Nodal points

The unknowns in this equation are the local coordinates of the foot (i.e. and 7]). After insertion of the global coordinates of the foot found at step 6 in the left-hand side, and the global coordinates of the nodal points in a given element in the right-hand side of this equation, it is solved using the Newton-Raphson method. If the foot is actually inside the selected element then for a quadrilateral element its local coordinates must be between -1 and +1 (a suitable criteria should be used in other types of elements). If the search is not successful then another element is selected and the procedure is repeated. 

CALCULATE PRESSURE L STRESS AT NODAL POINT.S (VARIATIONAL RECOVERY) ... 

Nodal points of the platform require special attention for corrosion protection. Therefore the anodes have to be installed in the vicinity of these points, as indicated in Fig. 16-4. The spacing must be sufficiently large that the welded Joints of the nodes do not lie in the area of the lap Joints. The effort for calculating the optimal distribution with the lowest weight of anodes is considerable and has led to computer programs by which the anode distribution can be estimated [11]. 

The radial transducers should be placed within three inches of the bearing, and there should be two radial transducers at each bearing. Care should be taken not to place the probe at the nodal points. The two probes should be mounted 90° apart ( 5°) at a 45° ( 5°) angle from each side of the vertical center. Viewed from the drive end of the machine train, the x probe will be on the right side of the vertical, and the i probe will be on the left side of the vertical. Figures 4-10 and 4-11 show protection systems for a turbine and a gear box respectively. 

The direct correlation function c is the sum of all graphs in h with no nodal points. The cluster expansions for the correlation functions were first obtained and analyzed in detail by Madden and Glandt [15,16]. However, the exact equations for the correlation functions, which have been called the replica Ornstein-Zernike (ROZ) equations, have been derived by Given and Stell [17-19]. These equations, for a one-component fluid in a one-component matrix, have the following form... 

Knoten-linie, /. nodal line, -punkt, m. nodal point junction, -wurz,/. figwort, Pharm.) scrophularia. -zahl, /. nodal number number of nodes. 

Brown J, Plutzky J (2007) PPARs as transcriptional nodal points and therapeutic targets. Circulation 115 518-533... 

Newton, R., 517, 536,539,560 Newton-Raphson method, 86 Newton s method, 79,80 Newton, T. 0., 555 Neyman-Pearson lemma, 306 Nodal point, 326 Node, 326 proper, 326 Noise... 

If the coefficient k x) is discontinuous at the middle nodal points x = Xj j/2 and the coefficients q x) and f x) are discontinuous at the points x = Xj, the half-sums of the left and right limiting values have to be substituted into formulae (19). As a final result we get... 

When the available functions k x), q x) and f[x) happen to be of the class 1] and their discontinuity points are known, a non-equidistant grid can be made so that all discontinuity points of the coefficients k, q and / would be nodal points of such a grid. We denote by any such... 

In the case of continuous coefficients expressions (5) imply that Oj = ki i, di = qi and ipi = fi- If discontinuity points coincide with nodal points of the grid uij, that is, x = Xi j2, then the members a, di and [Pg.170]

As a result, a considerable amount of effort has been expended in designing various methods for providing difference approximations of differential equations. The simplest and, in a certain sense, natural method is connected with selecting a, suitable pattern and imposing on this pattern a difference equation with undetermined coefficients which may depend on nodal points and step. Requirements of solvability and approximation of a certain order cause some limitations on a proper choice of coefficients. However, those constraints are rather mild and we get an infinite set (for instance, a multi-parameter family) of schemes. There is some consensus of opinion that this is acceptable if we wish to get more and more properties of schemes such as homogeneity, conservatism, etc., leaving us with narrower classes of admissible schemes. 

In particular, it is always possible to choose a grid so that would be one of the nodal point and... 

The accurate account of the error z can be done as in Section 4, leading to the same rate of convergence. No progress is achieved for a = a in line with approved rules, because the choice of the coefficient should not cause the emergence of a higher-order accuracy. From the formula = 9 Q+0 h) it is easily seen that i]n+i — 0(h) and, hence, z = 0(h +T" ) if = 0, meaning that the heat source is located at one of the nodal points. 

If the coefficient k x,t) and the right-hand side f x,t) possess only a finite number of immovable discontinuities, the grid = u>i [K) will be so chosen that all discontinuity lines will pass through the nodal points (the... 

This problem can be solved by the standard elimination method rec uiring 0 /h) = 0 N) operations, the amount of which is proportional to the total number N of nodal points of the grid = k,- = ih, 0 [Pg.548]

What is more, it seems clear from the preceding examples that coincides with u x,i) at all nodal points. 

Here the boundary conditions for may be imposed only on some part r of the entire boundary F consisting of the points of the intersection of F with possible lines parallel to the axis Ox and passing through any inner point x G. The nodal points x 7/, belong to that part Fc,. 

In the estimation of the function v we write down equation (31) in the canonical form (28) by regarging P = x to nodal points of the p-dimensional grid... 

Free-free vibration of rod supported at nodal points, circular cross section... 

Fig. 20.2. Indexing of nodal blocks in a finite difference grid, showing point (7,./) and it nearest neighbors. Properties of the nodal blocks are projected onto nodal points located at the center of each block.

Each nodal block represents a distinct system, as we have defined it (Fig. 2.1). Conceptually, the properties of the entire block are projected onto a nodal point at the block s center (Fig. 20.2). A single value for any variable is carried per node in a transport or reactive transport simulation. There is one Ca++ concentration, one pH, one porosity, and so on. In other words, there is no accounting in the finite difference method for the extent to which the properties of a groundwater or the... 

In a finite difference model, the differential equation representing mass transport (Eqn. 20.24 or 20.25) is converted into an approximate, algebraic form that can readily be evaluated using a computer. A derivative of concentration in space evaluated between nodal points (/, J) and (7 + 1, J), for example, can be written,... 

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