Design Methodology for Real-Time FPGA-Based Sound Synthesis

Explicit finite difference (FD) schemes can realise highly realistic physical models of musical instruments but are computationally complex. A design methodology is presented for the creation of FPGA-based micro-architectures for FD schemes which can be applied to a range of applications with varying computational requirements, excitation and output patterns and boundary conditions. It has been applied to membrane and plate-based sound producing models, resulting in faster than real-time performance on a Xilinx XC2VP50 device which is 10 to 35 times faster than general purpose and DSP processors. The models have developed in such a way to allow a wide range of interaction (by a musician) thereby leading to the possibility of creating a highly realistic digital musical instrument.

Instability and evolution of nonlinearly interacting water waves

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrodinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.

Modulational instability and localized excitations of dust-ion acoustic waves

Theoretical and numerical studies are carried out of the nonlinear amplitude modulation of dust-ion acoustic waves propagating in an unmagnetized weakly coupled plasma comprised of electrons, positive ions, and charged dust grains, considering perturbations oblique to the carrier wave propagation direction. The stability analysis, based on a nonlinear Schrodinger-type equation, exhibits a wide instability region, which depends on both the angle theta between the modulation and propagation directions and the dust number density n(d). Explicit expressions for the instability increment and threshold are obtained. The possibility and conditions for the existence of different types of localized excitations are also discussed. (C) 2003 American Institute of Physics.

Ion-acoustic waves in a plasma consisting of adiabatic warm ions, non-isothermal electrons and a weakly relativistic electron beam: linear and higher-order nonlinear effects

The nonlinear propagation of finite amplitude ion acoustic solitary waves in a plasma consisting of adiabatic warm ions, nonisothermal electrons, and a weakly relativistic electron beam is studied via a two-fluid model. A multiple scales technique is employed to investigate the nonlinear regime. The existence of the electron beam gives rise to four linear ion acoustic modes, which propagate at different phase speeds. The numerical analysis shows that the propagation speed of two of these modes may become complex-valued (i.e., waves cannot occur) under conditions which depend on values of the beam-to-background-electron density ratio , the ion-to-free-electron temperature ratio , and the electron beam velocity v0; the remaining two modes remain real in all cases. The basic set of fluid equations are reduced to a Schamel-type equation and a linear inhomogeneous equation for the first and second-order potential perturbations, respectively. Stationary solutions of the coupled equations are derived using a renormalization method. Higher-order nonlinearity is thus shown to modify the solitary wave amplitude and may also deform its shape, even possibly transforming a simple pulse into a W-type curve for one of the modes. The dependence of the excitation amplitude and of the higher-order nonlinearity potential correction on the parameters , , and v0 is numerically investigated.

Parametric study of nonlinear electrostatic waves in two-dimensional quantum dusty plasmas

The nonlinear properties of two-dimensional cylindrical quantum dust-ion-acoustic (QDIA) and quantum dust-acoustic (QDA) waves are studied in a collisionless, unmagnetized and dense (quantum) dusty plasma. For this purpose, the reductive perturbation technique is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev–Petviashvili (CKP) equations. The effects of quantum diffraction, as well as quantum statistical and geometric effects on the profiles of QDIA and QDA solitary waves are examined. It is found that the amplitudes and widths of the nonplanar QDIA and QDA waves are significantly affected by the quantum electron tunneling effect. The addition of a dust component to a quantum plasma is seen to affect the propagation characteristics of localized QDIA excitations. In the case of low-frequency QDA waves, this effect is even stronger, since the actual form of the potential solitary waves, in fact, depends on the dust charge polarity (positive/negative) itself (allowing for positive/negative potential forms, respectively). The relevance of the present investigation to metallic nanostructures is highlighted.

Speeds of sound and isentropic compressibilities of binary mixtures containing trialkylamines with alkanes and mono-alkylamines at 303.15 and 313.15 K

Isentropic compressibilities ?S, and excess isentropic compressibilities ?SE have been determined from measurements of speeds of sound u and densities ? of 14 binary mixtures of triethylamine (TEA) and tri-n-butylamine (TBA) with n-hexane, n-octane, iso-octane, n-propylamine, n-butylamine, n-hexylamine and n-octylamine. The relative magnitude and sign of ?SE have been interpreted in terms of molecular interactions and interstitial accommodation. The values of ?SE for TEA + alkane are positive while for TBA + alkane are negative. The values of ?SE for TEA + primary amine become progressively less positive and eventually to negative with the increase in chain length of alkylamine. In case of TBA + primary amine, the values of ?SE increase from n-propylamine to n-butylamine, and then decrease with chain length of primary amine. The experimental speeds of sound u have been analyzed in terms of collision factor theory, free length theory and Prigogine–Flory–Patterson statistical theory of solutions.

