Value cube

Students will assemble a value cube, creating a design that continues from one surface of the cube to another (Level Three). 

Level Three Three-Dimensional Value Cube... 

Handout 1.3 Pattern for a Three-Dimensional Value Cube.61... 

All extrema within a 3D seismic volume can be represented by two sparse 3D cubes, containing only information about the minimum and maximum events in the seismic data. A vertical trace of the first cube contains the actual maximum or minimum seismic amplitude values along this trace, stored in the vertically closest voxel along the trace. This cube is referred to as the extrema value cube. The second cube, denoted the extrema position cube, contains sub-sample information about the exact location of the extrema, i.e., the vertical correction to the seismic sampling resolution. Both extrema cubes are sparse cubes, with value zero at voxel positions not falling on an extremum. The set of voxels containing extrema data is the same for the two cubes, but contains amplitudes and sub-sample positions respectively. 

Figure 1 shows an example of a sparse extrema representation of a seismic section, illustrating the cube containing amplitude values. All events from the original seismic section are preserved in the extrema value cube, but are represented only through the position of its minimum or maximum. 

Fig. 1. The left image shows a vertical section through a seismic cube. The right image shows the corresponding section of the sparse extrema value cube, where only minimum or maximum positions have non-zero values.

The first term on the right is the common inverse cube law, the second is taken to be the empirically more important form for moderate film thickness (and also conforms to the polarization model, Section XVII-7C), and the last term allows for structural perturbation in the adsorbed film relative to bulk liquid adsorbate. In effect, the vapor pressure of a thin multilayer film is taken to be P and to relax toward P as the film thickens. The equation has been useful in relating adsorption isotherms to contact angle behavior (see Section X-7). Roy and Halsey [73] have used a similar equation earlier, Halsey [74] allowed for surface heterogeneity by assuming a distribution of Uq values in Eq. XVII-79. Dubinin s equation (Eq. XVII-75) has been mentioned another variant has been used by Bonnetain and co-workers [7S]. 

The numerical values of and a, for a particular sample, which will depend on the kind of linear dimension chosen, cannot be calculated a priori except in the very simplest of cases. In practice one nearly always has to be satisfied with an approximate estimate of their values. For this purpose X is best taken as the mean projected diameter d, i.e. the diameter of a circle having the same area as the projected image of the particle, when viewed in a direction normal to the plane of greatest stability is determined microscopically, and it includes no contributions from the thickness of the particle, i.e. from the dimension normal to the plane of greatest stability. For perfect cubes and spheres, the value of the ratio x,/a ( = K, say) is of course equal to 6. For sand. Fair and Hatch found, with rounded particles 6T, with worn particles 6-4, and with sharp particles 7-7. For crushed quartz, Cartwright reports values of K ranging from 14 to 18, but since the specific surface was determined by nitrogen adsorption (p. 61) some internal surface was probably included. f... 

Bentonite has expected sihca content of 0.5 weight percent (F is 0.005). Silica density (A ) is 2.4 gm per cii cm, and bentonite (Ag) is 2.6. The calculation requires knowledge of mineral properties described by the factor (fghd ). Value of the factor can be estabhshed from fundamental data (Gy) or be derived from previous experience. In this example, data from testing a shipment of bentonite of 10 mesh top-size screen analysis determined value of the mineral factor to be 0.28. This value is scaled by the cube of diameter to ys-in screen size of the example shipment. The mineral factor is scaled from 0.28 to 52 by multiplying 0.28 with the ratio of cubed 9.4 mm (ys-in screen top-size of the shipment to be tested) and cubed 1.65 mm (equivalent to 10 mesh). 

In lead zh conate, PbZrOs, the larger lead ions are displaced alternately from the cube corner sites to produce an antifeiToelectric. This can readily be converted to a feiToelectric by dre substitution of Ti" + ions for some of the Zr + ions, the maximum value of permittivity occumirg at about the 50 50 mixture of PbZrOs and PbTiOs. The resulting PZT ceramics are used in a number of capacitance and electro-optic applicahons. The major problem in dre preparation of these solid soluhons is the volatility of PbO. This is overcome by... 

Now that we have the mass M, we can calculate the thickness t from eqn (7.2). Values of t for various materials are given in Table 7.1. The glass mirror has to be about 1 m thick (and real mirrors are about this thick) the CFRP-backed mirror need only be 0.38 m thick. The polyurethane foam mirror has to be very thick - although there is no reason why one could not make a 6 m cube of such a foam. 

The equations have been expressed as proportionals however, they can be used by simply ratioing an old to a new value. To add credibility to fan law adaptation, recall the flow coefficient, Equation 5.19, The term Qj/N is used which shows a direct proportion between volume Qj and speed N. Equation 5.12 indicates the head, Hp, to be a function of the tip speed, squared. The tip speed is, in turn, a direct function of speed making head proportional to speed. Finally, the power, Wp, is a function of head multiplied by flow, from which the deduction of power, proper tional to the speed cubed, may be made. 

The premise of the above analysis is the fact that it has treated the interfacial and bulk viscoelasticity equally (linearly viscoelastic experiencing similar time scales of relaxation). Falsafi et al. make an assumption that the adhesion energy G is constant in the course of loading experiments and its value corresponds to the thermodynamic work of adhesion W. By incorporating the time-dependent part of K t) into the left-hand side (LHS) of Eq. 61 and convoluting it with the evolution of the cube of the contact radius in the entire course of the contact, one can generate a set of [LHS(t), P(0J data. By applying the same procedure described for the elastic case, now the set of [LHS(t), / (Ol points can be fitted to the Eq. 61 for the best values of A"(I) and W. 

FIGURE 7.80 CDF-predicted values of maximum velocity V, temperature differential, ( C), and airflow, q (Us), in the horizontal cross-section of the buoyant plume above the heated cube (0.66 m x 0.66 m X 0.66 m, 22SW).i ... 

In the square brackets are given the exact values found in the literature. Surface area S, in the table, is the normalized per face of the unit cube L, surface area S of the interface in the unit cell, S = S/1, L = N - )h. The energy is given per unit volume. 

In the compression test, four or five sample cubes of the slurry are allowed to cure for a specified period of time. The cement cubes are placed in a compression testing machine and the compressive strength of each sample cube obtained experimentally. The average value of the samples is obtained and reported as the compressive strength of the set cement. 

K value is the ratio of the cube root of a boiling temperature to gravity. There are two widely used methods to calculate the K factor K, and the K, p. The equations used for calculating both factors are as follows ... 

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