Virtual Waves

Virtual Waves, by Synoptic, is a synthesis programming system for PC-compatible computers which includes not only elementary sound synthesis tools but also sound processing and sound analysis facilities. 

The basic building blocks of Virtual Waves for making instruments are called modules. The system provides a number of highly advanced modules, some of which implement fairly sophisticated synthesis techniques. For example, the system includes a module which alone is almost equivalent to the Yamaha DX7 synthesiser it contains a six-operator FM synthesis architecture with thirty-two preset algorithms. 

The complete list of modules is located to the left of the workspace and a module is selected simply by clicking on its name. When the mouse is moved over the workspace area an icon for the selected module automatically appears, and it can be placed anywhere within the area. The modules of the system are divided into three categories Generators, Processes and 

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The modules of the Analysis category analyse the signal passed through them without changing it in any way. Their purpose is solely to generate a visual representation of the analysis data. The available analysis techniques include SIFT (see Chapter 3) and sonogram. 

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Maxima of the second kind occur in concentrated solutions of the supporting electrolyte. They have various forms, mostly virtual waves on the limiting current (on the plateau). These humps are observed usually at the mercury flow rates higher than 2mgs" These effects may be eliminated in decreasing the mercury flow-rate and in diminishing the concentration of the base electrolyte cf. [66]. 

Figure 2.33 The Spectral Sketch Pad module of Virtual Waves allows for the creation of sounds graphically on a sketch pad area...

This technique was originally designed for a synthesis system developed by Ircam in Paris, called Chant (in French chant means sing). Ircam s Diphone system (in the folder diphone on the accompanying CD-ROM) provides a Chant module whereby the composer can either specify the FOF parameters manually or infer them automatically from the analysis of given samples. Also, Virtual Waves for PC-compatible under Windows (in the folder virwaves) provides an FOF unit generator as part of its repertoire of synthesis modules. 

Figure 8.27 The friendly graphic interface of Virtual Waves facilitates the straightforward creation of instruments, which are produced by interconnecting unit generators...

Projecting the nuclear solutions Xt( ) oti the Hilbert space of the electronic states (r, R) and working in the projected Hilbert space of the nuclear coordinates R. The equation of motion (the nuclear Schrddinger equation) is shown in Eq. (91) and the Lagrangean in Eq. (96). In either expression, the terms with represent couplings between the nuclear wave functions X (K) and X (R). that is, (virtual) transitions (or admixtures) between the nuclear states. (These may represent transitions also for the electronic states, which would get expressed in finite electionic lifetimes.) The expression for the transition matrix is not elementaiy, since the coupling terms are of a derivative type. 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

Melting, a major physical event, has small, subtle effects on shock-compression wave profiles. The relatively small volume changes and limited mixed-phase regions result in modest, localized changes in loading wave speed. Consequently, shock-induced melting and freezing remains an area with little data and virtually no information on the influence of solid properties and defects on its kinetics. 

For each occupied orbital, there will typically be one corresponding virtual orbital. This leads naturally to [n, m]-CASSCF wave functions where n and m are identical or nearly so. 

Just as the variational condition for an HF wave function can be formulated either as a matrix equation or in terms of orbital rotations (Sections 3.5 and 3.6), the CPFIF may also be viewed as a rotation of the molecular orbitals. In the absence of a perturbation the molecular orbitals make the energy stationary, i.e. the derivatives of the energy with respect to a change in the MOs are zero. This is equivalent to the statement that the off-diagonal elements of the Fock matrix between the occupied and virtual MOs are zero. 

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