic charge response of the dimer Mott insulator $\kappa$-(BEDT-TTF)$_2$\-Cu$_2$(CN)$_3$ by dc conductivity, Hall effect and dielectric spectroscopy. At room temperature the Hall coefficient is positive and close to the value expected from stoichiometry; the temperature behavior follows the dc resistivity $\rho(T)$. Within the planes the dc conductivity is well described by variable-range hopping in two dimensions; this model, however, fails for the out-of-plane direction. An unusually broad in-plane dielectric relaxation is detected below about 60 K; it slows down much faster than the dc conductivity following an Arrhenius law. At around 17 K we can identify a pronounced dielectric anomaly concomitantly with anomalous features in the mean relaxation time and spectral broadening. The out-of-plane relaxation, on the other hand, shows a much weaker dielectric anomaly; it closely follows the temperature behavior of the respective dc resistivity. At lower temperatures, the dielectric constant becomes smaller both within and perpendicular to the planes; also the relaxation levels off. The observed behavior bears features of relaxor-like ferroelectricity. Because heterogeneities impede its long-range development, only a weak tunneling-like dynamics persists at low temperatures. We suggest that the random potential and domain structure gradually emerge due to the coupling to the anion network.Comment: 14 pages, 13 figure

Attitudes politiques de Tunis dans le conflit entre Aragonais et Français en Sicile autour de 1282

International audienceSimulating the deformation of the human anatomy is a central element of Medical Image Computing and Computer Assisted Interventions. Such simulations play a key role in non-rigid registration, augmented reality, and several other applications. Although the Finite Element Method is widely used as a numerical approach in this area, it is often hindered by the need for an optimal meshing of the domain of interest. The derivation of meshes from imaging modalities such as CT or MRI can be cumbersome and time-consuming. In this paper we use the Immersed Boundary Method (IBM) to bridge the gap between these imaging modalities and the fast simulation of soft tissue deformation on complex shapes represented by a surface mesh directly retrieved from binary images. A high resolution surface, that can be obtained from binary images using a marching cubes approach, is embedded into a hexahedral simulation grid. The details of the surface mesh are properly taken into account in the hexahedral mesh by adapting the Mirtich integration method. In addition to not requiring a dedicated meshing approach, our method results in higher accuracy for less degrees of freedom when compared to other element types. Examples on brain deformation demonstrate the potential of our method

Angular Resolution of the LISA Gravitational Wave Detector

We calculate the angular resolution of the planned LISA detector, a space-based laser interferometer for measuring low-frequency gravitational waves from galactic and extragalactic sources. LISA is not a pointed instrument; it is an all-sky monitor with a quadrupolar beam pattern. LISA will measure simultaneously both polarization components of incoming gravitational waves, so the data will consist of two time series. All physical properties of the source, including its position, must be extracted from these time series. LISA's angular resolution is therefore not a fixed quantity, but rather depends on the type of signal and on how much other information must be extracted. Information about the source position will be encoded in the measured signal in three ways: 1) through the relative amplitudes and phases of the two polarization components, 2) through the periodic Doppler shift imposed on the signal by the detector's motion around the Sun, and 3) through the further modulation of the signal caused by the detector's time-varying orientation. We derive the basic formulae required to calculate the LISA's angular resolution $\Delta \Omega_S$ for a given source. We then evaluate $\Delta \Omega_S$ for two sources of particular interest: monchromatic sources and mergers of supermassive black holes. For these two types of sources, we calculate (in the high signal-to-noise approximation) the full variance-covariance matrix, which gives the accuracy to which all source parameters can be measured. Since our results on LISA's angular resolution depend mainly on gross features of the detector geometry, orbit, and noise curve, we expect these results to be fairly insensitive to modest changes in detector design that may occur between now and launch. We also expect that our calculations could be easily modified to apply to a modified design.Comment: 15 pages, 5 figures, RevTex 3.0 fil

Measuring gravitational waves from binary black hole coalescences: II. the waves' information and its extraction, with and without templates

We discuss the extraction of information from detected binary black hole (BBH) coalescence gravitational waves, focusing on the merger phase that occurs after the gradual inspiral and before the ringdown. Our results are: (1) If numerical relativity simulations have not produced template merger waveforms before BBH detections by LIGO/VIRGO, one can band-pass filter the merger waves. For BBHs smaller than about 40 solar masses detected via their inspiral waves, the band pass filtering signal to noise ratio indicates that the merger waves should typically be just barely visible in the noise for initial and advanced LIGO interferometers. (2) We derive an optimized (maximum likelihood) method for extracting a best-fit merger waveform from the noisy detector output; one "perpendicularly projects" this output onto a function space (specified using wavelets) that incorporates our prior knowledge of the waveforms. An extension of the method allows one to extract the BBH's two independent waveforms from outputs of several interferometers. (3) If numerical relativists produce codes for generating merger templates but running the codes is too expensive to allow an extensive survey of the merger parameter space, then a coarse survey of this parameter space, to determine the ranges of the several key parameters and to explore several qualitative issues which we describe, would be useful for data analysis purposes. (4) A complete set of templates could be used to test the nonlinear dynamics of general relativity and to measure some of the binary parameters. We estimate the number of bits of information obtainable from the merger waves (about 10 to 60 for LIGO/VIRGO, up to 200 for LISA), estimate the information loss due to template numerical errors or sparseness in the template grid, and infer approximate requirements on template accuracy and spacing.Comment: 33 pages, Rextex 3.1 macros, no figures, submitted to Phys Rev

Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors

This paper addresses the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on pre-computed fine-scale correctors. The exponential decay of these correctors and their localisation to local cell problems is rigorously justified. The stabilization eliminates scale-dependent pre-asymptotic effects as they appear for standard finite element discretizations of highly oscillatory problems, e.g., the poor $L^2$ approximation in homogenization problems or the pollution effect in high-frequency acoustic scattering