Connectivity-consistent mapping method for 2-D discrete fracture networks

International audienceWe present a new flow computation method in 2-D discrete fracture networks (DFN) intermediary between the classical DFN flow simulation method and the projection onto continuous grids. The method divides the simulation complexity by solving for flows successively at a local mesh scale and at the global domain scale. At the local mesh scale, flows are determined by classical DFN flow simulations and approximated by an equivalent hydraulic matrix (EHM) relating heads and flow rates discretized on the mesh borders. Assembling the equivalent hydraulic matrices provides for a domain-scale discretization of the flow equation. The equivalent hydraulic matrices transfer the connectivity and flow structure complexities from the local mesh scale to the domain scale. Compared to existing geometrical mapping or equivalent tensor methods, the EHM method broadens the simulation range of flow to all types of 2-D fracture networks both below and above the representative elementary volume (REV). Additional computation linked to the derivation of the local mesh-scale equivalent hydraulic matrices increases the accuracy and reliability of the method. Compared to DFN methods, the EHM method first provides a simpler domain-scale alternative permeability model. Second, it enhances the simulation capacities to larger fracture networks where flow discretization on the DFN structure yields system sizes too large to be solved using the most advanced multigrid and multifrontal methods. We show that the EHM method continuously moves from the DFN method to the tensor representation as a function of the local mesh-scale discretization. The balance between accuracy and model simplification can be optimally controlled by adjusting the domain-scale and local mesh-scale discretizations

Efficient representation of head-related transfer functions in continuous space-frequency domains

Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by replacing SHs with four-dimensional (4D) continuous functional models in which frequency is imagined as another physical dimension. Recently developed hyperspherical harmonic (HSH) representation is compared with models defined in spherindrical coordinate system by merging SHs with one-dimensional basis functions. The efficiency of both approaches is evaluated based on the reproduction errors for individual HRTFs from HUTUBS database, including detailed analysis of its dependency on chosen orders of approximation in frequency and space. Employing continuous functional models defined in 4D coordinate systems allows HRTF magnitude spectra to be expressed as a small set of coefficients which can be decoded back into values at any direction and frequency. The best performance was noted for HSHs and SHs merged with reverse Fourier-Bessel series, with the former featuring better compression abilities, achieving slightly higher accuracy for low number of coefficients. The presented models can serve multiple purposes, such as interpolation, compression or parametrization for machine learning applications, and can be applied not only to HRTFs but also to other types of directivity functions, e.g. sound source directivity.Comment: 33 pages, 9 figures, preprint of published paper submitted for green open access to fulfill funding institution mandat

Determination of articulatory parameters from speech waveforms

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Parametric Model of Head Related Transfer Functions Based on Systematic Movements of Poles and Zeros with Sound Location for Pole/Zero Models

Directional transfer functions (DTFs), the directional components of the Head Related Transfer Functions (HRTFs), are generally measured at finite locations in azimuth and elevation. Thus models are needed to synthesize DTFs at finer spatial resolution than the measured data to create complete virtual auditory displays. In this research, minimum-phase all-pole and all-zero models were used for modeling both human and cat DTFs. Real cepstrum analysis has been used to represent minimum phase HRTFs in the time domain. For the human DTFs, model orders were chosen to achieve specific objective error criteria published in previous studies that were based on subjective listening tests. Because subjective listening tests are not always feasible in animals, objective methods must be used to assess the quality of the DTF reconstructions. The same error criteria reported in subjective tests of human DTF reconstructions was used to constrain models of cat DTFs on the assumption that if humans cannot discriminate reconstructed vs empirical DTFs for a given objective reconstruction error criteria, then cats won\u27t be able to either. All-pole and all-zero models of orders as low as 25 were able to model DTFs with errors comparable to previous research findings and preserve the main spectral features in both human and cat DTFs. A hypothesis that a systematic relation (i.e., parametric equations) can be found to describe the movements of the poles/zeros of the successful models with the change in sound source location was tested. Polynomials of different orders were extracted to describe the movements of the poles in all-pole models and zeros in all-zero models with the change in sound source location. The reconstructed DTFs were compared to the measured ones of same locations. The reconstructed DTFs preserved the main shape of the spectra, provided satisfactory RMS errors compared to the measured ones and accurately preserved the first notch spectral feature

Developing the MTO Formalism

We review the simple linear muffin-tin orbital method in the atomic-spheres approximation and a tight-binding representation (TB-LMTO-ASA method), and show how it can be generalized to an accurate and robust Nth order muffin-tin orbital (NMTO) method without increasing the size of the basis set and without complicating the formalism. On the contrary, downfolding is now more efficient and the formalism is simpler and closer to that of screened multiple-scattering theory. The NMTO method allows one to solve the single-electron Schroedinger equation for a MT-potential -in which the MT-wells may overlap- using basis sets which are arbitrarily minimal. The substantial increase in accuracy over the LMTO-ASA method is achieved by substitution of the energy-dependent partial waves by so-called kinked partial waves, which have tails attached to them, and by using these kinked partial waves at N+1 arbitrary energies to construct the set of NMTOs. For N=1 and the two energies chosen infinitesimally close, the NMTOs are simply the 3rd-generation LMTOs. Increasing N, widens the energy window, inside which accurate results are obtained, and increases the range of the orbitals, but it does not increase the size of the basis set and therefore does not change the number of bands obtained. The price for reducing the size of the basis set through downfolding, is a reduction in the number of bands accounted for and -unless N is increased- a narrowing of the energy window inside which these bands are accurate. A method for obtaining orthonormal NMTO sets is given and several applications are presented.Comment: 85 pages, Latex2e, Springer style, to be published in: Lecture notes in Physics, edited by H. Dreysse, (Springer Verlag

INDIVIDUALIZATION OF HEAD RELATED TRANSFER FUNCTION

Head related transfer functions (HRTFs) are needed to present virtual spatial sound sources via headphones. Since individually measured HRTFs are very costly and time consuming, in this paper the individualization of the dummyhead's HRTFs will be discussed. Here, the individualization is based on a scalable ellipsoidal head model. From this model the individualization is splitted into the individualization of the interaural time difference (ITD) and the spectral domain. The ellipsoidal modeling of the ITD gives quantitatively good results, considering the individual measurements. The second approach in spectral domain scales the transfer function in frequency. An angle dependent factor is calculated by the head dimensions of the subject. Afterwards, the scaling results are compared and discussed with individual measurements

Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems

In these lecture notes, we present a pedagogical review of a number of related {\it numerically exact} approaches to quantum many-body problems. In particular, we focus on methods based on the exact diagonalization of the Hamiltonian matrix and on methods extending exact diagonalization using renormalization group ideas, i.e., Wilson's Numerical Renormalization Group (NRG) and White's Density Matrix Renormalization Group (DMRG). These methods are standard tools for the investigation of a variety of interacting quantum systems, especially low-dimensional quantum lattice models. We also survey extensions to the methods to calculate properties such as dynamical quantities and behavior at finite temperature, and discuss generalizations of the DMRG method to a wider variety of systems, such as classical models and quantum chemical problems. Finally, we briefly review some recent developments for obtaining a more general formulation of the DMRG in the context of matrix product states as well as recent progress in calculating the time evolution of quantum systems using the DMRG and the relationship of the foundations of the method with quantum information theory.Comment: 51 pages; lecture notes on numerically exact methods. Pedagogical review appearing in the proceedings of the "IX. Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors", Vietri sul Mare (Salerno, Italy, October 2004