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.

Ixaru's Extended Frequency Dependent Quadrature Rules for Slater Integrals: Parallel Computation Issues

We describe recent progress of an ongoing research programme aimed at producing computational science software that can exploit high performance architectures in the atomic physics application domain. We examine the computational bottleneck of matrix construction in a suite of two-dimensional R-matrix propagation programs, 2DRMP, that are aimed at creating virtual electron collision experiments on HPC architectures. We build on Ixaru's extended frequency dependent quadrature rules (EFDQR) for Slater integrals and examine the challenge of constructing Hamiltonian matrices in parallel across an m-processor compute node in a block cyclic distribution for subsequent diagonalization by ScaLAPACK.

Resolution theory, and static and frequency-dependent cross-talk in piezoresponse force microscopy

Probing the functionality of materials locally by means of scanning probe microscopy (SPM) requires a reliable framework for identifying the target signal and separating it from the effects of surface morphology and instrument non-idealities, e.g. instrumental and topographical cross-talk. Here we develop a linear resolution theory framework in order to describe the cross-talk effects, and apply it for elucidation of frequency-dependent cross-talk mechanisms in piezoresponse force microscopy. The use of a band excitation method allows electromechanical/electrical and mechanical/topographic signals to be unambiguously separated. The applicability of a functional fit approach and multivariate statistical analysis methods for identification of data in band excitation SPM is explored.

A Frequency-Dependent Equivalence Between Groove Gap Waveguide and Rectangular Waveguide

Recently gap waveguides have been shown as a potential alternative to conventional waveguides in the millimeter-wave band. Groove Gap Waveguide (GGW) has until now been studied though direct correspondence with rectangular waveguide with the same propagation channel dimensions. However there have been observed differences in the above cutoff propagation characteristics between these waveguide types. Furthermore, the behaviour of GGW below cutoff remains unknown. This work presents a discussion of below and above cutoff propagation characteristics, and introduces a simple model that explains observed GGW behavior and establishes its propagation characteristics.

Impact of gate-source/drain channel architecture on the performance of an operational transconductance amplifier (OTA)

In this work, we report on the significance of gate-source/drain extension region (also known as underlap design) optimization in double gate (DG) FETs to improve the performance of an operational transconductance amplifier (OTA). It is demonstrated that high values of intrinsic voltage gain (A(VO_OTA)) > 55 dB and unity gain frequency (f(T_OTA)) similar to 57 GHz in a folded cascode OTA can be achieved with gate-underlap channel design in 60 nm DG MOSFETs. These values correspond to 15 dB improvement in A(VO_OTA) and three fold enhancement in f(T_OTA) over a conventional non-underlap design. OTA performance based on underlap single gate SOI MOSFETs realized in ultra-thin body (UTB) and ultra-thin body BOX (UTBB) technologies is also evaluated. A(VO_OTA) values exhibited by a DG MOSFET-based OTA are 1.3-1.6 times higher as compared to a conventional UTB/UTBB single gate OTA. f(T_OTA) values for DG OTA are 10 GHz higher for UTB OTAs whereas a twofold improvement is observed with respect to UTBB OTAs. The simultaneous improvement in A(VO_OTA) and f(T_OTA) highlights the usefulness of underlap channel architecture in improving gain-bandwidth trade-off in analog circuit design. Underlap channel OTAs demonstrate high degree of tolerance to misalignment/oversize between front and back gates without compromising the performance, thus relaxing crucial process/technology-dependent parameters to achieve 'idealized' DG MOSFETs. Results show that underlap OTAs designed with a spacer-to-straggle (s/sigma) ratio of 3.2 and operated below a bias current (IBIAS) of 80 mu A demonstrate optimum performance. The present work provides new opportunities for realizing future ultra-wide band OTA design with underlap DG MOSFETs.

Piezoresponse force microscopy of ferroelectric thin films: Frequency dependence of phase imaging

The objective of this work is an evaluation of quantitative measurements of piezoresponse force microscopy for nanoscale characterization of ferroelectric films. To this end, we investigate how the piezoresponse phase difference Delta Phi between c domains depends on the frequency omega of the applied ac field much lower than the cantilever first resonance frequency. The main specimen under study was a 102 nm thick film of Pb(Zr(0.2)Ti(0.8))O(3). For the sake of comparison, a 100 nm thick PbTiO(3) film was also used. From our measurements, we conclude a frequency dependent behavior Delta Phi similar to omega(-1), which can only be partially explained by the presence of adsorbates on the surface. (C) 2008 American Institute of Physics.

