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The lagrangian point of view is adopted to study turbulent premixed combustion. The evolution of the volume fraction of combustion products is established by the Reynolds transport theorem. It emerges that the burned-mass fraction is led by the turbulent particle motion, by the flame front velocity, and by the mean curvature of the flame front. A physical requirement connecting particle turbulent dispersion and flame front velocity is obtained from equating the expansion rates of the flame front progression and of the unburned particles spread. The resulting description compares favorably with experimental data. In the case of a zero-curvature flame, with a non-markovian parabolic model for turbulent dispersion, the formulation yields the Zimont equation extended to all elapsed times and fully determined by turbulence characteristics. The exact solution of the extended Zimont equation is calculated and analyzed to bring out different regimes.

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Echo-reconstruction techniques for non-intrusive imaging have wide application, from subsurface and underwater imaging to medical and industrial diagnostics. The techniques are based on experiments in which a collection of short acoustic or electromagnetic impulses, emitted at the surface, illuminate a certain volume and are backscattered by inhomogeneities of the medium. The inhomogeneities act as re ecting surfaces or interfaces which cause signal echoing; the echoes are then recorded at the surface and processed through a "computational lens" de ned by a propagation model to yield an image of the same inhomogeneities. The most sophisticated of these processing techniques involve simple acoustic imaging in seismic exploration, for which the huge data sets and stringent performance requirements make high performance computing essential. Migration, based on the scalar wave equation, is the standard imaging technique for seismic applications (1). In the migration process, the recorded pressure waves are used as initial conditions for a wave eld governed by the scalar wave equation in an inhomogeneous medium. Any migration technique begins with an a priori estimate of the velocity eld obtained from well logs and an empirical analysis of seismic traces. By interpreting migrated data, comparing the imaged interfaces with the discontinuities of the estimated velocity model, insu ciencies of the velocity eld can be detected and the estimate improved (2), allowing the next migration step to image more accurately. The iterative process (turnaround) of correcting to a velocity model consistent with the migrated data can last several computing weeks, and is particularly crucial for imaging complex geological structures, including those which are interesting for hydrocarbon prospecting. Subsurface depth imaging, being as it is the outcome of repeated steps of 3D seismic data migration, requires Gbytes of data which must be reduced, transformed, visualized and interpreted to obtain meaningful information. Severe performance requirements have led in the direction of high performance computing hardware and techniques. In addition, an enormous e ort has historically gone into simplifying the migration model so as to reduce the cost of the operation while retaining the essential features of the wave propagation. The phase-shift-plus-interpolation (PSPI) algorithm can be an e ective method for seismic migration using the "one-way" scalar wave equation; it is particularly well suited to data parallelism because of, among other things, its decoupling of the problem in the frequency domain. Exploding Re ector ModelThe PSPI method will be discussed in the context of coincident source-receiver experiments. With the seismic data compression technique known as stacking, signals corresponding to all source-receiver pairs having the common midpoint (x; y; 0) are collected into a single zero-o set trace which simulates a coincident source-receiver experiment. In such an experiment, the downward raypath and traveltime t=2 from the source t...

Comparative studies of methods of reverse time migration (RTM) show that spectral methods for calculating the Laplacian impose the least stringent demands on discretization stepsize; thus with spectral methods, the grid re nements often required by other methods can be avoided. Implemented with absorbing boundary conditions, which are energy-tuned to give good absorption at the boundaries, these spectral methods can be used e ectively for migration, without su ering the problems of wraparound which have traditionally plagued them (Furumyra and Takenaka, 1995).