Initial dimensions

The user must determine the initial dimensions of the volume source plume before exercising the SCREEN model volume source. Table 3 provides guidance on determining these inputs. 

Initial dimensions of the puff (e.g., from an explosion) may be approximated by finding a virtual distance simihir to tliat for area sources to give the appropriate initial standard deviation for each direction. Then Oy will be determined as a function of v +. Xy, a. as a function of v + x and as a function of x + x,. 

Figure 6. The initial dimensions of the ion population as defined by the diameter of the electron beam and the length of the cell.

Suppose the network is ideal, with N chain units between cross- links, while the initial dimensions are Zx° Zy° and lz (Figure 5.2). The network is then deformed to the dimensions lx, ly, lz. Statistical calculation of the number of possible chain conformations between the cross-links results, with S = k ln W, in ... 

With Cu-Zr, in an interval of 1000°C it amounts to 1 %. If initial dimensions, LCu and LZr, are 1 cm each, then the relative displacement of the phases is 100 pm which value is close on the order of magnitude to layer thicknesses encountered in reaction-diffusion experiments. With brittle compound layers formed and insufficiently ductile initial phases, this appears to be more than sufficient to cause any couple to rupture. 

Throughout this text we refer to the relationship between external mechanical loading and cellular response that affects the physiology of ECM. Inasmuch as mechanical terms are used repeatedly, some of these terms are listed in Table 1.4. These terms refer to the ability of tissue to change its shape and to deform. Strain refers to the changes in tissue dimensions with respect to the initial dimensions, and extensibility refers to the strain a tissue can undergo before failure. The force per unit cross-sectional area of a tissue is referred to as stress the stress at which a tissue tears is... 

Another approach to robust PCA has been proposed by Hubert et al. [52] and is called ROBPCA. This method combines ideas of both projection pursuit and robust covariance estimation. The projection pursuit part is used for the initial dimension reduction. Some ideas based on the MCD estimator are then applied to this lowerdimensional data space. Simulations have shown that this combined approach yields more accurate estimates than the raw projection pursuit algorithm RAPCA. The complete description of the ROBPCA method is quite involved, so here we will only outline the main stages of the algorithm. 

Gaylord and Lohse (10) have calculated the stress-strain relation for cilia and tie molecules in a spherical domain morphology using the same type of three-chain model as Meier. It is assumed that the overall sample deformation is affine while the domains are undeformable. It is predicted that the stress increases rapidly with increasing strain for both types of chains. The rate of stress rise is greatly accelerated as the ratio of the domain thickness to the initial interdomain separation increases. The results indicate that it is not correct to use the stress-strain equation obtained by Gaussian elasticity theory, even if it is multiplied by a filler effect correction term. No connection is made between the initial dimensions and the volume fractions of the domain and interdomain material in this theory. 

Note that the classic SLSP model for a square lattice ABCO would provide a percolation trajectory connecting opposite sites OA and CB (see Fig. 32). On the other hand, for visualization of dynamic percolation we shall consider an effective three-dimensional static representation of a percolation trajectory connecting ribs OA and ED spaced distance Lh (see Fig. 33). Such a consideration allows us to return to the lattice OEDA, with the initial dimension <7 = 2, which is non-square and characterized by the two dimensionless sizes Lh 11 and L/l. The new lattice size of the system can be determined from the rectangular triangle OEQ by... 

In uniaxial macroscopic deformation, the term draw ratio (DR) is customarily used to denote nominal draw (not molecular draw), or the change from the sample s initial dimension to its deformed state at each drawing step. Even though this is by no means a rigorous definition, it applies to deformations induced during simple sample extension or during stretching by differential roll speed. DR assumes full extension efficiency. 

L = initial dimension (tangential direction or radial direction) at certain moisture content,... 

For a cube of unit initial dimensions, di = iodX = dX and the stress cr is equal to the force /. Equation (2.70) is thus equivalent to... 

Initial dimensions of the RVE Current dimensions of the RVE Polyamide 6 Polyethylene-octene Polypropylene... 

Ganago et alP formulated a theory for predicting the order parameter (P2) in gels that are expanded or compressed without change in volume. If a gel is compressed along the x and y axes (or expanded along the z axis), the director n is parallel to the z axis. The deformed gel dimensions are related to the initial dimensions l, ly, /j by... 

There is an essential difference between the decomposition rates expressed by the quantities J and k. Unlike J, which does not depend on the particle size, k is inversely proportional to the initial dimensions of the particle. For pro = 1 (e.g., for p = 2,000 kg m and rg = 0.5 mm = 5 x 10 m), the rates J and k are numerically equal. The difference between these rates increases proportionately with increasing size and density of the particles. Equation 3.32 permits conversion from relative values of the rate constants k expressed in per second to the absolute rates J in units of kg m s. This opens up an attractive possibility for the interpretation of data obtained by traditional measurement of the a—t kinetic curves in terms of the Langmuir vaporization equations. 

The irradiated samples were tested for mechanical properties such as Young s modulus at room temperature using the ASTM D638 specification. Samples were prepared in a dog-bone shape of initial dimensions corresponding to gauge length of 10 mm and width of 2.8 mm. An Instron... 

A generic name for polymeric substances with enhanced plastic-elastic behaviour, which is characteristic for vulcanised rubber-like synthetic or natural polymers. Elastomers, at room temperature, return rapidly to approximately their initial dimensions and shape even after substantial deformation by a weak stress and release of the stress. 

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