Modeling Frequency-Dependent Boundaries as Digital Impedance Filters in FDTD and K-DWM Room Acoustics Simulations

A new method for modeling-frequency-dependent boundaries in finite-difference time-domain (FDTD) and Kirchhoff variable digital waveguide mesh (K-DWM) room acoustics simulations is presented. The proposed approach allows the direct incorporation of a digital impedance filter (DIF) in the Multidimensional (2D or 3D) FDTD boundary model of a locally reacting surface. An explicit boundary update equation is obtained by carefully constructing a Suitable recursive formulation. The method is analyzed in terms of pressure wave reflectance for different wall impedance filters and angles of incidence. Results obtained from numerical experiments confirm the high accuracy of the proposed digital impedance filter boundary model, the reflectance of which matches locally reacting surface (LRS) theory closely. Furthermore a numerical boundary analysis (NBA) formula is provided as a technique for an analytic evaluation of the numerical reflectance of the proposed digital impedance filter boundary formulation.

Formulation of Locally Reacting Surfaces in FDTD/K-DWM Modelling of Acoustic Spaces

In this paper, we present new methods for constructing and analysing formulations of locally reacting surfaces that can be used in finite difference time domain (FDTD) simulations of acoustic spaces. Novel FDTD formulations of frequency-independent and simple frequency-dependent impedance boundaries are proposed for 2D and 3D acoustic systems, including a full treatment of corners and boundary edges. The proposed boundary formulations are designed for virtual acoustics applications using the standard leapfrog scheme based on a rectilinear grid, and apply to FDTD as well as Kirchhoff variable digital waveguide mesh (K-DWM) methods. In addition, new analytic evaluation methods that accurately predict the reflectance of numerical boundary formulations are proposed. numerical experiments and numerical boundary analysis (NBA) are analysed in time and frequency domains in terms of the pressure wave reflectance for different angles of incidence and various impedances. The results show that the proposed boundary formulations structurally adhere well to the theoretical reflectance. In particular, both reflectance magnitude and phase are closely approximated even at high angles of incidence and low impedances. Furthermore, excellent agreement was found between the numerical boundary analysis and the experimental results, validating both as tools for researching FDTD boundary formulations.

Common Breast Cancer Susceptibility Alleles and the Risk of Breast Cancer for BRCA1 and BRCA2 Mutation Carriers: Implications for Risk Prediction

The known breast cancer susceptibility polymorphisms in FGFR2, TNRC9/TOX3, MAP3K1, LSP1, and 2q35 confer increased risks of breast cancer for BRCA1 or BRCA2 mutation carriers. We evaluated the associations of 3 additional single nucleotide polymorphisms (SNPs), rs4973768 in SLC4A7/NEK10, rs6504950 in STXBP4/COX11, and rs10941679 at 5p12, and reanalyzed the previous associations using additional carriers in a sample of 12,525 BRCA1 and 7,409 BRCA2 carriers. Additionally, we investigated potential interactions between SNPs and assessed the implications for risk prediction. The minor alleles of rs4973768 and rs10941679 were associated with increased breast cancer risk for BRCA2 carriers (per-allele HR - 1.10, 95% CI: 1.03-1.18, P - 0.006 and HR - 1.09, 95% CI: 1.01-1.19, P = 0.03, respectively). Neither SNP was associated with breast cancer risk for BRCA1 carriers, and rs6504950 was not associated with breast cancer for either BRCA1 or BRCA2 carriers. Of the 9 polymorphisms investigated, 7 were associated with breast cancer for BRCA2 carriers (FGFR2, TOX3, MAP3K1, LSP1, 2q35, SLC4A7, 5p12, P 7 = 10 x (11) - 0.03), but only TOX3 and 2q35 were associated with the risk for BRCA1 carriers (P = 0.0049, 0.03, respectively). All risk-associated polymorphisms appear to interact multiplicatively on breast cancer risk for mutation carriers. Based on the joint genotype distribution of the 7 risk-associated SNPs in BRCA2 mutation carriers, the 5% of BRCA2 carriers at highest risk (i.e., between 95th and 100th percentiles) were predicted to have a probability between 80% and 96% of developing breast cancer by age 80, compared with 42%

Evaluation of a candidate breast cancer associated SNP in ERCC4 as a risk modifier in BRCA1 and BRCA2 mutation carriers. Results from the Consortium of Investigators of Modifiers of BRCA1/BRCA2 (CIMBA)

BACKGROUND: In this study we aimed to evaluate the role of a SNP in intron I of the ERCC4 gene (rs744154), previously reported to be associated with a reduced risk of breast cancer in the general population, as a breast cancer risk modifier in BRCA1 and BRCA2 mutation carriers.

A simple non-linear global-local finite element methodology for composite structures

A simple non-linear global-local finite element methodology is presented. A global coarse model, using 2-D shell elements, is solved non-linearly and the displacements and rotations around a region of interest are applied, as displacement boundary conditions, to a refined local 3-D model using Kirchhoff plate assumptions. The global elements' shape functions are used to interpolate between nodes. The local model is then solved non-linearly with an incremental scheme independent of that used for the global model.

Electromagnetic Focusing and Imaging in Stratified Media Using Gradient Phase Profiled Conjugating Lens

High-resolution imaging of a dipole source in stratified medium based on negative refraction is presented in this paper. Compensation of the material parameter contrast at the stratified media interface is achieved using a gradient phase profiled conjugating lens (GPCL). It is shown both analytically and numerically that the phase gradient applied across the GPCL positioned at the interface of vertically stratified media enables a high-quality image of a dipole source in a mirror symmetric position with respect to the lens plane. The analytical closed form expression of the phase gradient function is derived using Huygens-Kirchhoff principle. The result is applicable to media with arbitrary stratification and material parameters, including lossy materials. The mechanism for formation of the dipole image in the stratified medium and aberration due to the dielectric contrast at the interface, particularly electromagnetic loss, is discussed in detail. The efficacy of gradient phase and amplitude aberration compensations mechanisms available through the GPCL is articulated. The results of the study are of importance in a wide range of imaging problems in stratified media for medical, civil, and military applications.