One-dimensional cavity

The optical mode density of a one-dimensional cavity for emission along the cavity axis is given by... 

As the -ide" ending suggests, the electrons in electrides take on the role of anions.[ This implies that electrides are crystalline ionic compounds with one electron per cation. They could be viewed as salts that contain stoichiometric F-centers. with electrons as the only anions. But because one cannot suppress the quantum nature of electrons, these "anions" are special. The line between localized weakly interacting electrons and delocalized, or metallic electrons is blurred, and both extremes are encountered in electrides. Because most of the electron density in electrides is present in otherwise empty, well-defined pseudo-one-dimensional cavities and channels, they could also be viewed as forming lowdimensional correlated electron gasses. 

One-dimensional model Onsanger cavity field Onsanger equation Orbital polarization Ordered phase Ordered state... 

The basic principle underlying the development of images is simple (Lauterber, 1973). Consider a body cavity containing two pools of water in different quantities. In a uniform magnetic field, the NMR spectrum will consist of a single peak, since all the water molecules will process at the same frequency, irrespective of their spatial location. If, however, a linear field gradient is applied in the x -direction, the Larmor frequency of the water will increase linearly across the sample as a function of the x -coordinate, thereby creating a one-dimensional profile, or spectrum, of the sample (Fig. 7.21). 

The short calculations we presented here are all 3-dimensional cavities with trivial topology ( For example of not like the region between co-axial cylinders or cones, co-centric spheres or tori (Ahmedov and Duru, 2003) ). The known results ( including the present ones ) for three dimensional cavities are... 

To demonstrate the method an example of a slow-wave optical structure is modelled. Such structures consist of a cascade of directly coupled optical resonators in order to enhance the nonlinear effects. The structure used here was recently defined within Working Group 2 of the European Action COST Pll (http //w3.uniromal.it/energetica/slow waves.doc). One period of the structure consists of one-dimensional Fabry-Perot cavity placed between two distributed Bragg reflectors (DBR) and can be described by the sequence... 

One direct approach to the separation of chiral compounds is called molecular imprint polymers (MIPs) that involves the formation of a three-dimensional cavity with the shape and electronic features that are complementary to the imprinted or target molecule. 

Binding of the guest molecule to the cavity is accompanied by van der Waals stabilization (H dw), which is calculated by using Hill s potential (52). Freedom of one-dimensional rotation is assumed to be allowed for the inclusion complex (S ol(1.D)). 

In order to construct a hydrophobic three-dimensional cavity that is in-tramolecularly limited in space, we have prepared cage-type cyclophanes by linking macrocyclic rings. First we prepared a macropolycyclic host, which is constructed with two rigid macrocyclic skeletons of different size, tetraaza[3.3.3.3]paracyclophane as the larger one and tetraazacyclotetradecane as the smaller one, and four flexible hydrocarbon chains that connect the two macrocycles [40]. The flexibility of four hydrocarbon chains connecting the two macrocycles allows the induced-fit host-guest interaction in aqueous media. 

In the simplest case under consideration (Newtonian, isothermal, and inertialess motion in the absence of structuring) at h(t) 8 the flow may be assumed to be quasi-one-dimensional, and the distorsions of velocity and pressure profiles in the vicinity of a front and the gate into a forming cavity may be neglected. The basic equation will then have the form ... 

The trajectory of an ion moving in such a potential presents a sequence of rectilinear sections placed between the points of elastic reflections of an ion from the walls of the well. We consider two variants of such a model related to one-dimensional and spatial motion of ion, depicted, respectively, in Figs. 47a and 47b. In the first variant the ion s motion during its lifetime59 presents periodic oscillations on the rectilinear section 2 lc between two reflection points. In the second variant we consider a spherically symmetric potential well, to which a spherical hollow cavity corresponds with the radius lc. 

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