One-dimensional structures

Laminated plates are one of the simplest and most widespread practical applications of composite laminates. Laminated beams are, of course, simpler. However, such essentially one-dimensional structural elements do not display well the unique two-dimensional capabilities and characteristics of composite laminates. 

The synthesis of molecular carbon structures in the form of C q and other fullerenes stimulated an intense interest in mesoscopic carbon structures. In this respect, the discovery of carbon nanotubes (CNTs) [1] in the deposit of an arc discharge was a major break through. In the early days, many theoretical efforts have focused on the electronic properties of these novel quasi-one-dimensional structures [2-5]. Like graphite, these mesoscopic systems are essentially sp2 bonded. However, the curvature and the cylindrical symmetry cause important modifications compared with planar graphite. 

Meerchaut, A. Rouxel, J. in Crystal Chemistry and Properties of Materials with Quasi-one Dimensional Structures, Rouxel, J., Ed. Reidel, Dordrecht, 1986, p. 205. 

One-dimensional structures do not exist. Structures are always three-dimensional. The term one-dimensional is acceptable to express specifically named, highly anisotropic properties, such as one-dimensionalconductivity , one-dimensionalconnection or onedimensional disorder . The dimensionality of a structure is a meaningless phrase. 

As pointed out by Sessoli and coworker in their review, a possible approach to increasing the energy barrier of lanthanide-based SMMs is by assembling together several lanthanide ions which interact magnetically either in a zero-dimensional structure (SMMs) or in a one-dimensional structure (Single-Chain Magnets) [26]. The last several years have indeed seen a flurry of results from synthetic chemists in this respect. Especially in our recent review about Dy-based SMMs, polynuclear... 

I described a simple method suitable for rigorous modelling of nonlinear one-dimensional structures in the frequency domain. The method was applied to model COST Pll task on slow-wave optieal structures. It was demonstrated that the use of slow-wave structures significantly decreases bistablity threshold. 

Nano structural materials are divided into three main types one-dimensional structures (more commonly known as multilayers) made of alternate thin layers of different composition, two-dimensional structures (wire-type elements suspended within a three-dimensional matrix), and three-dimensional constructs, which may be made of a distribution of fine particles suspended within a matrix (in either periodic or random fashion) or an aggregate of two or more phases with a nanometric grain size (these are illustrated in Fig. 17.1). 

Morel, R. and Pouget, J. P. (1986). In Crystal Chemistry and Properties of Materials with Quasi-One-Dimensional Structures, ed. J. Rouxel. Dordrecht D. Reidel Publishing Company. 

This is in contrast with the crystal structure of the complex [CdL2(H20)3] (HL = 4-aminobenzoic acid) here the metal is in a seven-coordinate N2Os environment, with the ligand acting as a bridge to form a polymeric one-dimensional structure.249... 

In conclusion let us direct the reader s attention to the curious gasdynamic and kinetic features of detonation in systems of liquid fuel film + gaseous oxidizer, 38 and also in low-velocity regimes of propagation of detonation. In these systems, which are characterized by a very non-one-dimensional structure of the detonation wave, a primary role is played by interactions between the shock waves and rarefaction waves propagating in different layers of the explosive system with different speeds. 

The stability analysis [32] of the lamellar (one-dimensional) structure shows that it is stable only for weak coupling between the splay of polarization and molecular tilt. When Kv is larger than some critical value, layers start to undulate. 

Note that a spring reverb is essentially a one-dimensional structure, plate reverbs are primarily two-dimensional, and concert halls are three-dimensional. Since each of these increases in dimensionality is associated with a significant increase in quality, it is reasonable to conjecture that simulated reverberation in four dimensions or more may be even better. 

It has been observed that tbe conductivity was actually higher than the conductivity reported for pure diimide anion radical salts, because dendrimeric structures may produce 7t-s lac king formation in three dimensions, a structural feature differing from the usual one-dimensional structures of small molecular stacks. 

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