Self linear behavior with

Further support for the correlation of self-diffusion behavior with crystallization rate is provided by data on linear POE (3 kg/mol, = 59 °C) terminated with hydroxyl or methoxyl... 

A wide variety of polymeric materials exhibit self-similar relaxation behavior with positive or negative relaxation exponents. Positive exponents are only found with highly entangled chains if the chains are linear, flexible, and of uniform length [61] the power law spectrum here describes the relaxation behavior in the entanglement and flow region. 

The values of Km and T2d from Eq.(36) can be obtained from the transfer function of the linearized model at the equilibrium point, applying conventional methods from the linear control theory (see [1]). In order to investigate the self-oscillating behavior, one can determine the linearized system at the equilibrium point, and the corresponding complex eigenvalues with zero real part, when the parameters Km and of the PI controller are varied. For example, taking into account Eq.(34), the Jacobian matrix of the linearized system at dimensionless set point temperature xs is the following ... 

These self-discharge behaviors have been demonstrated with different capacitor samples. BCAP0007 and BCAP0008 are Maxwell commercial products. They show only a diffusion-driven self-discharge mechanism. BCAPproto which is a prototype with a high impurity content undergoes oxidation-reduction reactions. The two different plots show the respective linear drop in their respective representation. 

As we already noted, for the n-simplex lattice with n odd, a collapsed phase with a finite density of the polymer is not found. For the modified rectangular lattice, the behavior of linear polymer with self-attraction was studied in [35], Here the number of variables needed to describe the polymer with self-attraction becomes rather large. For example, to describe closed loops it is necessary to introduce additional weights b[ A2. etc., where the subscript 1(2) indicates the number of extra corner sites of the r -order are visited, a total of eleven variables. To describe open chains, we would need 17 additional variables, making a total of 28 variables- a rather formidable number. However, as in case of n-simplex lattices many of these variables are irrelevant and may be set equal to zero. Equivalently, we study collapse when the attractive interaction is restricted to the first order rectangles. If we restrict ourselves to the analysis of closed polygons, we require only the five variables defined earlier in section 4.3. 

The first analysis of the wrinkled flame structure was carried out by Barenblatt, Zeldovich and Istratov (1962) but in the diffusive-thermal model where the gas expansion effects i) and ii) are neglected. This model was extensively used these ten last years to culminate in the derivation by G. Sivashinsky (1977) of a non linear differential equation for the flame motion describing a self turbulizing behavior of the cellular structures (Michelson 6e Sivashinsky 1977). The main interest of this model is to provide us with a simple framework for studying systematically all the d3mamical effects that can possibely be produced by the diffusion of heat and mass. The asymptotic technique applied to solve this model in the limit of large values of the Zeldovich number is presented in the paper of Jou 1 in 6e Clavin (1979)... 

In 2011, Rowan and Weder et al. described the self-healing properties of a linear metallopolymer. fii order to obtain self-healing behavior, the authors used UV light [44], For this purpose, poly (ethylene-co-butylene) was functionalized with two 2,6-fi/s(l -methylbenzimidazolyl)pyridine moieties at the termini and the subsequent addition of zinc di[Z>/s(trifluoromethylsulfonyl)imide] or lanthanum tri[6/s(trifluoromethylsulfonyl)imide] led to a linear metallopolymer. 

As an alternative approach, flexible coil parts in rod-coil molecules can be structurally modihed into dendritic shapes. In comparison to linear-type coils, dendritic coils would cause a larger steric repulsion at the rod/coil interface, which influences rod-packing structures. Lee et al. devised a dumbbellshaped molecule (12) based on an elongated dodeca-para-phenylene rod block and aliphatic polyether dendritic coils with chiral carbon centers, and investigated the self-assembly behavior in aqueous solution [54]. In remarkable contrast to ordinary one-dimensional fibers, the aggregate structures... 

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