X and y direction

For the case of a double-D coil we multiply each matrix element with an element shifted by a constant distance of the same line. This is done in x- and y-direction. The distance between the two elements is the correlation length X for filtering in x-direction and a second correlation length for the movement in y-direction. Thus one gets two new matrices Ax and Ax for the filtering from the left to the right (positiv x-direction) and vice versa (negativ x-direction). 

The measurements are done at a table with two in X- and Y- direction moveable axes. The measured structures, by an Aluminium-alloy, are situated at the X-axis. The sensor at the Y-axis scans the structure step by step. The position and the electoral signal are measured for every step. A computer controls the movement of the sensor and the data acquisition. 

The GAMMASCAN 1500 HR is a combined system for two-dimensional (2D-CT) and three-dimensional (3D-CT) computed tomography, as well as digital radiography (DR). The system is equipped with two separate detector systems for the fan-beam and cone-beam CT. The sire of the objects is limited to a height of four meters, maximum diameters of 1.5 meters and a weight of up to 15 tons. The turntable which carries the test samples can be moved along and across the beam direction ( X- and Y- direction). The radiation source and the detector systems can be moved in Z- direction, both, simultaneously and independently. 

This type of scanning produces positioning data which is false in both x- and y-direction caused by the fact that acqusition software operates assuming that the shape of the test object is cylindrical. 

Equation (3.85) T is a translation vector that maps each position into an equivalent ition in a neighbouring cell, r is a general positional vector and k is the wavevector ich characterises the wavefunction. k has components k, and ky in two dimensions and quivalent to the parameter k in the one-dimensional system. For the two-dimensional lare lattice the Schrodinger equation can be expressed in terms of separate wavefunctions ng the X- and y-directions. This results in various combinations of the atomic Is orbitals, ne of which are shown in Figure 3.13. These combinations have different energies. The /est-energy solution corresponds to (k =0, ky = 0) and is a straightforward linear... 

Pressure gradients in the x and y directions do not depend on 2, hence the integration of the components of the equation of motion, subject to conditions (5.42), yields... 

Beeause there are no terms in this equation that couple motion in the x and y directions (e.g., no terms of the form x yb or 3/3x 3/3y or x3/3y), separation of variables can be used to write / as a product /(x,y)=A(x)B(y). Substitution of this form into the Schrodinger equation, followed by collecting together all x-dependent and all y-dependent terms, gives ... 

In the X- and y-directions (Figure 49.5b), an ion trajectory is more difficult to visualize. It is essentially the sum of two main effects one a simple oscillation caused by the rapid cyclic alternations of the RF field (Figure 49.5c), the other a more complicated drift or guided motion due to the inhomogeneity of the RF field within the space between all four rods. 

After the forces are evaluated for each cylinder of a multistage compressor, all forces must be summed in the x and y direction. For the max imum shaking forces, the value of the crank angle, which contributes the maximum force, should be used. This involves taking the respective sine and cosine functions to their maximum. For example, a vertical cylinder will have the maximum component force at a crank angle of 0 and 180 . At this time, the horizontal components, primary and secondary, are zero. 

The direct strains in the global X and Y directions will be given by (see Appendix C for details)... 

If the material is subjected to biaxial stresses in both the x and y directions then the strains will be... 

Two-dimensional flow is in the x and y directions, while three-dimensional flow is in the x, y, and 2 directions. 

The negative sign indicates that the flow is in the negative x and y directions, i.e., toward the hood face. The applicability of this model was verified by tVnastas and Hughes- and Drkal, who compared theoretical to experimental centerline velocities and found close agreement. 

For a theoretical analysis of SFA experiments it is prudent to start from a somewhat oversimplified model in which a fluid is confined by two parallel substrates in the z direction (see Fig. 1). To eliminate edge effects, the substrates are assumed to extend to infinity in the x and y directions. The system in the thermodynamic sense is taken to be a lamella of the fluid bounded by the substrate surfaces and by segments of the (imaginary) planes x = 0, jc = y = 0, and y = Sy. Since the lamella is only a virtual construct it is convenient to associate with it the computational cell in later practical... 

Two situations are considered which differ in the number of constraints imposed. In the first one the shear strain in x and y directions is fixed, infinitesimal, reversible transformations are governed by the thermodynamic potential [see Eq. (9)], and X is the relevant partition function [see Eq. (52)]. Here the shear stress is computed as a function of the registry... 

FIG. 19 Scheme of a simple fluid confined by a chemically heterogeneous model pore. Fluid modecules (grey spheres) are spherically symmetric. Each substrate consists of a sequence of crystallographic planes separated by a distance 8 along the z axis. The surface planes of the two opposite substrates are separated by a distance s,. Periodic boundary conditions are imposed in the x and y directions (see text) (from Ref. 77). 

This concept has been known for over a century. Expressed as Brewster s Constant law, it states that the index of refraction in a strained material becomes directional, and the change of the index is proportional to the magnitude of the stress (or strain) present. Therefore, a polarized beam in the clear plastic splits into two wave fronts in the X and Y directions that contain vibrations oriented along the directions of principal stresses. An analyzing filter passes only vibrations parallel to its own transmitting plane (Chapter 4, TRANSPARENT AND OPTICAL PRODUCT, Polarized Lighting). 

A simple Michelson interferometer. If we place two mirrors at the end of two orthogonal arms of length L oriented along the x and y directions, a beamsplitter plate at the origin of our coordinate system and send photons in both arms trough the beamsplitter. Photons that were sent simultaneously will return on the beamsplitter with a time delay which will depend on which arm they propagated in. The round trip time difference, measured at the beamsplitter location, between photons that went in the a -arm (a -beam) and photons that went in the y arm (y-beam) is... 

By scanning the laser beam in the x and y directions, the LDV technique can be extended to full area measurement and display. This technique scans an area on a point-by-... 

Fig. 11—Pressure and film thickness profiles along x and y directions, in comparison with the corresponding results of dry contact, (a) Pressure and film thickness profiles along the x direction at y = 0. (b) Pressure and film thickness profiles along the y direction at x=0.

When the plane moves at 0.1 mm/s and under a normal load of 38.29 N, the numerical mixed lubrication model yields the solutions of film thickness and pressure distribution shown in Fig. 11 where the profiles are taken along the central lines in the x and y directions, respectively. Corresponding results from dry contact analyses are given in the same hgure for comparison. Excellent agreements observed... 

To create a two-dimensional image, two gradients are applied along the X- and y-directions, and a series of one-dimensional images recorded in different directions in the xy-plane. A technique known as back-projection... 

Helical undulators build on this principle by using two orthogonal magnetic field arrays [82, 83]. These permit transverse excursions in perpendicular x and y directions. If the arrays have a relative longitudinal shift, this introduces a phase to the induced perpendicular excursions and when the phase is 90° the electron trajectory can follow left- or right-handed corkscrew paths The emitted radiation is correspondingly right- or left-handed CPL. 

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