Speeds of sound, isentropic compressibilities, and excess molar volumes of cycloalkanes, alkanes and aromatic hydrocarbons at 303.15 K. II. Results for cycloalkanes+aromatic hydrocarbons

The speeds of sound u, isentropic compressibilities ?S, molar sound functions R, excess isentropic compressibilities ?SE and excess molar volumes VE for eight binary mixtures of cyclopentane, cyclohexane, cyclooctane and methylcyclohexane with benzene and of cyclohexane with toluene, ethyl benzene, p-xylene and propyl benzene at 303.15 K are reported. The effects of molecular sizes and shapes of the component molecules and of interaction energy in the mixture have been discussed. The Prigogine–Flory–Patterson theory has been applied to analyze the present binary mixtures along with the mixtures of cis- and trans-decalins with benzene and toluene taken from the literature.

Densities, speeds of sound, isentropic compressibilities, refractive indices and viscosities of binary mixtures of tetrahydrofuran with hydrocarbons at 303.15 K

Isentropic compressibilities, Rao's molar sound functions, molar refractions, excess isentropic compressibilities, excess molar volumes, viscosity deviations and excess Gibbs energies of activation of viscous flow for seven binary mixtures of tetrahydrofuran (THF) with cyclohexane, methylcyclohexane, n-hexane, benzene, toluene, p-xylene and propylbenzene over the entire range of composition at 303.15 K have been derived from experimental densities, speeds of sound, refractive indices and viscosities. The excess partial molar volumes of THF in different solvents have been estimated. The experimental results have been analyzed in terms of the Prigogine–Flory–Patterson theory.

Densities, speeds of sound, isentropic compressibilities, refractive indexes, and viscosities of tetrahydrofuran with haloalkane or alkyl ethanoate at T = 303.15 K

Isentropic compressibilities ?S, excess isentropic compressibilities image, excess molar volumes VE, viscosity deviations ??, and excess Gibbs energy of activation of viscous flow ?G*E for nine binary mixtures of C4H8O with CCl4, CHCl3, CHCl2CHCl2, 1-C6H13Cl, 1-C6H13Br, CH3CO2CH3, CH3CO2C2H5, CH3CO2C4H9, and CH3CO2C5H11 at 303.15 K have been derived from experimental densities ?, speeds of sound u, refractive indexes nD and viscosities ?. The limiting values of excess partial molar volumes of C4H8O at infinite dilution image in different solvents have been estimated. The results obtained for dynamic viscosity of binary mixtures were used to test the semi-empirical relations of Grunberg–Nissan, Tamura–Kurata, Hind–McLaughlin–Ubbelohde, Katti–Chaudhri, McAllister, Heric, and Auslaender. Finally, the experimental refractive indexes were compared with the predicted results for Lorentz–Lorenz, Dale–Gladstone, Eykman, Arago–Boit, Newton, Oster, Heller, and Wiener equations.

Speeds of sound, isentropic compressibilities, viscosities, and excess molar volumes of binary mixtures of alkanoates with tetra- and trichloromethanes at 303.15 K

Speeds of sound u, isentropic compressibilities ?S, viscosities ?, excess isentropic compressibilities ?SE, excess molar volumes VE, viscosity deviations ??, and excess Gibbs energies of activation ?G*E of viscous flow have been investigated for six binary mixtures of diethyl malonate, diethyl bromomalonate, and ethyl chloroacetate with tetra- and trichloromethane at 303.15 K. The values of ?SE, VE, ??, and ?G*E are highly dependent on the type of components involved and the composition curves are unsymmetrical. The results obtained for viscosity of binary mixtures were used to test the semi-empirical relations of Grunberg-Nissan, Tamura-Kurata, Hind-McLaughlin-Ubbelohde, Katti-Chaudhri, McAllister, Heric-Brewer and Auslaender. The experimental speeds of sound have been analyzed in terms of collision factor theory and free length theory of solutions.

Estimation of speed of sound of ionic liquids using surface tensions and densities: A volume based approach

The limited availability of experimental data and their quality have been preventing the development of predictive methods and Computer Aided Molecular Design (CAMD) of ionic liquids (ILs). Based on experimental speed of sound data collected from the literature, the inter-relationship of surface tension (s), density (?), and speed of sound (u) has been examined for imidazolium based ILs containing hexafluorophosphate (PF6), tetrafluoroborate (BF4), bis(trifluoromethanesulphonyl) amide (NTf2), methyl sulphate (MeSO4), ethyl sulphate (EtSO4), and trifluoromethanesulphonate (CF3SO3) anions, covering wide ranges of temperature, 278.15–343.15 K and speed of sound, 1129.0–1851.0 m s-1. The speed of sound was correlated with a modified Auerbach's relation, by using surface tension and density data obtained from volume based predictive methods previously proposed by the authors. It is shown that a good agreement with literature data is obtained. For 133 data points of 14 ILs studied a mean percent deviation (MPD) of 1.96% with a maximum deviation inferior to 5% was observed. The correlations developed here can thus be used to evaluate the speeds of sound of new ionic liquids.