Obstacle distance

Collision avoidance of the base trajectory relies only on base-to-obstacle distance sensor. Consequently, if the arm is unfolded and extends beyond the base during base motion, a collision between the arm and a human is possible. A very slow base movement is tolerated. This case is the same as the example of Section 2.2. The safety invariant is The arm must not be extended beyond the base when the base is moving (with speed higher than Vq). 

For the robust estimation of the pair potentials, some obstacles had to be overcome. There are a huge number of different triples (si, Sk,i — k), and to find densities, we needed a way to group them in a natural way together into suitable classes. A look at the cumulative distribution functions (cdf s) of the half squared distances Cjfc at residue distance d = i — k (w.l.o.g. >0), displayed in Figure 1, shows that the residue distances 8 and higher behave very similarly so in a first step we truncated all residue distances larger than 8 to 8. 

If the average distance between obstacles is L, the run time between obstacles is... 

Graphical interpretation of the factors influencing the critical distance from air supply to the linear obstacle with a height for air supply through a slot diffuser with height Ioq and for air supply through a round nozzle with outlet diameter are presented in Fig. 7.43. Nonisothermal flow has an influence on... 

FIGURE 7.43 Critical height of an obstacle vs. distance from supply slot with a height hj (a) and supply nozzle with diameter do (b) Reproduced from Nielsen. ... 

One could assume that this characteristic behavior of the mobility of the polymers is also reflected by the typical relaxation times r of the driven chains. Indeed, in Fig. 28 we show the relaxation time T2, determined from the condition g2( Z2) = - g/3 in dependence on the field B evidently, while for B < B t2 is nearly constant (or rises very slowly), for B > Be it grows dramatically. This result, as well as the characteristic variation of with B (cf. Figs. 27(a-c)), may be explained, at least phenomenologically, if the motion of a polymer chain through the host matrix is considered as consisting of (i) nearly free drift from one obstacle to another, and (ii) a period of trapping, r, of the molecule at the next obstacle. If the mean distance between obstacles is denoted by ( and the time needed by the chain to travel this distance is /, then - (/ t + /), whereby from Eq. (57) / = /Vq — k T/ DqBN). This gives a somewhat better approximation for the drift velocity... 

Obstacles introduced in unconfined cylindrical bubbles resulted only in local flame acceleration. Pressures measured at some distance from the cylindrical bubble were, in general, two to three times the pressure measured in the absence of obstacles. 

Most investigators used tubes open only at the end opposite the point of ignition. For tubes with very large aspect ratios (length/diameter), the positive feedback mechanism resulted in a transition to detonation for many fuels, even when the tubes were unobstructed. Introduction of obstacles into tubes reduced considerably the distance required for transition to detonation. 

When these are close together, most of the simultaneously measured velocities will relate to fluid in the same eddy and the correlation coefficient will be high. When the points are further apart the correlation coefficient will fall because in an appreciable number of the pairs of measurements the two velocities will relate to different eddies. Thus, the distance apart of the measuring stations at which the correlation coefficient becomes very poor is a measure of scale of turbulence. Frequently, different scales of turbulence can be present simultaneously. Thus, when a fluid in a tube flows past an obstacle or suspended particle, eddies may form in the wake of the particles and their size will be of the same order as the size of the particle in addition, there will be larger eddies limited in size only by the diameter of the pipe. 

In fluid dynamics the behavior in this system is described by the full set of hydrodynamic equations. This behavior can be characterized by the Reynolds number. Re, which is the ratio of characteristic flow scales to viscosity scales. We recall that the Reynolds number is a measure of the dominating terms in the Navier-Stokes equation and, if the Reynolds number is small, linear terms will dominate if it is large, nonlinear terms will dominate. In this system, the nonlinear term, (u V)u, serves to convert linear momentum into angular momentum. This phenomena is evidenced by the appearance of two counter-rotating vortices or eddies immediately behind the obstacle. Experiments and numerical integration of the Navier-Stokes equations predict the formation of these vortices at the length scale of the obstacle. Further, they predict that the distance between the vortex center and the obstacle is proportional to the Reynolds number. All these have been observed in our 2-dimensional flow system obstructed by a thermal plate at microscopic scales. ... 

Here Lqp is the distance between points q and p. Note that G q, p) is called a Green s function. There are an infinite number of such functions and all of them have a singularity at the observation point p. Inasmuch as the second Green s formula has been derived assuming that singularities of the functions U and G are absent within volume V, we cannot directly use this function G in Equation (1.99). To avoid this obstacle, let us surround the point by a small spherical surface S and apply Equation (1.99) to the volume enclosed by surfaces S and S, as is shown in Fig. 1.9. Further we will be mainly interested by only cases, when masses are absent inside the volume V, that is. 

Langevin MP and Chilowsky MC (1918) Precedes et appareils pour la production de signaux sous-marins diriges et pour la localization a distance d obstacles sous marins, French Patent No. 502913... 

---