Profile double-parabolic

Homogeneous function profiles 16-6 Separable profiles 16-7 Example Infinite linear profile 16-8 Example Double parabolic profile... 

We next consider the fundamental modes of the double parabolic profile waveguide, which has the profile of Eq. (16-30), illustrated in Fig. 16-2(b). Despite the fact that such a waveguide is unphysical for the reasons given in Section 14-4, it provides the siiriplest perturbation problem for any two-fiber waveguide. The unperturbed fiber has the infinite parabolic profile... 

We derived the exact solution of the scalar wave equation for the double parabolic profile in Section 16-8. The propagation constants for the fundamental modes are given implicitly by the eigenvalue equations of Eq. (16-35). If the normalized separation is sufficiently large to satisfy d/p > it can be readily verified that the... 

An important feature of the EOF is its flat flow profile, compared to the parabolic profile of hydrodynamic flows (Fig. 17.4). The reason for this characteristic is that the EOF originates almost at the wall of the capillary, owing to the extremely small size of the double layer... 

Fig. 16-2 Contours of constant refractive index for (a) the infinite linear profile of Eq. (16-24) and (b) the double parabolic fiber profile of Eq. (16-30), where d is the separation of the fiber centers.

Assume laminar flow and a parabolic velocity distribution. Calculate the temperature and composition profiles in the reactor. Start with 7=4 and double until your computer cries for mercy. Consider two cases (a) 7 = 0.01 m (b) 7 = 0.20 m. 

CA 45 7792(1951) [Combustion profiles of lamelae of a double-base proplnt consisting of NC 69.1, DEGDN 20.6 St EtCentr 6.9% were detd in air and inert gases, with or w/o wrappings of different thermal conductivity. An interpretation of the various profiles obtd(inverted V, rectilinear, concave or parabolic) was proposed. The factor which mainly detd the geometry of the combustion profile is heat transfer from the flame front to the solid lamelae, thru the ambient media) 8)P. Tavernier St P.Prache, MP 34, 255-75(1952) Sc CA 48, 11060(1954)(Rate of combustion of proplnts in an inert atm under pressure) 9)H. Muraour 8t G. Aunis, MP 35, 287-301(1953) CA 49, 13651(1955) Ger translation by Dr. A. Schmidt in Explosivst 1954, 154-7 1955 6-9(Laws of combustion of colloidal proplnts. A survey of French research between WWI St WWII) 10)C. A. Heller A.S, Gordon, JPhysChem 59, 773-77(1955)... 

The flow of liquid caused by electro-osmosis displays a pluglike profile because the driving force is uniformly distributed along the capillary tube. Consequently, a uniform flow velocity vector occurs across the capillary. The flow velocity approaches zero only in the region of the double layer very close to the capillary surface. Therefore, no peak broadening is caused by sample transport carried out by the electro-osmotic flow. This is in contrast to the laminar or parabolic flow profile generated in a pressure-driven system, where there is a strong pressure drop across the capillary caused by frictional forces at the liquid-solid boundary. A schematic representation of the flow profile due... 

If a pressure gradient is imposed on the fluid, a flow which contains charges appears and thus generates an electrostatic field due to the charge displacement. The electrostatic potential that is derived from this field is called the streaming potential. Without a pressure gradient, the fluid can be moved using an electrical field hence an electroosmotic flow appears. The fluid velocity profile which develops without the electric double-layer (EDL) effect is parabolic the... 

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