Two-dimensional propagator

It is also possible to perform a two-dimensional PFG spin-echo experiment employing two orthogonal magnetic field gradients. This yields a two-dimensional propagator Ps X, Y, A) that corresponds to the joint probability for molecular displacements X and Y in time A. Results have been obtained on a packed bed of glass spheres and on a sandstone, and have been compared with those predicted by numerical simulation of the flow assuming pore network models. ... 

Two-dimensional propagation of self-complementary coordination provides a more robust network system for electrical conduction, since the network is not fully disrupted by defect formation in the structure. This property... 

In the earlier communication, Das et al. [67] reported results of the investigation on the one-dimensional propagation of yellow/red mercuric iodide. In a later communication, Das et al. [68] reported new results on the two-dimensional propagation of a red/yellow wave of mercuric iodide, in gel media in batch, DPL and gel-ring reactors. Salient features of the investigation are as follows Precipitation was carried out in a DPL continuous flow reactor, as described earlier, in which the concentration and level of the entering reagent in the empty space were always kept constant. Experiments were... 

The two-dimensional propagation of delaminations in isotropic plates and cross-ply laminates (0 /90°)2s was analyzed by using an interface element. The dimensions of the laminates and the material properties of each layer are the same as in the models of the previous section. Owing to the symmetry, a quarter of the plate was analyzed. Circular initial delaminations of radius 2.5 mm were situated at its center. Figure 14 shows the relationships between the applied load and the center deflection where a finite element mesh is shown. The propagation of delaminations occurred first at the center interlaminar plane where the energy... 

In order to ensure perpendicular beam incidence on the cylindrical specimen, the circular B-scan profiles were acquired by high frequency (narrow beam) transducers in a synthetic circular aperture array. From these profiles two-dimensional reflection tomograms were reconstructed using a filtered backprojection technique. Straight line propagation was assumed. Several artificial discontinuity types in a cylindrical Plexiglas (Perspex) specimen were compared with similar artificial discontinuities in a cylindrical A/Si-alloy [2]. Furthermore, examples of real discontinuities (an inclusion and a feed head) in the cylindrical AlSi-alloy are presented. 

Zaikin A N and Zhabotinsky A M 1970 Concentration wave propagation in two-dimensional liquid-phase self-oscillating system Nature 225 535-7... 

J.W. Swegle, TOODY IV—A Computer Program for Two-Dimensional Wave Propagation, SAND78-0552, Sandia National Laboratories, Albuquerque, NM, 1978. 

The only computational approach found in the literature to modeling flash-hre radiation is that of Raj and Emmons (1975), who modeled a flash fire as a two-dimensional, turbulent flame propagating at a constant speed. The model is based on the following experimental observations ... 

The model is a straightforward extension of a pool-fire model developed by Steward (1964), and is, of course, a drastic simplification of reality. Figure 5.4 illustrates the model, consisting of a two-dimensional, turbulent-flame front propagating at a given, constant velocity S into a stagnant mixture of depth d. The flame base of width W is dependent on the combustion process in the buoyant plume above the flame base. This fire plume is fed by an unbumt mixture that flows in with velocity Mq. The model assumes that the combustion process is fully convection-controlled, and therefore, fully determined by entrainment of air into the buoyant fire plume. 

The simplest binary valued CA proven to be computation universal is John Conway s two-dimensional Life rule, about which we will have much to say later in this chapter. Many of the key ingredients necessary to prove universality, however, such as sets of propagating structures out of which analogs of conventional hardware components (i.e., wires, gates and memory) may be explicitly constructed, appear, at least in principle, to be supported by certain one-dimensional rules as well. The most basic component required is a mechanism for transporting localized packets of information from one part of the lattice to another i.e., particle-like persistent propagating patterns, whose presence is usually indicative of class c4 behavior. 

Rules for which A is near Ac appear to support propagating solitoii structures, suggesting that the most complex rules (i.e. those belonging to Wolfram s class c4) lie within this transition region - A for Conway s Life rule, for example, is equal to 0.273 and lies within the transition region for k = 2, A/ = 9 two dimensional CA,... 

The actual computation is broken down into two steps (1) A Collision Step, during which the value of a site is sent to a computation look-up table, with its input written to the display screen memory as in CAM-6. RAPl s screen memory consists of 16 256 x 512 planes, (2) A Propagation Step, during which the system is decomposed into a set of one-bit two-dimensional planes (one plane for each bit of each site), and the bits of each site are displaced to one of the site s neighbors by a translation of the entire plane. 

Since it was proposed in the early 1980s [6, 7], spin-relaxation has been extensively used to determine the surface-to-volume ratio of porous materials [8-10]. Pore structure has been probed by the effect on the diffusion coefficient [11, 12] and the diffusion propagator [13,14], Self-diffusion coefficient measurements as a function of diffusion time provide surface-to-volume ratio information for the early times, and tortuosity for the long times. Recent techniques of two-dimensional NMR of relaxation and diffusion [15-21] have proven particularly interesting for several applications. The development of portable NMR sensors (e.g., NMR logging devices [22] and NMR-MOUSE [23]) and novel concepts for ex situ NMR [24, 25] demonstrate the potential to extend the NMR technology to a broad application of field material testing. 

---