Investigation of tanpura string vibrations using a two-dimensional time-domain model incorporating coupling and bridge friction

Tanpura string vibrations have been investigated previously using numerical models based on energy conserving schemes derived from a Hamiltonian description in one-dimensional form. Such time-domain models have the property that, for the lossless case, the numerical Hamiltonian (representing total energy of the system) can be proven to be constant from one time step
to the next, irrespective of any of the system parameters; in practice the Hamiltonian can be shown to be conserved within machine precision. Models of this kind can reproduce a jvari effect, which results from the bridge-string interaction. However the one-dimensional formulation has recently been shown to fail to replicate the jvaris strong dependence on the thread placement. As a first step towards simulations which accurately emulate this sensitivity to the thread placement, a twodimensional model is proposed, incorporating coupling of controllable level between the two string polarisations at the string termination opposite from the barrier. In addition, a friction force acting when the string slides across the bridge in horizontal direction is introduced, thus effecting a further damping mechanism. In this preliminary study, the string is terminated at the position of the thread. As in the one-dimensional model, an implicit scheme has to be used to solve the system, employing Newton's method to calculate the updated positions and momentums of each string segment. The two-dimensional model is proven to be energy conserving when the loss parameters are set to zero, irrespective of the coupling constant. Both frequency-dependent and independent losses are then added to the string, so that the model can be compared to analogous instruments. The influence of coupling and the bridge friction are investigated.

Discrete-time modelling of woodwind instrument bores using wave variables

A method for simulation of acoustical bores, useful in the context of sound synthesis by physical modeling of woodwind instruments, is presented. As with previously developed methods, such as digital waveguide modeling (DWM) [Smith, Comput. Music J. 16, pp 74-91 (1992)] and the multi convolution algorithm (MCA) [Martinez et al., J. Acoust. Soc. Am. 84, pp 1620-1627 (1988)], the approach is based on a one-dimensional model of wave propagation in the bore. Both the DWM method and the MCA explicitly compute the transmission and reflection of wave variables that represent actual traveling pressure waves. The method presented in this report, the wave digital modeling (WDM) method, avoids the typical limitations associated with these methods by using a more general definition of the wave variables. An efficient and spatially modular discrete-time model is constructed from the digital representations of elemental bore units such as cylindrical sections, conical sections, and toneholes. Frequency-dependent phenomena, such as boundary losses, are approximated with digital filters. The stability of a simulation of a complete acoustic bore is investigated empirically. Results of the simulation of a full clarinet show that a very good concordance with classic transmission-line theory is obtained.

Nonlinear response of permanent dipoles in a uniaxial potential to alternating fields

It is shown how the existing theory of the dynamic Kerr effect and nonlinear dielectric relaxation based on the noninertial Brownian rotation of noninteracting rigid dipolar particles may be generalized to take into account interparticle interactions using the Maier-Saupe mean field potential. The results (available in simple closed form) suggest that the frequency dependent nonlinear response provides a method of measuring the Kramers escape rate (or in the analogous problem of magnetic relaxation of fine single domain ferromagnetic particles, the superparamagnetic relaxation time).

A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

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.

Wideband and Isotropic Room Acoustics Simulation Using 2-D Interpolated FDTD Schemes

In this paper, a complete method for finite-difference time-domain modeling of rooms in 2-D using compact explicit schemes is presented. A family of interpolated schemes using a rectilinear, nonstaggered grid is reviewed, and the most accurate and isotropic schemes are identified. Frequency-dependent boundaries are modeled using a digital impedance filter formulation that is consistent with locally reacting surface theory. A structurally stable and efficient boundary formulation is constructed by carefully combining the boundary condition with the interpolated scheme. An analytic prediction formula for the effective numerical reflectance is given, and a stability proof provided. The results indicate that the identified accurate and isotropic schemes are also very accurate in terms of numerical boundary reflectance, and outperform directly related methods such as Yee's scheme and the standard digital waveguide mesh. In addition, one particular scheme-referred to here as the interpolated wideband scheme-is suggested as the best scheme for most applications.

Time domain wave separation using multiple microphones

Methods of measuring the acoustic behavior of tubular systems can be broadly characterized as steady state measurements, where the measured signals are analyzed in terms of infinite duration sinusoids, and reflectometry measurements which exploit causality to separate the forward and backward going waves in a duct. This paper sets out a multiple microphone reflectometry technique which performs wave separation by using time domain convolution to track the forward and backward going waves in a cylindrical source tube. The current work uses two calibration runs (one for forward going waves and one for backward going waves) to measure the time domain transfer functions for each pair of microphones. These time domain transfer functions encode the time delay, frequency dependent losses and microphone gain ratios for travel between microphones. This approach is applied to the measurement of wave separation, bore profile and input impedance. The work differs from existing frequency domain methods in that it combines the information of multiple microphones within a time domain algorithm, and differs from existing time domain methods in its inclusion of the effect of losses and gain ratios in intermicrophone transfer functions.