Balloon models

To determine f a) we invoke the requirement that the electrostatic potential, which is to be a solution to a second order differential equation, must be continuous and vary smoothly across the boundary that separates the ion ai r = a from its surroundings. For ease of further mathematical manipulations we now adopt a representation for an ion as a sphere whose entire charge, Qe, is uniformly distributed inside its surface—the balloon model of an ion. This may be justified by appealing to a consequence of Gauss law a uniform charge distribution within an enclosed sphere has the same effect on the outside world as the entire charge would have if it were concentrated at the center. The balloon model simply represents a very convenient special uniform charge distribution within the sphere. 

Butorphanol is used as an analgesic in horses. Butorphanol (0.1 mg/kg i.v.) increased the pain threshold in a rectal balloon model in mares (Skarda Muir 2003). It had analgesic efficacy for 60 min in a cecal balloon model (Muir Robertson... 

A balloon model of the electron clouds repelling each other in a molecule of methane. 

The balloon model represents the clouds of bonding electrons on either side of the carbon atom. A linear molecule results because of repulsion between the two clouds. ... 

Figure 4.7 Balloon models representing the arrangements of two to six valence shell electron pair domains.

FIGURE 5.6 Balloon models of electron-pair geometries for two to six electron pairs. Balloons of similar size and shape, when tied together, naturally assume the arrangements shown. 

Balloon models used to predict bond angles. (a)Two balloons assume a linear shape with a bond angle of 180° about the tie point. (b)Three balloons assume a trigonal planar shape with bond angles of 120° about the tie point, (c) Four balloons assume a tetrahedral shape with bond angles of 109.5° about the tie point. 

Archaeologists do not always have to dig deep to unearth artifacts. Aerial archaeology involves conducting bird s-eye view reconnaissance missions using cameras mounted on kites, remote-controlled parachutes, hot-air balloons, model airplanes, and helicopters. 

The balloon models shown in Figure 9.5 can be used very effectively in classroom presentations of VSEPR. 

Figure 4.6 When balloons of the same size and shape are tied together, they will assume positions like those taken by pairs of valence electrons around a central atom. Where would the central atom be located in these balloon models ...

When further considering this balloon model, the nitrogen atoms can be replaced by carbon atoms (or clusters of carbon atoms) which are of course bonded to each other chemically to... 

On the other hand, in the interior of the balloon, the electrostatic field vanishes by Gauss law since no charge is enclosed. (Hence, the clever adoption of the balloon model ,) then e = 0 for r < u, whence... 

This model is useful, first, because we can calculate in mathematical detail just how much push a billiard ball exerts on a cushion at each rebound, and, second, because exactly the same mathematics describes the pressure behavior of gas in a balloon. The success of the model leads to new directions of thought. For example, we might now wonder whether the pressure-volume behavior of oxygen, as shown in Table l-II (p. 14), can be explained in terms of the particle model of a gas. 

Levy El, Sauvageau E, Hanel RA, Parikh R, Hopkins LN. Self-expanding versus balloon-mounted stents for vessel recanalization following embolic occlusion in the canine model technical feasibility study. Am J Neuroradiol 2006 27 2069-2072. 

Eompre Cultured cells are a useful model for pathology. If you want to see what is happening in atherosclerosis, for example, it is very difficult to work on the atherosclerotic plaque, because there are many cell types involved. In culture you can reproduce some of the events. For example, we have done balloon injury in the rat, and we lose RyRs when cells proliferate in situ. 

If they are available, use inflated balloons or molecule modeling kits to construct each of the arrangements in Figure 4.11. How do these models compare with your bubble models ... 

The rat carotid artery injured by a balloon catheter has been widely used as a model of angioplasty. The rat model is a proliferation model without foam cells (93). This form of injury causes immediate coagulation and thrombosis cascade in which platelets adhere, spread, and degranulate on the denuded surface of the artery, and approximately 24 hours later SMC begin to proliferate. Liposomal BPs, clodronate, and alendronate were injected to male sabra rats, 15 and 3mg/kg, respectively (52,69,76). Marked neointimal formation and decreased luminal area were observed in control animals. Neointima/media (N/M) ratio was 1.3 0.2, and luminal stenosis was 44 3%. LC and LA suppressed intimal growth when administered intravenously on day -1 and day 6. N/M ratios were reduced by 60% and 69% for LC and LA, respectively. 

---