Balling, defined

Prior to the actual tests, the ball was run in at a load of 5N with a speed of 31.4mm/min for 2h outside the region to be analyzed, in order to create a flat spot on the ball, defining the apparent contact area in the tribotest that followed. 

A ball rolls downhill until it reaches the bottom, and then stays there. The bottom is its equilibrium position. Equilibrium defines where a system tends to go and stay. The force f on the ball defines the strength of its tendency toward equilibrium ... 

The first bUhard ball (defined as the system) stops rolling after the colhsion. 

The terms wetting and nonwetting as employed in various practical situations tend to be defined in terms of the effect desired. Usually, however, wetting means that the contact angle between a liquid and a solid is zero or so close to zero that the liquid spreads over the solid easily, and nonwetting means that the angle is greater than 90° so that the liquid tends to ball up and run off the surface easily. 

The ASA (now ANSI) performance code for Safety Glazing Materials was revised in 1966 to incorporate these improvements in windshield constmction. The addition of test no. 26 requiring support of a 2.3-kg ball dropped from 3.7 m defined this level of improvement. It was based on a correlation estabUshed between 10-kg, instmmented, head-form impacts on windshields, on 0.6 x 0.9-m flat laminates, and the standard 0.3 x 0.3-m laminate with the 2.3-kg ball (28). Crash cases involving the two windshield interlayer types were matched for car impact speeds and were compared (29). The improved design produced fewer, less extensive, and less severe facial lacerations than those produced in the pre-1966 models. 

This consists of loading a pointed diamond or a hardened steel ball and pressing it into the surface of the material to be examined. The further into the material the indenter (as it is called) sinks, the softer is the material and the lower its yield strength. The true hardness is defined as the load (F) divided by the projected area of the indent, A. (The Vickers hardness, H , unfortunately was, and still is, defined as F divided by the total surface area of the indent. Tables are available to relate H to Ff .)... 

Energy since there is such a close analogy between the BBM and its CA incarnation, we may well ask whether there is, within the BBMCA, some conserved quantity analogous to physical energy in the BBM Well, we know that the total number of balls, or total number of Ts, is conserved. Let cTx,y t) equal the value of site (x,y), and define Px,y(t) = (rx,y t) - (Tx,y t - 1). We see that p y 1 if and only if the value of site (x,y) changes from time t—ltot. Since a moving ... 

The quantum levels of an electron bound to an atom are cmdely analogous to the gravitational potential energies available to a ball on a staircase. As illustrated in Figure 7-12. a ball may sit on any of the steps. If we define the top of the steps to be 5" = 0, the ball has a negative potential energy when it is on any of the lower steps. To move a ball from the bottom of the staircase to step 5 requires the addition of a specific amount of energy,... 

The Brinell test uses an indentor of 10 mm diameter hardened steel ball, and applies a load which is usually 3000 kg. The Brinell hardness number (BHN) is defined as the load, F (kilogrammes), divided by the surface area of the indentation. The expression given below describes the definition. 

The third step is to select the number of iterations or calculations of dose that are to be performed as a part of each simulation. For the analysis here, a total of 10,000 iterations based on the selection of input variables from each defined distribution were performed as part of each simulation. The large number of iterations performed, as well as the Latin hypercube sampling (non-random sampling) technique employed by the Crystal Ball simulation program, ensured that the input distributions were well characterized, that all portions of the distribution (such as the tails) were included in the analysis, and that the resulting exposure distributions were stable. 

Proton c can be defined by the fact that it is not equatorial and it is highly coupled. The multiplet at 3.82 ppm satisfies these requirements. It is in the right ball park for chemical shift and is highly complex in that this proton is already the X part of an ABX system coupled to both protons alpha to the chlorine (the AB part). It is then further coupled with a 10 Hz, axial-axial coupling (reciprocated in the dd at 2.07 ppm) and with a 2 Hz axial-equatorial coupling which is reciprocated in the ddd at 2.90 ppm. Note that c and d are not fully resolved from each other. Such overlap inevitably complicates the issue. 

Instead of a formal development of conditions that define a local optimum, we present a more intuitive kinematic illustration. Consider the contour plot of the objective function fix), given in Fig. 3-54, as a smooth valley in space of the variables X and x2. For the contour plot of this unconstrained problem Min/(x), consider a ball rolling in this valley to the lowest point offix), denoted by x. This point is at least a local minimum and is defined by a point with a zero gradient and at least nonnegative curvature in all (nonzero) directions p. We use the first-derivative (gradient) vector Vf(x) and second-derivative (Hessian) matrix V /(x) to state the necessary first- and second-order conditions for unconstrained optimality ... 

Balance of Forces It is convenient to define the L function L(x,Xy) =f(x) + g(xfX + h(xfv, along with "weights or multipliers X and v for the constraints. The stationarity condition (balance of forces acting on the ball) is then given by... 

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